Astronomy

What is wrong with this measurement of the synodic period of Mercury?

What is wrong with this measurement of the synodic period of Mercury?



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I'm measuring the synodic period of Mercury using Stellarium. When measuring the synodic period one needs to choose a reference point to start the measurement, and I choose the point when Mercury is on top of the Sun. This is the start date:

And this is the end date:

Inputting these two dates into a calculator gives a synodic period of 104 days. However, as one can see from Stellarium's data, Mercury's synodic period is actually 115.88 days. This measurement is off by more than 10 days.

Why is there such a large difference? It's not large in the absolute sense, but it seems well above the error margins. For example if instead I shift the start date to 9 April 2021, Mercury is discernibly not between us and the Sun.


Mercury's orbit is highly eccentric: 0.21 according to Wikipedia. Therefore, the actual time between repeating occurrences will vary depending on the year. If you were to perform your calculations for many periods, the average should approach the value given by Stellarium.

The theoretical synodic period, using the sidereal period of Earth and Mercury, is 115.9 days.


Addressing @Allure's comment below @ JohnHoltz's excellent answer, the synodic period is simply a function of the two periods.

It will return something like the average value between two successive events where the planets would line up if they orbited in the same plane, but it does not predict the exact times as pointed out in that answer.

In addition to the fact that the orbits can be elliptical producing jitter, they can also have very different inclinations. In that case they will usually not line up at all, even if the orbits are circular.

For a real-world example, try to use your same method to calculate the synodic period between Neptune and Pluto, with inclinations of about 2° and 17° and eccentricities of 0.01 and 0.25 respectively. Now imagine a body with an inclination of 90°!

Synodic period is just the period that is returned by the equation below, a function of two other periods, and you have to decide for yourself how applicable or useful the value is for your own application.

$$T_{syn} = frac{1}{frac{1}{T_1}-frac{1}{T_2}} = frac{T_1 T_2}{T_2-T_1}$$


Synodic day

A synodic day (or synodic rotation period or solar day) is the period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time.

The synodic day is distinguished from the sidereal day, which is one complete rotation in relation to distant stars, [1] which is the basis of sidereal time. This is different from the duration of a synodic day because the revolution of the body around its parent star would cause a single "day" to pass relative to a star, even if the body did not rotate itself.


Basic properties

Mercury orbits the sun at a mean distance of 0.387 astronomical units (AU), where 1 AU is the mean distance from Earth to the sun, or about 92,956,000 mi (149,600,000 km). The high eccentricity of the planet ’ s orbit (e = 0.206), however, dictates that it can be as far as 0.467 AU away from the sun, and as close as 0.307 AU. The high eccentricity attributed to Mercury ’ s orbit is the second largest in the solar system, only the dwarf planet Pluto has a more eccentric orbit. (Eccentricity in astronomy indicates that an orbit is not absolutely circular. The value of e = 1 indicates an orbit is shaped as a parabola. An ellipse is less than one, and a circle has zero eccentricity.)

Constrained as it is in an orbit close to the sun, Mercury is not an easy planet for naked-eye observers to locate. The greatest separation between the planet and the sun, as seen from Earth, is 28 ° and consequently

the planet is never visible against a truly dark sky. Even at its greatest angular separation from the sun, Mercury will either set within two hours of sunset, or rise no earlier than two hours before the sun. Nonetheless, Mercury has been known since the most ancient of times, with observations of the planet being reported as far back as several centuries BC Greek philosopher Plato (c. 427 – c. 347 BC) refers to the distinctive yellow color of Mercury in Book X of his Republic.

The sidereal period, or the time it takes Mercury to orbit the sun, is 87.969 days. The planet ’ s synodic period, which is the time required for Mercury to return to the same relative position with respect to the sun and Earth, is 116 days. As seen from Earth, Mercury undergoes a change of phase as it moves around the sun. These phase changes were first observed in the early seventeenth century by Polish astronomer Johannes Hewelcke (1611 – 1687), who is perhaps better known today through his latinized name, Hevelius. Zero phase occurs when Earth, the sun, and Mercury are directly in line, with Mercury on the opposite side of the sun to Earth. At this phase, Mercury is said to be at superior conjunction. Half phase occurs when Earth, the sun, and Mercury are once again in a line, but this time with Mercury being on the same side of the sun as Earth is. Mercury is said to be at inferior conjunction when it exhibits a half phase. While moving from inferior to superior conjunction Mercury passes through a quarter phase, during which the disk of the planet is half illuminated as seen from Earth. Mercury also passes through its greatest western elongation when moving from inferior to superior conjunction. Likewise, in moving from superior to inferior conjunction Mercury passes through greatest eastern elongation, and exhibits a second quarter phase, or half-disk illumination.

Because Mercury ’ s orbit is quite elongated, so that its distance from the sun varies significantly, the maximum angular separation between Mercury and the sun, as seen from Earth, can vary from a minimum of 18 ° to a maximum of 28 ° (Figure 1). The largest angular separation of 28 ° occurs when Mercury is at

either greatest western, or greatest eastern elongation and near its aphelion (its greatest distance from the sun). Irrespective of whether the planet is at aphelion or not, the best time to view Mercury in the evening is when the planet is near greatest eastern elongation. Because the synodic period of Mercury is about 116 days, the planet will be favorably placed for evening viewing three times each year. Similar conditions apply for viewing Mercury before sunrise.

The inclination of Mercury ’ s orbit to that of the ecliptic plane (the plane of Earth ’ s orbit about the sun) is 7.0 ° . This slight orbital tilt dictates that when Mercury is at inferior conjunction it is only rarely silhouetted against the sun ’ s disk as seen from Earth. On those rare occasions when Earth, Mercury, and the sun are in perfect alignment, however, a solar transit of Mercury can take place, and a terrestrial observer will see Mercury move in front of, and across the sun ’ s disk. A transit of Mercury can only occur when the planet is at inferior conjunction during the months of May and November. During these months, Earth is near the line along which the orbit of Mercury intersects the ecliptic plane — this is the line of nodes for Mercury ’ s orbit. Approximately a dozen solar transits of Mercury occur each century, and the final transit of the twentieth century occurred on 15 November 1999. The first solar transit of Mercury occurred in 2003, and the next one occured November 8, 2006.


Orbit, rotation, and longitude [ edit | edit source ]

Mercury has the most eccentric orbit of all the planets its eccentricity is 0.21 with its distance from the Sun ranging from 46,000,000 to 70,000,000 km (29,000,000 to 43,000,000 mi). It takes 87.969 Earth days to complete an orbit. The diagram on the right illustrates the effects of the eccentricity, showing Mercury's orbit overlaid with a circular orbit having the same semi-major axis. Mercury's higher velocity when it is near perihelion is clear from the greater distance it covers in each 5-day interval. In the diagram the varying distance of Mercury to the Sun is represented by the size of the planet, which is inversely proportional to Mercury's distance from the Sun. This varying distance to the Sun leads to Mercury's surface being flexed by tidal bulges raised by the Sun that are about 17 times stronger than the Moon's on Earth. Combined with a 3:2 spin-orbit resonance of the planet's rotation around its axis, it also results in complex variations of the surface temperature. The resonance makes a single solar day on Mercury last exactly two Mercury years, or about 176 Earth days.

Mercury's orbit is inclined by 7 degrees to the plane of Earth's orbit (the ecliptic), as shown in the diagram on the right. As a result, transits of Mercury across the face of the Sun can only occur when the planet is crossing the plane of the ecliptic at the time it lies between Earth and the Sun. This occurs about every seven years on average.

Mercury's axial tilt is almost zero, with the best measured value as low as 0.027 degrees. This is significantly smaller than that of Jupiter, which has the second smallest axial tilt of all planets at 3.1 degrees. This means that to an observer at Mercury's poles, the center of the Sun never rises more than 2.1 arcminutes above the horizon.

At certain points on Mercury's surface, an observer would be able to see the Sun rise about halfway, then reverse and set before rising again, all within the same Mercurian day. This is because approximately four Earth days before perihelion, Mercury's angular orbital velocity equals its angular rotational velocity so that the Sun's apparent motion ceases closer to perihelion, Mercury's angular orbital velocity then exceeds the angular rotational velocity. Thus, to a hypothetical observer on Mercury, the Sun appears to move in a retrograde direction. Four Earth days after perihelion, the Sun's normal apparent motion resumes. A similar effect would have occurred if Mercury had been in synchronous rotation: the alternating gain and loss of rotation over revolution would have caused a libration of 23.65° in longitude.

For the same reason, there are two points on Mercury's equator, 180 degrees apart in longitude, at either of which, around perihelion in alternate Mercurian years (once a Mercurian day), the Sun passes overhead, then reverses its apparent motion and passes overhead again, then reverses a second time and passes overhead a third time, taking a total of about 16 Earth-days for this entire process. In the other alternate Mercurian years, the same thing happens at the other of these two points. The amplitude of the retrograde motion is small, so the overall effect is that, for two or three weeks, the Sun is almost stationary overhead, and is at its most brilliant because Mercury is at perihelion, its closest to the Sun. This prolonged exposure to the Sun at its brightest makes these two points the hottest places on Mercury. Conversely, there are two other points on the equator, 90 degrees of longitude apart from the first ones, where the Sun passes overhead only when the planet is at aphelion in alternate years, when the apparent motion of the Sun in Mercury's sky is relatively rapid. These points, which are the ones on the equator where the apparent retrograde motion of the Sun happens when it is crossing the horizon as described in the preceding paragraph, receive much less solar heat than the first ones described above.

Mercury attains inferior conjunction (nearest approach to Earth) every 116 Earth days on average, but this interval can range from 105 days to 129 days due to the planet's eccentric orbit. Mercury can come as near as 82.2 gigametres (0.549 astronomical units 51.1 million miles) to Earth, and that is slowly declining: The next approach to within 82.1 Gm (51.0 million miles) is in 2679, and to within 82.0 Gm (51.0 million miles) in 4487, but it will not be closer to Earth than 80 Gm (50 million miles) until 28,622. Its period of retrograde motion as seen from Earth can vary from 8 to 15 days on either side of inferior conjunction. This large range arises from the planet's high orbital eccentricity.

Longitude convention [ edit | edit source ]

The longitude convention for Mercury puts the zero of longitude at one of the two hottest points on the surface, as described above. However, when this area was first visited, by Mariner 10, this zero meridian was in darkness, so it was impossible to select a feature on the surface to define the exact position of the meridian. Therefore, a small crater further west was chosen, called Hun Kal, which provides the exact reference point for measuring longitude. The center of Hun Kal defines the 20° West meridian. A 1970 International Astronomical Union resolution suggests that longitudes be measured positively in the westerly direction on Mercury. The two hottest places on the equator are therefore at longitudes 0°W and 180°W, and the coolest points on the equator are at longitudes 90°W and 270°W. However, the MESSENGER project uses an east-positive convention.

Spin-orbit resonance [ edit | edit source ]

For many years it was thought that Mercury was synchronously tidally locked with the Sun, rotating once for each orbit and always keeping the same face directed towards the Sun, in the same way that the same side of the Moon always faces Earth. Radar observations in 1965 proved that the planet has a 3:2 spin-orbit resonance, rotating three times for every two revolutions around the Sun. The eccentricity of Mercury's orbit makes this resonance stable - at perihelion, when the solar tide is strongest, the Sun is nearly still in Mercury's sky.

The rare 3:2 resonant tidal locking is stabilized by the variance of the tidal force along Mercury's eccentric orbit, acting on a permanent dipole component of Mercury's mass distribution. In a circular orbit there is no such variance, so the only resonance stabilized in such an orbit is at 1:1 (e.g., moon-earth), when the tidal force, stretching a body along the "center-body" line, exerts a torque that aligns the body's axis of least inertia (the "longest" axis, and the axis of the aforementioned dipole) to always point at the center. However, with noticeable eccentricity, like that of Mercury's orbit, the tidal force has a maximum at perihelion and thus stabilizes resonances, like 3:2, enforcing that the planet points its axis of least inertia roughly at the sun when passing through perihelion.

The original reason astronomers thought it was synchronously locked was that, whenever Mercury was best placed for observation, it was always nearly at the same point in its 3:2 resonance, hence showing the same face. This is because, coincidentally, Mercury's rotation period is almost exactly half of its synodic period with respect to Earth. Due to Mercury's 3:2 spin-orbit resonance, a solar day (the length between two meridian transits of the Sun) lasts about 176 Earth days. A sidereal day (the period of rotation) lasts about 58.7 Earth days.

Simulations indicate that the orbital eccentricity of Mercury varies chaotically from nearly zero (circular) to more than 0.45 over millions of years due to perturbations from the other planets. This was thought to explain Mercury's 3:2 spin-orbit resonance (rather than the more usual 1:1), because this state is more likely to arise during a period of high eccentricity. However, accurate modeling based on a realistic model of tidal response has demonstrated that Mercury was captured into the 3:2 spin-orbit state at a very early stage of its history, within 20 (more likely, 10) million years after its formation.

Numerical simulations show that a future secular orbital resonant perihelion interaction with Jupiter may cause the eccentricity of Mercury's orbit to increase to the point where there is a 1% chance that the planet may collide with Venus within the next five billion years.

Advance of perihelion [ edit | edit source ]

In 1859, the French mathematician and astronomer Urbain Le Verrier reported that the slow precession of Mercury's orbit around the Sun could not be completely explained by Newtonian mechanics and perturbations by the known planets. He suggested, among possible explanations, that another planet (or perhaps instead a series of smaller 'corpuscules') might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation. (Other explanations considered included a slight oblateness of the Sun.) The success of the search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place faith in this possible explanation, and the hypothetical planet was named Vulcan, but no such planet was ever found.

The perihelion precession of Mercury is 5,600 arcseconds (1.5556°) per century relative to Earth, or 574.10±0.65 arcseconds per century relative to the inertial ICRF. Newtonian mechanics, taking into account all the effects from the other planets, predicts a precession of 5,557 arcseconds (1.5436°) per century. In the early 20th century, Albert Einstein's general theory of relativity provided the explanation for the observed precession, by formalizing gravitation as being mediated by the curvature of spacetime. The effect is small: just 42.98 arcseconds per century for Mercury it therefore requires a little over twelve million orbits for a full excess turn. Similar, but much smaller, effects exist for other Solar System bodies: 8.62 arcseconds per century for Venus, 3.84 for Earth, 1.35 for Mars, and 10.05 for 1566 Icarus.


Contents

Mercury is one of four terrestrial planets in the Solar System, and is a rocky body like Earth. It is the smallest planet in the Solar System, with an equatorial radius of 2,439.7 kilometres (1,516.0 mi). [3] Mercury is also smaller—albeit more massive—than the largest natural satellites in the Solar System, Ganymede and Titan. Mercury consists of approximately 70% metallic and 30% silicate material. [23]

Internal structure

Mercury appears to have a solid silicate crust and mantle overlying a solid, iron sulfide outer core layer, a deeper liquid core layer, and a solid inner core. [24] [25] The planet's density is the second highest in the Solar System at 5.427 g/cm 3 , only slightly less than Earth's density of 5.515 g/cm 3 . [3] If the effect of gravitational compression were to be factored out from both planets, the materials of which Mercury is made would be denser than those of Earth, with an uncompressed density of 5.3 g/cm 3 versus Earth's 4.4 g/cm 3 . [26] Mercury's density can be used to infer details of its inner structure. Although Earth's high density results appreciably from gravitational compression, particularly at the core, Mercury is much smaller and its inner regions are not as compressed. Therefore, for it to have such a high density, its core must be large and rich in iron. [27]

Geologists estimate that Mercury's core occupies about 55% of its volume for Earth this proportion is 17%. Research published in 2007 suggests that Mercury has a molten core. [28] [29] Surrounding the core is a 500–700 km (310–430 mi) mantle consisting of silicates. [30] [31] Based on data from the Mariner 10 mission and Earth-based observation, Mercury's crust is estimated to be 35 km (22 mi) thick. [32] However, this model may be an overestimate and the crust could be 26 ± 11 km (16.2 ± 6.8 mi) thick based on an Airy isostacy model. [33] One distinctive feature of Mercury's surface is the presence of numerous narrow ridges, extending up to several hundred kilometers in length. It is thought that these were formed as Mercury's core and mantle cooled and contracted at a time when the crust had already solidified. [34] [35] [36]

Mercury's core has a higher iron content than that of any other major planet in the Solar System, and several theories have been proposed to explain this. The most widely accepted theory is that Mercury originally had a metal–silicate ratio similar to common chondrite meteorites, thought to be typical of the Solar System's rocky matter, and a mass approximately 2.25 times its current mass. [37] Early in the Solar System's history, Mercury may have been struck by a planetesimal of approximately 1/6 that mass and several thousand kilometers across. [37] The impact would have stripped away much of the original crust and mantle, leaving the core behind as a relatively major component. [37] A similar process, known as the giant impact hypothesis, has been proposed to explain the formation of the Moon. [37]

Alternatively, Mercury may have formed from the solar nebula before the Sun's energy output had stabilized. It would initially have had twice its present mass, but as the protosun contracted, temperatures near Mercury could have been between 2,500 and 3,500 K and possibly even as high as 10,000 K. [38] Much of Mercury's surface rock could have been vaporized at such temperatures, forming an atmosphere of "rock vapor" that could have been carried away by the solar wind. [38]

A third hypothesis proposes that the solar nebula caused drag on the particles from which Mercury was accreting, which meant that lighter particles were lost from the accreting material and not gathered by Mercury. [39] Each hypothesis predicts a different surface composition, and there are two space missions set to make observations. MESSENGER, which ended in 2015, found higher-than-expected potassium and sulfur levels on the surface, suggesting that the giant impact hypothesis and vaporization of the crust and mantle did not occur because potassium and sulfur would have been driven off by the extreme heat of these events. [40] BepiColombo, which will arrive at Mercury in 2025, will make observations to test these hypotheses. [41] The findings so far would seem to favor the third hypothesis however, further analysis of the data is needed. [42]

Surface geology

Mercury's surface is similar in appearance to that of the Moon, showing extensive mare-like plains and heavy cratering, indicating that it has been geologically inactive for billions of years. It is more heterogeneous than either Mars's or the Moon's, both of which contain significant stretches of similar geology, such as maria and plateaus. [43] Albedo features are areas of markedly different reflectivity, which include impact craters, the resulting ejecta, and ray systems. Larger albedo features correspond to higher reflectivity plains. [44] Mercury has dorsa (also called "wrinkle-ridges"), Moon-like highlands, montes (mountains), planitiae (plains), rupes (escarpments), and valles (valleys). [45] [46]

The planet's mantle is chemically heterogeneous, suggesting the planet went through a magma ocean phase early in its history. Crystallization of minerals and convective overturn resulted in layered, chemically heterogeneous crust with large-scale variations in chemical composition observed on the surface. The crust is low in iron but high in sulfur, resulting from the stronger early chemically reducing conditions than is found in the other terrestrial planets. The surface is dominated by iron-poor pyroxene and olivine, as represented by enstatite and forsterite, respectively, along with sodium-rich plagioclase and minerals of mixed magnesium, calcium, and iron-sulfide. The less reflective regions of the crust are high in carbon, most likely in the form of graphite. [47]

Names for features on Mercury come from a variety of sources. Names coming from people are limited to the deceased. Craters are named for artists, musicians, painters, and authors who have made outstanding or fundamental contributions to their field. Ridges, or dorsa, are named for scientists who have contributed to the study of Mercury. Depressions or fossae are named for works of architecture. Montes are named for the word "hot" in a variety of languages. Plains or planitiae are named for Mercury in various languages. Escarpments or rupēs are named for ships of scientific expeditions. Valleys or valles are named for abandoned cities, towns, or settlements of antiquity. [48]

Impact basins and craters

Mercury was heavily bombarded by comets and asteroids during and shortly following its formation 4.6 billion years ago, as well as during a possibly separate subsequent episode called the Late Heavy Bombardment that ended 3.8 billion years ago. [49] Mercury received impacts over its entire surface during this period of intense crater formation, [46] facilitated by the lack of any atmosphere to slow impactors down. [50] During this time Mercury was volcanically active basins were filled by magma, producing smooth plains similar to the maria found on the Moon. [51] [52] An unusual crater with radiating troughs has been discovered that scientists called "the spider". [53] It was later named Apollodorus. [54]

Craters on Mercury range in diameter from small bowl-shaped cavities to multi-ringed impact basins hundreds of kilometers across. They appear in all states of degradation, from relatively fresh rayed craters to highly degraded crater remnants. Mercurian craters differ subtly from lunar craters in that the area blanketed by their ejecta is much smaller, a consequence of Mercury's stronger surface gravity. [55] According to International Astronomical Union (IAU) rules, each new crater must be named after an artist that was famous for more than fifty years, and dead for more than three years, before the date the crater is named. [56]

The largest known crater is Caloris Planitia, or Caloris Basin, with a diameter of 1,550 km. [57] The impact that created the Caloris Basin was so powerful that it caused lava eruptions and left a concentric mountainous ring

2 km tall surrounding the impact crater. The floor of the Caloris Basin is filled by a geologically distinct flat plain, broken up by ridges and fractures in a roughly polygonal pattern. It is not clear whether they are volcanic lava flows induced by the impact or a large sheet of impact melt. [55]

At the antipode of the Caloris Basin is a large region of unusual, hilly terrain known as the "Weird Terrain". One hypothesis for its origin is that shock waves generated during the Caloris impact traveled around Mercury, converging at the basin's antipode (180 degrees away). The resulting high stresses fractured the surface. [58] Alternatively, it has been suggested that this terrain formed as a result of the convergence of ejecta at this basin's antipode. [59]

Overall, 46 impact basins have been identified. [60] A notable basin is the 400 km wide, multi-ring Tolstoj Basin that has an ejecta blanket extending up to 500 km from its rim and a floor that has been filled by smooth plains materials. Beethoven Basin has a similar-sized ejecta blanket and a 625 km diameter rim. [55] Like the Moon, the surface of Mercury has likely incurred the effects of space weathering processes, including solar wind and micrometeorite impacts. [61]

Plains

There are two geologically distinct plains regions on Mercury. [55] [62] Gently rolling, hilly plains in the regions between craters are Mercury's oldest visible surfaces, [55] predating the heavily cratered terrain. These inter-crater plains appear to have obliterated many earlier craters, and show a general paucity of smaller craters below about 30 km in diameter. [62]

Smooth plains are widespread flat areas that fill depressions of various sizes and bear a strong resemblance to the lunar maria. Unlike lunar maria, the smooth plains of Mercury have the same albedo as the older inter-crater plains. Despite a lack of unequivocally volcanic characteristics, the localisation and rounded, lobate shape of these plains strongly support volcanic origins. [55] All the smooth plains of Mercury formed significantly later than the Caloris basin, as evidenced by appreciably smaller crater densities than on the Caloris ejecta blanket. [55]

Compressional features

One unusual feature of Mercury's surface is the numerous compression folds, or rupes, that crisscross the plains. As Mercury's interior cooled, it contracted and its surface began to deform, creating wrinkle ridges and lobate scarps associated with thrust faults. The scarps can reach lengths of 1000 km and heights of 3 km. [63] These compressional features can be seen on top of other features, such as craters and smooth plains, indicating they are more recent. [64] Mapping of the features has suggested a total shrinkage of Mercury's radius in the range of

1 to 7 km. [65] Most activity along the major thrust systems probably ended about 3.6–3.7 billion years ago. [66] Small-scale thrust fault scarps have been found, tens of meters in height and with lengths in the range of a few km, that appear to be less than 50 million years old, indicating that compression of the interior and consequent surface geological activity continue to the present. [63] [65]

The Lunar Reconnaissance Orbiter discovered that similar but smaller thrust faults exist on the Moon. [67]

Volcanism

There is evidence for pyroclastic flows on Mercury from low-profile shield volcanoes. [68] [69] [70] 51 pyroclastic deposits have been identified, [71] where 90% of them are found within impact craters. [71] A study of the degradation state of the impact craters that host pyroclastic deposits suggests that pyroclastic activity occurred on Mercury over a prolonged interval. [71]

A "rimless depression" inside the southwest rim of the Caloris Basin consists of at least nine overlapping volcanic vents, each individually up to 8 km in diameter. It is thus a "compound volcano". [72] The vent floors are at least 1 km below their brinks and they bear a closer resemblance to volcanic craters sculpted by explosive eruptions or modified by collapse into void spaces created by magma withdrawal back down into a conduit. [72] Scientists could not quantify the age of the volcanic complex system but reported that it could be of the order of a billion years. [72]

Surface conditions and exosphere

The surface temperature of Mercury ranges from 100 to 700 K (−173 to 427 °C −280 to 800 °F) [19] at the most extreme places: 0°N, 0°W, or 180°W. It never rises above 180 K at the poles, [13] due to the absence of an atmosphere and a steep temperature gradient between the equator and the poles. The subsolar point reaches about 700 K during perihelion (0°W or 180°W), but only 550 K at aphelion (90° or 270°W). [74] On the dark side of the planet, temperatures average 110 K. [13] [75] The intensity of sunlight on Mercury's surface ranges between 4.59 and 10.61 times the solar constant (1,370 W·m −2 ). [76]

Although the daylight temperature at the surface of Mercury is generally extremely high, observations strongly suggest that ice (frozen water) exists on Mercury. The floors of deep craters at the poles are never exposed to direct sunlight, and temperatures there remain below 102 K, far lower than the global average. [77] This creates a cold trap where ice can accumulate. Water ice strongly reflects radar, and observations by the 70-meter Goldstone Solar System Radar and the VLA in the early 1990s revealed that there are patches of high radar reflection near the poles. [78] Although ice was not the only possible cause of these reflective regions, astronomers think it was the most likely. [79]

The icy regions are estimated to contain about 10 14 –10 15 kg of ice, [80] and may be covered by a layer of regolith that inhibits sublimation. [81] By comparison, the Antarctic ice sheet on Earth has a mass of about 4 × 10 18 kg, and Mars's south polar cap contains about 10 16 kg of water. [80] The origin of the ice on Mercury is not yet known, but the two most likely sources are from outgassing of water from the planet's interior or deposition by impacts of comets. [80]

Mercury is too small and hot for its gravity to retain any significant atmosphere over long periods of time it does have a tenuous surface-bounded exosphere [82] containing hydrogen, helium, oxygen, sodium, calcium, potassium and others [15] [16] at a surface pressure of less than approximately 0.5 nPa (0.005 picobars). [3] This exosphere is not stable—atoms are continuously lost and replenished from a variety of sources. Hydrogen atoms and helium atoms probably come from the solar wind, diffusing into Mercury's magnetosphere before later escaping back into space. Radioactive decay of elements within Mercury's crust is another source of helium, as well as sodium and potassium. MESSENGER found high proportions of calcium, helium, hydroxide, magnesium, oxygen, potassium, silicon and sodium. Water vapor is present, released by a combination of processes such as: comets striking its surface, sputtering creating water out of hydrogen from the solar wind and oxygen from rock, and sublimation from reservoirs of water ice in the permanently shadowed polar craters. The detection of high amounts of water-related ions like O + , OH − , and H3O + was a surprise. [83] [84] Because of the quantities of these ions that were detected in Mercury's space environment, scientists surmise that these molecules were blasted from the surface or exosphere by the solar wind. [85] [86]

Sodium, potassium and calcium were discovered in the atmosphere during the 1980–1990s, and are thought to result primarily from the vaporization of surface rock struck by micrometeorite impacts [87] including presently from Comet Encke. [88] In 2008, magnesium was discovered by MESSENGER. [89] Studies indicate that, at times, sodium emissions are localized at points that correspond to the planet's magnetic poles. This would indicate an interaction between the magnetosphere and the planet's surface. [90]

On November 29, 2012, NASA confirmed that images from MESSENGER had detected that craters at the north pole contained water ice. MESSENGER 's principal investigator Sean Solomon is quoted in The New York Times estimating the volume of the ice to be large enough to "encase Washington, D.C., in a frozen block two and a half miles deep". [73]

Magnetic field and magnetosphere

Despite its small size and slow 59-day-long rotation, Mercury has a significant, and apparently global, magnetic field. According to measurements taken by Mariner 10 , it is about 1.1% the strength of Earth's. The magnetic-field strength at Mercury's equator is about 300 nT . [91] [92] Like that of Earth, Mercury's magnetic field is dipolar. [90] Unlike Earth's, Mercury's poles are nearly aligned with the planet's spin axis. [93] Measurements from both the Mariner 10 and MESSENGER space probes have indicated that the strength and shape of the magnetic field are stable. [93]

It is likely that this magnetic field is generated by a dynamo effect, in a manner similar to the magnetic field of Earth. [94] [95] This dynamo effect would result from the circulation of the planet's iron-rich liquid core. Particularly strong tidal heating effects caused by the planet's high orbital eccentricity would serve to keep part of the core in the liquid state necessary for this dynamo effect. [30] [96]

Mercury's magnetic field is strong enough to deflect the solar wind around the planet, creating a magnetosphere. The planet's magnetosphere, though small enough to fit within Earth, [90] is strong enough to trap solar wind plasma. This contributes to the space weathering of the planet's surface. [93] Observations taken by the Mariner 10 spacecraft detected this low energy plasma in the magnetosphere of the planet's nightside. Bursts of energetic particles in the planet's magnetotail indicate a dynamic quality to the planet's magnetosphere. [90]

During its second flyby of the planet on October 6, 2008, MESSENGER discovered that Mercury's magnetic field can be extremely "leaky". The spacecraft encountered magnetic "tornadoes" – twisted bundles of magnetic fields connecting the planetary magnetic field to interplanetary space – that were up to 800 km wide or a third of the radius of the planet. These twisted magnetic flux tubes, technically known as flux transfer events, form open windows in the planet's magnetic shield through which the solar wind may enter and directly impact Mercury's surface via magnetic reconnection [97] This also occurs in Earth's magnetic field. The MESSENGER observations showed the reconnection rate is ten times higher at Mercury, but its proximity to the Sun only accounts for about a third of the reconnection rate observed by MESSENGER. [97]

Mercury has the most eccentric orbit of all the planets in the Solar System its eccentricity is 0.21 with its distance from the Sun ranging from 46,000,000 to 70,000,000 km (29,000,000 to 43,000,000 mi). It takes 87.969 Earth days to complete an orbit. The diagram illustrates the effects of the eccentricity, showing Mercury's orbit overlaid with a circular orbit having the same semi-major axis. Mercury's higher velocity when it is near perihelion is clear from the greater distance it covers in each 5-day interval. In the diagram, the varying distance of Mercury to the Sun is represented by the size of the planet, which is inversely proportional to Mercury's distance from the Sun. This varying distance to the Sun leads to Mercury's surface being flexed by tidal bulges raised by the Sun that are about 17 times stronger than the Moon's on Earth. [98] Combined with a 3:2 spin–orbit resonance of the planet's rotation around its axis, it also results in complex variations of the surface temperature. [23] The resonance makes a single solar day (the length between two meridian transits of the Sun) on Mercury last exactly two Mercury years, or about 176 Earth days. [99]

Mercury's orbit is inclined by 7 degrees to the plane of Earth's orbit (the ecliptic), the largest of all eight known solar planets. [100] As a result, transits of Mercury across the face of the Sun can only occur when the planet is crossing the plane of the ecliptic at the time it lies between Earth and the Sun, which is in May or November. This occurs about every seven years on average. [101]

Mercury's axial tilt is almost zero, [102] with the best measured value as low as 0.027 degrees. [103] This is significantly smaller than that of Jupiter, which has the second smallest axial tilt of all planets at 3.1 degrees. This means that to an observer at Mercury's poles, the center of the Sun never rises more than 2.1 arcminutes above the horizon. [103]

At certain points on Mercury's surface, an observer would be able to see the Sun peek up a little more than two-thirds of the way over the horizon, then reverse and set before rising again, all within the same Mercurian day. [c] This is because approximately four Earth days before perihelion, Mercury's angular orbital velocity equals its angular rotational velocity so that the Sun's apparent motion ceases closer to perihelion, Mercury's angular orbital velocity then exceeds the angular rotational velocity. Thus, to a hypothetical observer on Mercury, the Sun appears to move in a retrograde direction. Four Earth days after perihelion, the Sun's normal apparent motion resumes. [23] A similar effect would have occurred if Mercury had been in synchronous rotation: the alternating gain and loss of rotation over revolution would have caused a libration of 23.65° in longitude. [104]

For the same reason, there are two points on Mercury's equator, 180 degrees apart in longitude, at either of which, around perihelion in alternate Mercurian years (once a Mercurian day), the Sun passes overhead, then reverses its apparent motion and passes overhead again, then reverses a second time and passes overhead a third time, taking a total of about 16 Earth-days for this entire process. In the other alternate Mercurian years, the same thing happens at the other of these two points. The amplitude of the retrograde motion is small, so the overall effect is that, for two or three weeks, the Sun is almost stationary overhead, and is at its most brilliant because Mercury is at perihelion, its closest to the Sun. This prolonged exposure to the Sun at its brightest makes these two points the hottest places on Mercury. Maximum temperature occurs when the Sun is at an angle of about 25 degrees past noon due to diurnal temperature lag, at 0.4 Mercury days and 0.8 Mercury years past sunrise. [105] Conversely, there are two other points on the equator, 90 degrees of longitude apart from the first ones, where the Sun passes overhead only when the planet is at aphelion in alternate years, when the apparent motion of the Sun in Mercury's sky is relatively rapid. These points, which are the ones on the equator where the apparent retrograde motion of the Sun happens when it is crossing the horizon as described in the preceding paragraph, receive much less solar heat than the first ones described above. [106]

Mercury attains inferior conjunction (nearest approach to Earth) every 116 Earth days on average, [3] but this interval can range from 105 days to 129 days due to the planet's eccentric orbit. Mercury can come as near as 82,200,000 kilometres (0.549 astronomical units 51.1 million miles) to Earth, and that is slowly declining: The next approach to within 82,100,000 km (51.0 million miles) is in 2679, and to within 82,000,000 km (51 million miles) in 4487, but it will not be closer to Earth than 80,000,000 km (50 million miles) until 28,622. [107] Its period of retrograde motion as seen from Earth can vary from 8 to 15 days on either side of inferior conjunction. This large range arises from the planet's high orbital eccentricity. [23] Essentially because Mercury is closest to the Sun, when taking an average over time, Mercury is the closest planet to the Earth, [108] and—in that measure—it is the closest planet to each of the other planets in the Solar System. [109] [110] [d]

Longitude convention

The longitude convention for Mercury puts the zero of longitude at one of the two hottest points on the surface, as described above. However, when this area was first visited, by Mariner 10 , this zero meridian was in darkness, so it was impossible to select a feature on the surface to define the exact position of the meridian. Therefore, a small crater further west was chosen, called Hun Kal, which provides the exact reference point for measuring longitude. [111] [112] The center of Hun Kal defines the 20° west meridian. A 1970 International Astronomical Union resolution suggests that longitudes be measured positively in the westerly direction on Mercury. [113] The two hottest places on the equator are therefore at longitudes 0° W and 180° W, and the coolest points on the equator are at longitudes 90° W and 270° W. However, the MESSENGER project uses an east-positive convention. [114]

Spin-orbit resonance

For many years it was thought that Mercury was synchronously tidally locked with the Sun, rotating once for each orbit and always keeping the same face directed towards the Sun, in the same way that the same side of the Moon always faces Earth. Radar observations in 1965 proved that the planet has a 3:2 spin-orbit resonance, rotating three times for every two revolutions around the Sun. The eccentricity of Mercury's orbit makes this resonance stable—at perihelion, when the solar tide is strongest, the Sun is nearly still in Mercury's sky. [115]

The rare 3:2 resonant tidal locking is stabilized by the variance of the tidal force along Mercury's eccentric orbit, acting on a permanent dipole component of Mercury's mass distribution. [116] In a circular orbit there is no such variance, so the only resonance stabilized in such an orbit is at 1:1 (e.g., Earth–Moon), when the tidal force, stretching a body along the "center-body" line, exerts a torque that aligns the body's axis of least inertia (the "longest" axis, and the axis of the aforementioned dipole) to point always at the center. However, with noticeable eccentricity, like that of Mercury's orbit, the tidal force has a maximum at perihelion and therefore stabilizes resonances, like 3:2, enforcing that the planet points its axis of least inertia roughly at the Sun when passing through perihelion. [116]

The original reason astronomers thought it was synchronously locked was that, whenever Mercury was best placed for observation, it was always nearly at the same point in its 3:2 resonance, hence showing the same face. This is because, coincidentally, Mercury's rotation period is almost exactly half of its synodic period with respect to Earth. Due to Mercury's 3:2 spin-orbit resonance, a solar day lasts about 176 Earth days. [23] A sidereal day (the period of rotation) lasts about 58.7 Earth days. [23]

Simulations indicate that the orbital eccentricity of Mercury varies chaotically from nearly zero (circular) to more than 0.45 over millions of years due to perturbations from the other planets. [23] [117] This was thought to explain Mercury's 3:2 spin-orbit resonance (rather than the more usual 1:1), because this state is more likely to arise during a period of high eccentricity. [118] However, accurate modeling based on a realistic model of tidal response has demonstrated that Mercury was captured into the 3:2 spin-orbit state at a very early stage of its history, within 20 (more likely, 10) million years after its formation. [119]

Numerical simulations show that a future secular orbital resonant perihelion interaction with Jupiter may cause the eccentricity of Mercury's orbit to increase to the point where there is a 1% chance that the planet will collide with Venus within the next five billion years. [120] [121]

Advance of perihelion

In 1859, the French mathematician and astronomer Urbain Le Verrier reported that the slow precession of Mercury's orbit around the Sun could not be completely explained by Newtonian mechanics and perturbations by the known planets. He suggested, among possible explanations, that another planet (or perhaps instead a series of smaller 'corpuscules') might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation. [122] (Other explanations considered included a slight oblateness of the Sun.) The success of the search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place faith in this possible explanation, and the hypothetical planet was named Vulcan, but no such planet was ever found. [123]

The perihelion precession of Mercury is 5,600 arcseconds (1.5556°) per century relative to Earth, or 574.10±0.65 arcseconds per century [124] relative to the inertial ICRF. Newtonian mechanics, taking into account all the effects from the other planets, predicts a precession of 5,557 arcseconds (1.5436°) per century. [124] In the early 20th century, Albert Einstein's general theory of relativity provided the explanation for the observed precession, by formalizing gravitation as being mediated by the curvature of spacetime. The effect is small: just 42.98 arcseconds per century for Mercury it therefore requires a little over twelve million orbits for a full excess turn. Similar, but much smaller, effects exist for other Solar System bodies: 8.62 arcseconds per century for Venus, 3.84 for Earth, 1.35 for Mars, and 10.05 for 1566 Icarus. [125] [126]

There may be scientific support, based on studies reported in March 2020, for considering that parts of the planet Mercury may have been habitable, and perhaps that life forms, albeit likely primitive microorganisms, may have existed on the planet. [127] [128]


Contents

Discovery Edit

Captain Dimitrios Kontos ( Δημήτριος Κοντός ) and a crew of sponge divers from Symi island discovered the Antikythera shipwreck during the spring of 1900, and recovered artefacts during the first expedition with the Hellenic Royal Navy, in 1900–01. [26] This wreck of a Roman cargo ship was found at a depth of 45 metres (148 ft) off Point Glyphadia on the Greek island of Antikythera. The team retrieved numerous large artefacts, including bronze and marble statues, pottery, unique glassware, jewellery, coins, and the mechanism. The mechanism was retrieved from the wreckage in 1901, most probably in July of that year. [27] It is not known how the mechanism came to be on the cargo ship, but it has been suggested that it was being taken from Rhodes to Rome, together with other looted treasure, to support a triumphal parade being staged by Julius Caesar. [28]

All of the items retrieved from the wreckage were transferred to the National Museum of Archaeology in Athens for storage and analysis. The mechanism appeared at the time to be little more than a lump of corroded bronze and wood it went unnoticed for two years, while museum staff worked on piecing together more obvious treasures, such as the statues. [22]

On 17 May 1902, archaeologist Valerios Stais found that one of the pieces of rock had a gear wheel embedded in it. He initially believed that it was an astronomical clock, but most scholars considered the device to be prochronistic, too complex to have been constructed during the same period as the other pieces that had been discovered. Investigations into the object were dropped until British science historian and Yale University professor Derek J. de Solla Price became interested in it in 1951. [29] In 1971, Price and Greek nuclear physicist Charalampos Karakalos made X-ray and gamma-ray images of the 82 fragments. Price published an extensive 70-page paper on their findings in 1974. [11]

Two other searches for items at the Antikythera wreck site in 2012 and 2015 have yielded a number of fascinating art objects and a second ship which may or may not be connected with the treasure ship on which the Mechanism was found. [30] Also found was a bronze disc, embellished with the image of a bull. The disc has four "ears" which have holes in them, and it was thought by some that it may have been part of the Antikythera Mechanism itself, as a "cog wheel". However, there appears to be little evidence that it was part of the Mechanism it is more likely that the disc was a bronze decoration on a piece of furniture. [31]

Origin Edit

The Antikythera mechanism is generally referred to as the first known analogue computer. [32] The quality and complexity of the mechanism's manufacture suggests that it must have had undiscovered predecessors made during the Hellenistic period. [33] Its construction relied on theories of astronomy and mathematics developed by Greek astronomers during the second century BC, and it is estimated to have been built in the late second century BC [4] or the early first century BC. [34] [5]

In 2008, continued research by the Antikythera Mechanism Research Project suggested that the concept for the mechanism may have originated in the colonies of Corinth, since they identified the calendar on the Metonic Spiral as coming from Corinth or one of its colonies in northwest Greece or Sicily. [7] Syracuse was a colony of Corinth and the home of Archimedes, and the Antikythera Mechanism Research project argued in 2008 that it might imply a connection with the school of Archimedes. [7] However, it was demonstrated in 2017 that the calendar on the Metonic Spiral is indeed of the Corinthian type but cannot be that of Syracuse. [35] Another theory suggests that coins found by Jacques Cousteau at the wreck site in the 1970s date to the time of the device's construction, and posits that its origin may have been from the ancient Greek city of Pergamon, [36] home of the Library of Pergamum. With its many scrolls of art and science, it was second in importance only to the Library of Alexandria during the Hellenistic period. [37]

The ship carrying the device also contained vases in the Rhodian style, leading to a hypothesis that it was constructed at an academy founded by Stoic philosopher Posidonius on that Greek island. [38] Rhodes was a busy trading port in antiquity and a centre of astronomy and mechanical engineering, home to astronomer Hipparchus, who was active from about 140 BC to 120 BC. The mechanism uses Hipparchus' theory for the motion of the Moon, which suggests the possibility that he may have designed it or at least worked on it. [22] In addition, it has recently been argued that the astronomical events on the Parapegma of the Antikythera mechanism work best for latitudes in the range of 33.3–37.0 degrees north [39] the island of Rhodes is located between the latitudes of 35.85 and 36.50 degrees north.

In 2014, a study by Carman and Evans argued for a new dating of approximately 200 BC based on identifying the start-up date on the Saros Dial as the astronomical lunar month that began shortly after the new moon of 28 April 205 BC. [18] [19] Moreover, according to Carman and Evans, the Babylonian arithmetic style of prediction fits much better with the device's predictive models than the traditional Greek trigonometric style. [18] A study by Paul Iversen published in 2017 reasons that the prototype for the device was indeed from Rhodes, but that this particular model was modified for a client from Epirus in northwestern Greece Iversen argues that it was probably constructed no earlier than a generation before the shipwreck, a date supported also by Jones. [40]

Further dives were undertaken in 2014, with plans to continue in 2015, in the hope of discovering more of the mechanism. [19] A five-year programme of investigations began in 2014 and ended in October 2019, with a new five-year session starting in May 2020. [41] [42]

The original mechanism apparently came out of the Mediterranean as a single encrusted piece. Soon afterward it fractured into three major pieces. Other small pieces have broken off in the interim from cleaning and handling, [43] and still others were found on the sea floor by the Cousteau expedition. Other fragments may still be in storage, undiscovered since their initial recovery Fragment F was discovered in that way in 2005. Of the 82 known fragments, seven are mechanically significant and contain the majority of the mechanism and inscriptions. There are also 16 smaller parts that contain fractional and incomplete inscriptions. [4] [7] [44]

Major fragments Edit

Fragment Size [mm] Weight [g] Gears Inscriptions Notes
A 180 × 150 369.1 27 Yes The main fragment contains the majority of the known mechanism. Clearly visible on the front is the large b1 gear, and under closer inspection further gears behind said gear (parts of the l, m, c, and d trains are clearly visible as gears to the naked eye). The crank mechanism socket and the side-mounted gear that meshes with b1 is on Fragment A. The back of the fragment contains the rearmost e and k gears for synthesis of the moon anomaly, noticeable also is the pin and slot mechanism of the k train. It is noticed from detailed scans of the fragment that all gears are very closely packed and have sustained damage and displacement due to their years in the sea. The fragment is approximately 30 mm thick at its thickest point.

Fragment A also contains divisions of the upper left quarter of the Saros spiral and 14 inscriptions from said spiral. The fragment also contains inscriptions for the Exeligmos dial and visible on the back surface the remnants of the dial face. Finally, this fragment contains some back door inscriptions.

Minor fragments Edit

Many of the smaller fragments that have been found contain nothing of apparent value however, a few have some inscriptions on them. Fragment 19 contains significant back door inscriptions including one reading ". 76 years . " which refers to the Callippic cycle. Other inscriptions seem to describe the function of the back dials. In addition to this important minor fragment, 15 further minor fragments have remnants of inscriptions on them. [15] : 7

Information on the specific data gleaned from the ruins by the latest inquiries is detailed in the supplement to Freeth's 2006 Nature article. [4]

Operation Edit

On the front face of the mechanism there is a fixed ring dial representing the ecliptic, the twelve zodiacal signs marked off with equal 30-degree sectors. This matched with the Babylonian custom of assigning one twelfth of the ecliptic to each zodiac sign equally, even though the constellation boundaries were variable. Outside that dial is another ring which is rotatable, marked off with the months and days of the Sothic Egyptian calendar, twelve months of 30 days plus five intercalary days. The months are marked with the Egyptian names for the months transcribed into the Greek alphabet. The first task, then, is to rotate the Egyptian calendar ring to match the current zodiac points. The Egyptian calendar ignored leap days, so it advanced through a full zodiac sign in about 120 years. [5]

The mechanism was operated by turning a small hand crank (now lost) which was linked via a crown gear to the largest gear, the four-spoked gear visible on the front of fragment A, the gear named b1. This moved the date pointer on the front dial, which would be set to the correct Egyptian calendar day. The year is not selectable, so it is necessary to know the year currently set, or by looking up the cycles indicated by the various calendar cycle indicators on the back in the Babylonian ephemeris tables for the day of the year currently set, since most of the calendar cycles are not synchronous with the year. The crank moves the date pointer about 78 days per full rotation, so hitting a particular day on the dial would be easily possible if the mechanism were in good working condition. The action of turning the hand crank would also cause all interlocked gears within the mechanism to rotate, resulting in the simultaneous calculation of the position of the Sun and Moon, the moon phase, eclipse, and calendar cycles, and perhaps the locations of planets. [46]

The operator also had to be aware of the position of the spiral dial pointers on the two large dials on the back. The pointer had a "follower" that tracked the spiral incisions in the metal as the dials incorporated four and five full rotations of the pointers. When a pointer reached the terminal month location at either end of the spiral, the pointer's follower had to be manually moved to the other end of the spiral before proceeding further. [4] : 10

Faces Edit

Front face Edit

The front dial has two concentric circular scales. The inner scale marks the Greek signs of the Zodiac, with division in degrees. The outer scale, which is a moveable ring that sits flush with the surface and runs in a channel, is marked off with what appear to be days and has a series of corresponding holes beneath the ring in the channel.

Since the discovery of the Mechanism, this outer ring has been presumed to represent the 365-day Egyptian civil calendar. However, recent research challenges this presumption and gives evidence it is most likely divided into 354 intervals. [47]

If one subscribes to the 365-day presumption, it is recognized the Mechanism predates the Julian calendar reform, but the Sothic and Callippic cycles had already pointed to a 365 1⁄4-day solar year, as seen in Ptolemy III's abortive calendrical reform of 238 BC. The dials are not believed to reflect his proposed leap day (Epag. 6), but the outer calendar dial may be moved against the inner dial to compensate for the effect of the extra quarter-day in the solar year by turning the scale backward one day every four years.

However, if one subscribes to the 354-day evidence, then the most likely interpretation is that the ring is a manifestation of a 354-day lunar calendar. Given the era of the Mechanism's presumed construction and the presence of Egyptian month names, it is possibly the first example of the Egyptian civil-based lunar calendar proposed by Richard Anthony Parker in 1950. [48] The lunar calendar’s purpose was to serve as a day-to-day indicator of successive lunations, and would also have assisted with the interpretation of the Lunar phase pointer, and the Metonic and Saros dials. Undiscovered gearing, synchronous with the rest of the Metonic gearing of the mechanism, is implied to drive a pointer around this scale. Movement and registration of the ring relative to the underlying holes served to facilitate both a one-in-76-year Callippic cycle correction, as well as convenient lunisolar intercalation.

The dial also marks the position of the Sun on the ecliptic corresponds to the current date in the year. The orbits of the Moon and the five planets known to the Greeks are close enough to the ecliptic to make it a convenient reference for defining their positions as well.

The following three Egyptian months are inscribed in Greek letters on the surviving pieces of the outer ring: [49]

The other months have been reconstructed, although some reconstructions of the mechanism omit the five days of the Egyptian intercalary month. The Zodiac dial contains Greek inscriptions of the members of the zodiac, which is believed to be adapted to the tropical month version rather than the sidereal: [15] : 8 [ failed verification ]

  • ΚΡΙΟΣ (Krios [Ram], Aries)
  • ΤΑΥΡΟΣ (Tauros [Bull], Taurus)
  • ΔΙΔΥΜΟΙ (Didymoi [Twins], Gemini)
  • ΚΑΡΚΙΝΟΣ (Karkinos [Crab], Cancer)
  • ΛΕΩΝ (Leon [Lion], Leo)
  • ΠΑΡΘΕΝΟΣ (Parthenos [Maiden], Virgo)
  • ΧΗΛΑΙ (Chelai [Scorpio's Claw or Zygos], Libra)
  • ΣΚΟΡΠΙΟΣ (Skorpios [Scorpion], Scorpio)
  • ΤΟΞΟΤΗΣ (Toxotes [Archer], Sagittarius)
  • ΑΙΓΟΚΕΡΩΣ (Aigokeros [Goat-horned], Capricorn)
  • ΥΔΡΟΧΟΟΣ (Hydrokhoos [Water carrier], Aquarius)
  • ΙΧΘΥΕΣ (Ichthyes [Fish], Pisces)

Also on the zodiac dial are a number of single characters at specific points (see reconstruction here: [50] ). They are keyed to a parapegma, a precursor of the modern day almanac inscribed on the front face above and beneath the dials. They mark the locations of longitudes on the ecliptic for specific stars. The parapegma above the dials reads (square brackets indicate inferred text):

Α ΑΙΓΟΚΕΡΩΣ ΑΡΧΕΤΑΙ ΑΝΑΤΕΛΛΕΙΝ [. ] Α Capricorn begins to rise Ι ΚΡΙΟΣ ΑΡΧΕΤΑΙ ΕΠΙΤΕΛΛΕΙΝ [. ] Α Aries begins to rise
ΤΡΟΠΑΙ ΧΕΙΜΕΡΙΝΑΙ [. ] Α Winter solstice ΙΣΗΜΕΡΙΑ ΕΑΡΙΝΗ [. ] Α Vernal equinox
Β [. ] ΕΙ ΕΣΠΕΡΙ . evening Κ [. ] ΕΣΠΕΡΙΑ [. ] ΙΑ . evening
Γ [. ] ΙΕΣΠΕΡΙ . evening Λ ΥΑΔΕΣ ΔΥΝΟΥΣΙΝ ΕΣΠΕΡΙΑΙ [. ] ΚΑ The Hyades set in the evening
Δ [. ] ΥΔΡΟΧΟΟΣ ΑΡΧΕΤΑΙ ΕΠΙΤΕΛΛΕΙΝΑ Aquarius begins to rise Μ ΤΑΥΡΟΣ ΑΡΧΕΤΑΙ Ε<π>ΙΤΕΛΛΕΙΝΑ Taurus begins to rise
Ε [. ] ΕΣΠΕΡΙΟΣ [. ] Ι . evening Ν ΛΥΡΑ ΕΠΙΤΕΛΛΕΙ ΕΣΠΕΡΙΛ [. ] Δ Lyra rises in the evening
Ζ [. ] ΡΙΑΙ [. ] Κ . Ξ ΠΛΕΙΑΣ ΕΠΙΤΕΛΛΕΙ ΕΩΙΑ [. ] Ι The Pleiades rise in the morning
Η ΙΧΘΥΕΣ ΑΡΧΟΝΤΑΙ ΕΠΙΤΕΛΛΕΙΝ [. ] Α Pisces begins to rise Ο ΥΑΣ ΕΠΙΤΕΛΛΕΙ ΕΩΙΑ [. ] Δ The Hyades rise in the morning
Θ [. ] <ι>Α Π ΔΙΔΥΜΟΙ ΑΡΧΟΝΤΑ ΕΠΙΤΕΛΛΕΙΝ [. ] Α Gemini begins to rise
Ρ ΑΕΤΟΣ ΕΠΙΤΕΛΛΕΙ ΕΣΠΕΡΙΟΣ Altair rises in the evening
Σ ΑΡΚΤΟΥΡΟΣ ΔΥΝΕΙ Ε<ω><ι>ΟΣ Arcturus sets in the morning

The parapegma beneath the dials reads:

Α ΧΗΛΑΙ ΑΡΧΟΝΤΑ ΕΠΙΤΕΛΛΕΙΝ [. ] Α Libra begins to rise Μ ΚΑΡΚΙΝΟΣ ΑΡΧΕΤΑΙ [. ] Α Cancer begins
ΣΗΜΕΡΙΑ ΦΟΙΝΟΠΩΡΙΝΗ [. ] Α Autumnal equinox ΤΡΟΠΑΙ ΘΕΡΙΝΑΙ [. ] Α Summer solstice
Β [. ] ΑΝΑΤΕΛΛΟΥΣΙΝ ΕΣΠΕΡΙΟΙΙΑ . rise in the evening Ν ΩΡΙΩΝ ΑΝΤΕΛΛΕΙ ΕΩΙΟΣ Orion precedes the morning
Γ [. ] ΑΝΑΤΕΛΛΕΙ ΕΣΠΕΡΙΑΙΔ . rise in the evening Ξ <κ>ΥΩΝ ΑΝΤΕΛΛΕΙ ΕΩΙΟΣ Canis Major precedes the morning
Δ [. ] ΤΕΛΛΕΙΙ . rise Ο ΑΕΤΟΣ ΔΥΝΕΙ ΕΩΙΟΣ Altair sets in the morning
Ε ΣΚΟΡΠΙΟΣ ΑΡΧΕΤΑΙ ΑΝΑΤΕΛΛΕΙΝΑ Scorpio begins to rise Π ΛΕΩΝ ΑΡΧΕΤΑΙ ΕΠΙΤΕΛΛΕΙΝ [. ] Α Leo begins to rise
Ζ [. ] Ρ [. ]
Η [. ] Σ [. ]
Θ [. ] Τ [. ]
Ι ΤΟΞΟΤΗΣ ΑΡΧΕΤΑΙ ΕΠΙΤΕΛΛΕΙΝ [. ] Α Sagittarius begins to rise Υ [. ]
Κ [. ] Φ [. ]
Λ [. ] Χ [. ]

At least two pointers indicated positions of bodies upon the ecliptic. A lunar pointer indicated the position of the Moon, and a mean Sun pointer also was shown, perhaps doubling as the current date pointer. The Moon position was not a simple mean Moon indicator that would indicate movement uniformly around a circular orbit it approximated the acceleration and deceleration of the Moon's elliptical orbit, through the earliest extant use of epicyclic gearing.

It also tracked the precession of the elliptical orbit around the ecliptic in an 8.88-year cycle. The mean Sun position is, by definition, the current date. It is speculated that since such pains were taken to get the position of the Moon correct, [15] : 20, 24 then there also was likely to have been a "true sun" pointer in addition to the mean Sun pointer likewise, to track the elliptical anomaly of the Sun (the orbit of Earth around the Sun), but there is no evidence of it among the ruins of the mechanism found to date. [5] Similarly, neither is there the evidence of planetary orbit pointers for the five planets known to the Greeks among the ruins. See Proposed planet indication gearing schemes below.

Mechanical engineer Michael Wright demonstrated that there was a mechanism to supply the lunar phase in addition to the position. [51] The indicator was a small ball embedded in the lunar pointer, half-white and half-black, which rotated to show the phase (new, first quarter, half, third quarter, full, and back) graphically. The data to support this function is available given the Sun and Moon positions as angular rotations essentially, it is the angle between the two, translated into the rotation of the ball. It requires a differential gear, a gearing arrangement that sums or differences two angular inputs.

Rear face Edit

In July 2008, scientists reported new findings in the journal Nature showing that the mechanism not only tracked the Metonic calendar and predicted solar eclipses, but also calculated the timing of several panhellenic athletic games, including the Ancient Olympic Games. [7] Inscriptions on the instrument closely match the names of the months that are used on calendars from Epirus in northwestern Greece and with the island of Corfu, which in antiquity was known as Corcyra. [52] [53] [54]

On the back of the mechanism, there are five dials: the two large displays, the Metonic and the Saros, and three smaller indicators, the so-called Olympiad Dial, [7] which has recently been renamed the Games dial as it did not track Olympiad years (the four-year cycle it tracks most closely is the Halieiad), [9] the Callippic, and the Exeligmos. [4] : 11

The Metonic Dial is the main upper dial on the rear of the mechanism. The Metonic cycle, defined in several physical units, is 235 synodic months, which is very close (to within less than 13 one-millionths) to 19 tropical years. It is therefore a convenient interval over which to convert between lunar and solar calendars. The Metonic dial covers 235 months in five rotations of the dial, following a spiral track with a follower on the pointer that keeps track of the layer of the spiral. The pointer points to the synodic month, counted from new moon to new moon, and the cell contains the Corinthian month names. [7] [55] [56]

  1. ΦΟΙΝΙΚΑΙΟΣ (Phoinikaios)
  2. ΚΡΑΝΕΙΟΣ (Kraneios)
  3. ΛΑΝΟΤΡΟΠΙΟΣ (Lanotropios)
  4. ΜΑΧΑΝΕΥΣ (Machaneus, "mechanic", referring to Zeus the inventor)
  5. ΔΩΔΕΚΑΤΕΥΣ (Dodekateus)
  6. ΕΥΚΛΕΙΟΣ (Eukleios)
  7. ΑΡΤΕΜΙΣΙΟΣ (Artemisios)
  8. ΨΥΔΡΕΥΣ (Psydreus)
  9. ΓΑΜΕΙΛΙΟΣ (Gameilios)
  10. ΑΓΡΙΑΝΙΟΣ (Agrianios)
  11. ΠΑΝΑΜΟΣ (Panamos)
  12. ΑΠΕΛΛΑΙΟΣ (Apellaios)

Thus, setting the correct solar time (in days) on the front panel indicates the current lunar month on the back panel, with resolution to within a week or so.

Based on the fact that the calendar month names are consistent with all the evidence of the Epirote calendar and that the Games dial mentions the very minor Naa games of Dodona (in Epirus), it has recently been argued that the calendar on the Antikythera Mechanism is likely to be the Epirote calendar, and that this calendar was probably adopted from a Corinthian colony in Epirus, possibly Ambracia. [56] It has also been argued that the first month of the calendar, Phoinikaios, was ideally the month in which the autumn equinox fell, and that the start-up date of the calendar began shortly after the astronomical new moon of 23 August 205 BC. [57]

The Callippic dial is the left secondary upper dial, which follows a 76-year cycle. The Callippic cycle is four Metonic cycles, and so this dial indicates the current Metonic cycle in the overall Callippic cycle. [ citation needed ]

The Games dial is the right secondary upper dial it is the only pointer on the instrument that travels in a counter-clockwise direction as time advances. The dial is divided into four sectors, each of which is inscribed with a year indicator and the name of two Panhellenic Games: the "crown" games of Isthmia, Olympia, Nemea, and Pythia and two lesser games: Naa (held at Dodona), [58] and the sixth and final set of Games recently deciphered as the Halieia of Rhodes. [59] The inscriptions on each one of the four divisions are: [4] [7]

Olympic dial
Year of the cycle Inside the dial inscription Outside the dial inscription
1 ΙΣΘΜΙΑ (Isthmia)
ΟΛΥΜΠΙΑ (Olympia)
2 ΝΕΜΕΑ (Nemea)
NAA (Naa)
3 ΙΣΘΜΙΑ (Isthmia)
ΠΥΘΙΑ (Pythia)
4 ΝΕΜΕΑ (Nemea)
ΑΛΙΕΙΑ (Halieia)

The Saros dial is the main lower spiral dial on the rear of the mechanism. [4] : 4–5, 10 The Saros cycle is 18 years and 11 + 1 ⁄ 3 days long (6585.333. days), which is very close to 223 synodic months (6585.3211 days). It is defined as the cycle of repetition of the positions required to cause solar and lunar eclipses, and therefore, it could be used to predict them—not only the month, but the day and time of day. Note that the cycle is approximately 8 hours longer than an integer number of days. Translated into global spin, that means an eclipse occurs not only eight hours later, but one-third of a rotation farther to the west. Glyphs in 51 of the 223 synodic month cells of the dial specify the occurrence of 38 lunar and 27 solar eclipses. Some of the abbreviations in the glyphs read: [ citation needed ]

  • Σ = ΣΕΛΗΝΗ ("Selene", Moon)
  • Η = ΗΛΙΟΣ ("Helios", Sun)
  • HM = ΗΜΕΡΑΣ ("Hemeras", of the day)
  • ωρ = ωρα ("hora", hour)
  • NY = ΝΥΚΤΟΣ ("Nuktos", of the night)

The glyphs show whether the designated eclipse is solar or lunar, and give the day of the month and hour. Solar eclipses may not be visible at any given point, and lunar eclipses are visible only if the moon is above the horizon at the appointed hour. [15] : 6 In addition, the inner lines at the cardinal points of the Saros dial indicate the start of a new full moon cycle. Based on the distribution of the times of the eclipses, it has recently been argued that the start-up date of the Saros dial was shortly after the astronomical new moon of 28 April 205 BC. [18]

The Exeligmos Dial is the secondary lower dial on the rear of the mechanism. The Exeligmos cycle is a 54-year triple Saros cycle that is 19,756 days long. Since the length of the Saros cycle is to a third of a day (eight hours), so a full Exeligmos cycle returns counting to integer days, hence the inscriptions. The labels on its three divisions are: [4] : 10

  • Blank or o ? (representing the number zero, assumed, not yet observed)
  • H (number 8) means add 8 hours to the time mentioned in the display
  • Iϛ (number 16) means add 16 hours to the time mentioned in the display

Thus the dial pointer indicates how many hours must be added to the glyph times of the Saros dial in order to calculate the exact eclipse times. [ citation needed ]

Doors Edit

The mechanism has a wooden casing with a front and a back door, both containing inscriptions. [7] [15] The back door appears to be the "instruction manual". On one of its fragments is written "76 years, 19 years" representing the Callippic and Metonic cycles. Also written is "223" for the Saros cycle. On another one of its fragments, it is written "on the spiral subdivisions 235" referring to the Metonic dial.

Gearing Edit

The mechanism is remarkable for the level of miniaturisation and the complexity of its parts, which is comparable to that of fourteenth-century astronomical clocks. It has at least 30 gears, although mechanism expert Michael Wright has suggested that the Greeks of this period were capable of implementing a system with many more gears. [46]

There is much debate as to whether the mechanism had indicators for all five of the planets known to the ancient Greeks. No gearing for such a planetary display survives and all gears are accounted for—with the exception of one 63-toothed gear (r1) otherwise unaccounted for in fragment D. [5]

Fragment D is a small quasi-circular constriction that, according to Xenophon Moussas, has a gear inside a somewhat larger hollow gear. The inner gear moves inside the outer gear reproducing an epicyclical motion that, with a pointer, gives the position of planet Jupiter. [60] [61] The inner gear is numbered 45, "ME" in Greek and the same number is written on two surfaces of this small cylindrical box.

The purpose of the front face was to position astronomical bodies with respect to the celestial sphere along the ecliptic, in reference to the observer's position on the Earth. That is irrelevant to the question of whether that position was computed using a heliocentric or geocentric view of the Solar System either computational method should, and does, result in the same position (ignoring ellipticity), within the error factors of the mechanism.

The epicyclic Solar System of Ptolemy (c. AD 100–170)—still 300 years in the future from the apparent date of the mechanism—carried forward with more epicycles, and was more accurate predicting the positions of planets than the view of Copernicus (1473–1543), until Kepler (1571–1630) introduced the possibility that orbits are ellipses. [62]

Evans et al. suggest that to display the mean positions of the five classical planets would require only 17 further gears that could be positioned in front of the large driving gear and indicated using individual circular dials on the face. [63]

Tony Freeth and Alexander Jones have modelled and published details of a version using several gear trains mechanically-similar to the lunar anomaly system allowing for indication of the positions of the planets as well as synthesis of the Sun anomaly. Their system, they claim, is more authentic than Wright's model as it uses the known skill sets of the Greeks of that period and does not add excessive complexity or internal stresses to the machine. [5]

The gear teeth were in the form of equilateral triangles with an average circular pitch of 1.6 mm, an average wheel thickness of 1.4 mm and an average air gap between gears of 1.2 mm. The teeth probably were created from a blank bronze round using hand tools this is evident because not all of them are even. [5] Due to advances in imaging and X-ray technology it is now possible to know the precise number of teeth and size of the gears within the located fragments. Thus the basic operation of the device is no longer a mystery and has been replicated accurately. The major unknown remains the question of the presence and nature of any planet indicators. [15] : 8

A table of the gears, their teeth, and the expected and computed rotations of various important gears follows. The gear functions come from Freeth et al. (2008) [7] and those for the lower half of the table from Freeth and Jones 2012. [5] The computed values start with 1 year/revolution for the b1 gear, and the remainder are computed directly from gear teeth ratios. The gears marked with an asterisk (*) are missing, or have predecessors missing, from the known mechanism these gears have been calculated with reasonable gear teeth counts. [7] [15]

The Antikythera Mechanism: known gears and accuracy of computation
Gear name [table 1] Function of the gear/pointer Expected simulated interval of a full circular revolution Mechanism formula [table 2] Computed interval Gear direction [table 3]
x Year gear 1 tropical year 1 (by definition) 1 year (presumed) cw [table 4]
b the Moon's orbit 1 sidereal month (27.321661 days) Time(b) = Time(x) * (c1 / b2) * (d1 / c2) * (e2 / d2) * (k1 / e5) * (e6 / k2) * (b3 / e1) 27.321 days [table 5] cw
r lunar phase display 1 synodic month (29.530589 days) Time(r) = 1 / (1 / Time(b2 [mean sun] or sun3 [true sun])) – (1 / Time(b))) 29.530 days [table 5]
n* Metonic pointer Metonic cycle () / 5 spirals around the dial = 1387.94 days Time(n) = Time(x) * (l1 / b2) * (m1 /l2) * (n1 / m2) 1387.9 days ccw [table 6]
o* Games dial pointer 4 years Time(o) = Time(n) * (o1 / n2) 4.00 years cw [table 6] [table 7]
q* Callippic pointer 27758.8 days Time(q) = Time(n) * (p1 / n3) * (q1 /p2) 27758 days ccw [table 6]
e* lunar orbit precession 8.85 years Time(e) = Time(x) * (l1 / b2) * (m1 / l2) * (e3 / m3) 8.8826 years ccw [table 8]
g* Saros cycle Saros time / 4 turns = 1646.33 days Time(g) = Time(e) * (f1 / e4) * (g1 / f2) 1646.3 days ccw [table 6]
i* Exeligmos pointer 19755.8 days Time(i) = Time(g) * (h1 / g2) * (i1 / h2) 19756 days ccw [table 6]
The following are proposed gearing from the 2012 Freeth and Jones reconstruction:
sun3* True sun pointer 1 mean year Time(sun3) = Time(x) * (sun3 / sun1) * (sun2 / sun3) 1 mean year [table 5] cw [table 9]
mer2* Mercury pointer 115.88 days (synodic period) Time(mer2) = Time(x) * (mer2 / mer1) 115.89 days [table 5] cw [table 9]
ven2* Venus pointer 583.93 days (synodic period) Time(ven2) = Time(x) * (ven1 / sun1) 584.39 days [table 5] cw [table 9]
mars4* Mars pointer 779.96 days (synodic period) Time(mars4) = Time(x) * (mars2 / mars1) * (mars4 / mars3) 779.84 days [table 5] cw [table 9]
jup4* Jupiter pointer 398.88 days (synodic period) Time(jup4) = Time(x) * (jup2 / jup1) * (jup4 / jup3) 398.88 days [table 5] cw [table 9]
sat4* Saturn pointer 378.09 days (synodic period) Time(sat4) = Time(x) * (sat2 / sat1) * (sat4 / sat3) 378.06 days [table 5] cw [table 9]

  1. ^ Change from traditional naming: X is the main year axis, turns once per year with gear B1. The B axis is the axis with gears B3 and B6, while the E axis is the axis with gears E3 and E4. Other axes on E (E1/E6 and E2/E5) are irrelevant to this table.
  2. ^ "Time" is the interval represented by one complete revolution of the gear.
  3. ^ As viewed from the front of the Mechanism. The "natural" view is viewing the side of the Mechanism the dial/pointer in question is actually displayed on.
  4. ^ The Greeks, being in the northern hemisphere, assumed proper daily motion of the stars was from east to west, ccw when the ecliptic and zodiac is viewed to the south. As viewed on the front of the Mechanism.
  5. ^ abcdefgh On average, due to epicyclic gearing causing accelerations and decelerations.
  6. ^ abcde Being on the reverse side of the box, the "natural" rotation is the opposite
  7. ^ This was the only visual pointer naturally travelling in the counter-clockwise direction.
  8. ^ Internal and not visible.
  9. ^ abcdef Prograde motion retrograde is obviously the opposite direction.

There are several gear ratios for each planet that result in close matches to the correct values for synodic periods of the planets and the Sun. The ones chosen above seem to provide good accuracy with reasonable tooth counts, but the specific gears that may have been used are, and probably will remain, unknown. [5]

Known gear scheme Edit

It is very probable that there were planetary dials, as the complicated motions and periodicities of all planets are mentioned in the manual of the mechanism. The exact position and mechanisms for the gears of the planets is not known. There is no coaxial system but only for the Moon. Fragment D that is an epicycloidal system is considered as a planetary gear for Jupiter (Moussas, 2011, 2012, 2014) or a gear for the motion of the Sun (University of Thessaloniki group). The Sun gear is operated from the hand-operated crank (connected to gear a1, driving the large four-spoked mean Sun gear, b1) and in turn drives the rest of the gear sets. The Sun gear is b1/b2 and b2 has 64 teeth. It directly drives the date/mean sun pointer (there may have been a second, "true sun" pointer that displayed the Sun's elliptical anomaly it is discussed below in the Freeth reconstruction). In this discussion, reference is to modelled rotational period of various pointers and indicators they all assume the input rotation of the b1 gear of 360 degrees, corresponding with one tropical year, and are computed solely on the basis of the gear ratios of the gears named. [4] [7] [65]

The Moon train starts with gear b1 and proceeds through c1, c2, d1, d2, e2, e5, k1, k2, e6, e1, and b3 to the Moon pointer on the front face. The gears k1 and k2 form an epicyclic gear system they are an identical pair of gears that don't mesh, but rather, they operate face-to-face, with a short pin on k1 inserted into a slot in k2. The two gears have different centres of rotation, so the pin must move back and forth in the slot. That increases and decreases the radius at which k2 is driven, also necessarily varying its angular velocity (presuming the velocity of k1 is even) faster in some parts of the rotation than others. Over an entire revolution the average velocities are the same, but the fast-slow variation models the effects of the elliptical orbit of the Moon, in consequence of Kepler's second and third laws. The modelled rotational period of the Moon pointer (averaged over a year) is 27.321 days, compared to the modern length of a lunar sidereal month of 27.321661 days. As mentioned, the pin/slot driving of the k1/k2 gears varies the displacement over a year's time, and the mounting of those two gears on the e3 gear supplies a precessional advancement to the ellipticity modelling with a period of 8.8826 years, compared with the current value of precession period of the moon of 8.85 years. [4] [7] [65]

The system also models the phases of the Moon. The Moon pointer holds a shaft along its length, on which is mounted a small gear named r, which meshes to the Sun pointer at B0 (the connection between B0 and the rest of B is not visible in the original mechanism, so whether b0 is the current date/mean Sun pointer or a hypothetical true Sun pointer is not known). The gear rides around the dial with the Moon, but is also geared to the Sun—the effect is to perform a differential gear operation, so the gear turns at the synodic month period, measuring in effect, the angle of the difference between the Sun and Moon pointers. The gear drives a small ball that appears through an opening in the Moon pointer's face, painted longitudinally half white and half black, displaying the phases pictorially. It turns with a modelled rotational period of 29.53 days the modern value for the synodic month is 29.530589 days. [4] [7] [65]

The Metonic train is driven by the drive train b1, b2, l1, l2, m1, m2, and n1, which is connected to the pointer. The modelled rotational period of the pointer is the length of the 6939.5 days (over the whole five-rotation spiral), while the modern value for the Metonic cycle is 6939.69 days. [4] [7] [65]

The Olympiad train is driven by b1, b2, l1, l2, m1, m2, n1, n2, and o1, which mounts the pointer. It has a computed modelled rotational period of exactly four years, as expected. Incidentally, it is the only pointer on the mechanism that rotates counter-clockwise all of the others rotate clockwise. [4] [7] [65]

The Callippic train is driven by b1, b2, l1, l2, m1, m2, n1, n3, p1, p2, and q1, which mounts the pointer. It has a computed modelled rotational period of 27758 days, while the modern value is 27758.8 days. [4] [7] [65]

The Saros train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, and g1, which mounts the pointer. The modelled rotational period of the Saros pointer is 1646.3 days (in four rotations along the spiral pointer track) the modern value is 1646.33 days. [4] [7] [65]

The Exeligmos train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, g1, g2, h1, h2, and i1, which mounts the pointer. The modelled rotational period of the Exeligmos pointer is 19,756 days the modern value is 19755.96 days. [4] [7] [65]

Apparently, gears m3, n1-3, p1-2, and q1 did not survive in the wreckage. The functions of the pointers were deduced from the remains of the dials on the back face, and reasonable, appropriate gearage to fulfill the functions was proposed, and is generally accepted. [4] [7] [65]

Proposed gear schemes Edit

Because of the large space between the mean Sun gear and the front of the case and the size of and mechanical features on the mean Sun gear it is very likely that the mechanism contained further gearing that either has been lost in or subsequent to the shipwreck or was removed before being loaded onto the ship. [5] This lack of evidence and nature of the front part of the mechanism has led to numerous attempts to emulate what the Greeks of the period would have done and, of course, because of the lack of evidence many solutions have been put forward.


Mercury (planet)

Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman god Mercurius (Mercury), god of commerce, messenger of the gods, and mediator between gods and mortals, corresponding to the Greek god Hermes (Ἑρμῆς). Like Venus, Mercury orbits the Sun within Earth's orbit as an inferior planet, and its apparent distance from the Sun as viewed from Earth never exceeds 28°. This proximity to the Sun means the planet can only be seen near the western horizon after sunset or the eastern horizon before sunrise, usually in twilight. At this time, it may appear as a bright star-like object but is often far more difficult to observe than Venus. From Earth, the planet telescopically displays the complete range of phases, similar to Venus and the Moon, which recurs over its synodic period of approximately 116 days.

Mercury rotates in a way that is unique in the Solar System. It is tidally locked with the Sun in a 3:2 spin–orbit resonance, [17] meaning that relative to the fixed stars, it rotates on its axis exactly three times for every two revolutions it makes around the Sun. [a] [18] As seen from the Sun, in a frame of reference that rotates with the orbital motion, it appears to rotate only once every two Mercurian years. An observer on Mercury would therefore see only one day every two Mercurian years.

Mercury's axis has the smallest tilt of any of the Solar System's planets (about 1 ⁄ 30 degree). Its orbital eccentricity is the largest of all known planets in the Solar System [b] at perihelion, Mercury's distance from the Sun is only about two-thirds (or 66%) of its distance at aphelion. Mercury's surface appears heavily cratered and is similar in appearance to the Moon's, indicating that it has been geologically inactive for billions of years. Having almost no atmosphere to retain heat, it has surface temperatures that vary diurnally more than on any other planet in the Solar System, ranging from 100 K (−173 °C −280 °F) at night to 700 K (427 °C 800 °F) during the day across the equatorial regions. [19] The polar regions are constantly below 180 K (−93 °C −136 °F). The planet has no known natural satellites.

Two spacecraft have visited Mercury: Mariner 10 flew by in 1974 and 1975 and MESSENGER, launched in 2004, orbited Mercury over 4,000 times in four years before exhausting its fuel and crashing into the planet's surface on April 30, 2015. [20] [21] [22] The BepiColombo spacecraft is planned to arrive at Mercury in 2025.

Physical characteristics

Mercury is one of four terrestrial planets in the Solar System, and is a rocky body like Earth. It is the smallest planet in the Solar System, with an equatorial radius of 2,439.7 kilometres (1,516.0 mi). [3] Mercury is also smaller—albeit more massive—than the largest natural satellites in the Solar System, Ganymede and Titan. Mercury consists of approximately 70% metallic and 30% silicate material. [23]

Internal structure

Mercury appears to have a solid silicate crust and mantle overlying a solid, iron sulfide outer core layer, a deeper liquid core layer, and a solid inner core. [24] [25] The planet's density is the second highest in the Solar System at 5.427 g/cm 3 , only slightly less than Earth's density of 5.515 g/cm 3 . [3] If the effect of gravitational compression were to be factored out from both planets, the materials of which Mercury is made would be denser than those of Earth, with an uncompressed density of 5.3 g/cm 3 versus Earth's 4.4 g/cm 3 . [26] Mercury's density can be used to infer details of its inner structure. Although Earth's high density results appreciably from gravitational compression, particularly at the core, Mercury is much smaller and its inner regions are not as compressed. Therefore, for it to have such a high density, its core must be large and rich in iron. [27]

Geologists estimate that Mercury's core occupies about 55% of its volume for Earth this proportion is 17%. Research published in 2007 suggests that Mercury has a molten core. [28] [29] Surrounding the core is a 500–700 km (310–430 mi) mantle consisting of silicates. [30] [31] Based on data from the Mariner 10 mission and Earth-based observation, Mercury's crust is estimated to be 35 km (22 mi) thick. [32] However, this model may be an overestimate and the crust could be 26 ± 11 km (16.2 ± 6.8 mi) thick based on an Airy isostacy model. [33] One distinctive feature of Mercury's surface is the presence of numerous narrow ridges, extending up to several hundred kilometers in length. It is thought that these were formed as Mercury's core and mantle cooled and contracted at a time when the crust had already solidified. [34] [35] [36]

Mercury's core has a higher iron content than that of any other major planet in the Solar System, and several theories have been proposed to explain this. The most widely accepted theory is that Mercury originally had a metal–silicate ratio similar to common chondrite meteorites, thought to be typical of the Solar System's rocky matter, and a mass approximately 2.25 times its current mass. [37] Early in the Solar System's history, Mercury may have been struck by a planetesimal of approximately 1/6 that mass and several thousand kilometers across. [37] The impact would have stripped away much of the original crust and mantle, leaving the core behind as a relatively major component. [37] A similar process, known as the giant impact hypothesis, has been proposed to explain the formation of the Moon. [37]

Alternatively, Mercury may have formed from the solar nebula before the Sun's energy output had stabilized. It would initially have had twice its present mass, but as the protosun contracted, temperatures near Mercury could have been between 2,500 and 3,500 K and possibly even as high as 10,000 K. [38] Much of Mercury's surface rock could have been vaporized at such temperatures, forming an atmosphere of "rock vapor" that could have been carried away by the solar wind. [38]

A third hypothesis proposes that the solar nebula caused drag on the particles from which Mercury was accreting, which meant that lighter particles were lost from the accreting material and not gathered by Mercury. [39] Each hypothesis predicts a different surface composition, and there are two space missions set to make observations. MESSENGER, which ended in 2015, found higher-than-expected potassium and sulfur levels on the surface, suggesting that the giant impact hypothesis and vaporization of the crust and mantle did not occur because potassium and sulfur would have been driven off by the extreme heat of these events. [40] BepiColombo, which will arrive at Mercury in 2025, will make observations to test these hypotheses. [41] The findings so far would seem to favor the third hypothesis however, further analysis of the data is needed. [42]

Surface geology

Mercury's surface is similar in appearance to that of the Moon, showing extensive mare-like plains and heavy cratering, indicating that it has been geologically inactive for billions of years. It is more heterogeneous than either Mars's or the Moon's, both of which contain significant stretches of similar geology, such as maria and plateaus. [43] Albedo features are areas of markedly different reflectivity, which include impact craters, the resulting ejecta, and ray systems. Larger albedo features correspond to higher reflectivity plains. [44] Mercury has dorsa (also called "wrinkle-ridges"), Moon-like highlands, montes (mountains), planitiae (plains), rupes (escarpments), and valles (valleys). [45] [46]

The planet's mantle is chemically heterogeneous, suggesting the planet went through a magma ocean phase early in its history. Crystallization of minerals and convective overturn resulted in layered, chemically heterogeneous crust with large-scale variations in chemical composition observed on the surface. The crust is low in iron but high in sulfur, resulting from the stronger early chemically reducing conditions than is found in the other terrestrial planets. The surface is dominated by iron-poor pyroxene and olivine, as represented by enstatite and forsterite, respectively, along with sodium-rich plagioclase and minerals of mixed magnesium, calcium, and iron-sulfide. The less reflective regions of the crust are high in carbon, most likely in the form of graphite. [47]

Names for features on Mercury come from a variety of sources. Names coming from people are limited to the deceased. Craters are named for artists, musicians, painters, and authors who have made outstanding or fundamental contributions to their field. Ridges, or dorsa, are named for scientists who have contributed to the study of Mercury. Depressions or fossae are named for works of architecture. Montes are named for the word "hot" in a variety of languages. Plains or planitiae are named for Mercury in various languages. Escarpments or rupēs are named for ships of scientific expeditions. Valleys or valles are named for abandoned cities, towns, or settlements of antiquity. [48]

Mercury was heavily bombarded by comets and asteroids during and shortly following its formation 4.6 billion years ago, as well as during a possibly separate subsequent episode called the Late Heavy Bombardment that ended 3.8 billion years ago. [49] Mercury received impacts over its entire surface during this period of intense crater formation, [46] facilitated by the lack of any atmosphere to slow impactors down. [50] During this time Mercury was volcanically active basins were filled by magma, producing smooth plains similar to the maria found on the Moon. [51] [52] An unusual crater with radiating troughs has been discovered that scientists called "the spider". [53] It was later named Apollodorus. [54]

Craters on Mercury range in diameter from small bowl-shaped cavities to multi-ringed impact basins hundreds of kilometers across. They appear in all states of degradation, from relatively fresh rayed craters to highly degraded crater remnants. Mercurian craters differ subtly from lunar craters in that the area blanketed by their ejecta is much smaller, a consequence of Mercury's stronger surface gravity. [55] According to International Astronomical Union (IAU) rules, each new crater must be named after an artist that was famous for more than fifty years, and dead for more than three years, before the date the crater is named. [56]

The largest known crater is Caloris Planitia, or Caloris Basin, with a diameter of 1,550 km. [57] The impact that created the Caloris Basin was so powerful that it caused lava eruptions and left a concentric mountainous ring

2 km tall surrounding the impact crater. The floor of the Caloris Basin is filled by a geologically distinct flat plain, broken up by ridges and fractures in a roughly polygonal pattern. It is not clear whether they are volcanic lava flows induced by the impact or a large sheet of impact melt. [55]

At the antipode of the Caloris Basin is a large region of unusual, hilly terrain known as the "Weird Terrain". One hypothesis for its origin is that shock waves generated during the Caloris impact traveled around Mercury, converging at the basin's antipode (180 degrees away). The resulting high stresses fractured the surface. [58] Alternatively, it has been suggested that this terrain formed as a result of the convergence of ejecta at this basin's antipode. [59]

Overall, 46 impact basins have been identified. [60] A notable basin is the 400 km wide, multi-ring Tolstoj Basin that has an ejecta blanket extending up to 500 km from its rim and a floor that has been filled by smooth plains materials. Beethoven Basin has a similar-sized ejecta blanket and a 625 km diameter rim. [55] Like the Moon, the surface of Mercury has likely incurred the effects of space weathering processes, including solar wind and micrometeorite impacts. [61]

There are two geologically distinct plains regions on Mercury. [55] [62] Gently rolling, hilly plains in the regions between craters are Mercury's oldest visible surfaces, [55] predating the heavily cratered terrain. These inter-crater plains appear to have obliterated many earlier craters, and show a general paucity of smaller craters below about 30 km in diameter. [62]

Smooth plains are widespread flat areas that fill depressions of various sizes and bear a strong resemblance to the lunar maria. Unlike lunar maria, the smooth plains of Mercury have the same albedo as the older inter-crater plains. Despite a lack of unequivocally volcanic characteristics, the localisation and rounded, lobate shape of these plains strongly support volcanic origins. [55] All the smooth plains of Mercury formed significantly later than the Caloris basin, as evidenced by appreciably smaller crater densities than on the Caloris ejecta blanket. [55]

One unusual feature of Mercury's surface is the numerous compression folds, or rupes, that crisscross the plains. As Mercury's interior cooled, it contracted and its surface began to deform, creating wrinkle ridges and lobate scarps associated with thrust faults. The scarps can reach lengths of 1000 km and heights of 3 km. [63] These compressional features can be seen on top of other features, such as craters and smooth plains, indicating they are more recent. [64] Mapping of the features has suggested a total shrinkage of Mercury's radius in the range of

1 to 7 km. [65] Most activity along the major thrust systems probably ended about 3.6–3.7 billion years ago. [66] Small-scale thrust fault scarps have been found, tens of meters in height and with lengths in the range of a few km, that appear to be less than 50 million years old, indicating that compression of the interior and consequent surface geological activity continue to the present. [63] [65]

The Lunar Reconnaissance Orbiter discovered that similar but smaller thrust faults exist on the Moon. [67]

There is evidence for pyroclastic flows on Mercury from low-profile shield volcanoes. [68] [69] [70] 51 pyroclastic deposits have been identified, [71] where 90% of them are found within impact craters. [71] A study of the degradation state of the impact craters that host pyroclastic deposits suggests that pyroclastic activity occurred on Mercury over a prolonged interval. [71]

A "rimless depression" inside the southwest rim of the Caloris Basin consists of at least nine overlapping volcanic vents, each individually up to 8 km in diameter. It is thus a "compound volcano". [72] The vent floors are at least 1 km below their brinks and they bear a closer resemblance to volcanic craters sculpted by explosive eruptions or modified by collapse into void spaces created by magma withdrawal back down into a conduit. [72] Scientists could not quantify the age of the volcanic complex system but reported that it could be of the order of a billion years. [72]

Surface conditions and exosphere

The surface temperature of Mercury ranges from 100 to 700 K (−173 to 427 °C −280 to 800 °F) [19] at the most extreme places: 0°N, 0°W, or 180°W. It never rises above 180 K at the poles, [13] due to the absence of an atmosphere and a steep temperature gradient between the equator and the poles. The subsolar point reaches about 700 K during perihelion (0°W or 180°W), but only 550 K at aphelion (90° or 270°W). [74] On the dark side of the planet, temperatures average 110 K. [13] [75] The intensity of sunlight on Mercury's surface ranges between 4.59 and 10.61 times the solar constant (1,370 W·m −2 ). [76]

Although the daylight temperature at the surface of Mercury is generally extremely high, observations strongly suggest that ice (frozen water) exists on Mercury. The floors of deep craters at the poles are never exposed to direct sunlight, and temperatures there remain below 102 K, far lower than the global average. [77] This creates a cold trap where ice can accumulate. Water ice strongly reflects radar, and observations by the 70-meter Goldstone Solar System Radar and the VLA in the early 1990s revealed that there are patches of high radar reflection near the poles. [78] Although ice was not the only possible cause of these reflective regions, astronomers think it was the most likely. [79]

The icy regions are estimated to contain about 10 14 –10 15 kg of ice, [80] and may be covered by a layer of regolith that inhibits sublimation. [81] By comparison, the Antarctic ice sheet on Earth has a mass of about 4 × 10 18 kg, and Mars's south polar cap contains about 10 16 kg of water. [80] The origin of the ice on Mercury is not yet known, but the two most likely sources are from outgassing of water from the planet's interior or deposition by impacts of comets. [80]

Mercury is too small and hot for its gravity to retain any significant atmosphere over long periods of time it does have a tenuous surface-bounded exosphere [82] containing hydrogen, helium, oxygen, sodium, calcium, potassium and others [15] [16] at a surface pressure of less than approximately 0.5 nPa (0.005 picobars). [3] This exosphere is not stable—atoms are continuously lost and replenished from a variety of sources. Hydrogen atoms and helium atoms probably come from the solar wind, diffusing into Mercury's magnetosphere before later escaping back into space. Radioactive decay of elements within Mercury's crust is another source of helium, as well as sodium and potassium. MESSENGER found high proportions of calcium, helium, hydroxide, magnesium, oxygen, potassium, silicon and sodium. Water vapor is present, released by a combination of processes such as: comets striking its surface, sputtering creating water out of hydrogen from the solar wind and oxygen from rock, and sublimation from reservoirs of water ice in the permanently shadowed polar craters. The detection of high amounts of water-related ions like O + , OH − , and H3O + was a surprise. [83] [84] Because of the quantities of these ions that were detected in Mercury's space environment, scientists surmise that these molecules were blasted from the surface or exosphere by the solar wind. [85] [86]

Sodium, potassium and calcium were discovered in the atmosphere during the 1980–1990s, and are thought to result primarily from the vaporization of surface rock struck by micrometeorite impacts [87] including presently from Comet Encke. [88] In 2008, magnesium was discovered by MESSENGER. [89] Studies indicate that, at times, sodium emissions are localized at points that correspond to the planet's magnetic poles. This would indicate an interaction between the magnetosphere and the planet's surface. [90]

On November 29, 2012, NASA confirmed that images from MESSENGER had detected that craters at the north pole contained water ice. MESSENGER 's principal investigator Sean Solomon is quoted in The New York Times estimating the volume of the ice to be large enough to "encase Washington, D.C., in a frozen block two and a half miles deep". [73]

Magnetic field and magnetosphere

Despite its small size and slow 59-day-long rotation, Mercury has a significant, and apparently global, magnetic field. According to measurements taken by Mariner 10 , it is about 1.1% the strength of Earth's. The magnetic-field strength at Mercury's equator is about 300 nT . [91] [92] Like that of Earth, Mercury's magnetic field is dipolar. [90] Unlike Earth's, Mercury's poles are nearly aligned with the planet's spin axis. [93] Measurements from both the Mariner 10 and MESSENGER space probes have indicated that the strength and shape of the magnetic field are stable. [93]

It is likely that this magnetic field is generated by a dynamo effect, in a manner similar to the magnetic field of Earth. [94] [95] This dynamo effect would result from the circulation of the planet's iron-rich liquid core. Particularly strong tidal heating effects caused by the planet's high orbital eccentricity would serve to keep part of the core in the liquid state necessary for this dynamo effect. [30] [96]

Mercury's magnetic field is strong enough to deflect the solar wind around the planet, creating a magnetosphere. The planet's magnetosphere, though small enough to fit within Earth, [90] is strong enough to trap solar wind plasma. This contributes to the space weathering of the planet's surface. [93] Observations taken by the Mariner 10 spacecraft detected this low energy plasma in the magnetosphere of the planet's nightside. Bursts of energetic particles in the planet's magnetotail indicate a dynamic quality to the planet's magnetosphere. [90]

During its second flyby of the planet on October 6, 2008, MESSENGER discovered that Mercury's magnetic field can be extremely "leaky". The spacecraft encountered magnetic "tornadoes" – twisted bundles of magnetic fields connecting the planetary magnetic field to interplanetary space – that were up to 800 km wide or a third of the radius of the planet. These twisted magnetic flux tubes, technically known as flux transfer events, form open windows in the planet's magnetic shield through which the solar wind may enter and directly impact Mercury's surface via magnetic reconnection [97] This also occurs in Earth's magnetic field. The MESSENGER observations showed the reconnection rate is ten times higher at Mercury, but its proximity to the Sun only accounts for about a third of the reconnection rate observed by MESSENGER. [97]

Orbit, rotation, and longitude

Mercury has the most eccentric orbit of all the planets in the Solar System its eccentricity is 0.21 with its distance from the Sun ranging from 46,000,000 to 70,000,000 km (29,000,000 to 43,000,000 mi). It takes 87.969 Earth days to complete an orbit. The diagram illustrates the effects of the eccentricity, showing Mercury's orbit overlaid with a circular orbit having the same semi-major axis. Mercury's higher velocity when it is near perihelion is clear from the greater distance it covers in each 5-day interval. In the diagram, the varying distance of Mercury to the Sun is represented by the size of the planet, which is inversely proportional to Mercury's distance from the Sun. This varying distance to the Sun leads to Mercury's surface being flexed by tidal bulges raised by the Sun that are about 17 times stronger than the Moon's on Earth. [98] Combined with a 3:2 spin–orbit resonance of the planet's rotation around its axis, it also results in complex variations of the surface temperature. [23] The resonance makes a single solar day (the length between two meridian transits of the Sun) on Mercury last exactly two Mercury years, or about 176 Earth days. [99]

Mercury's orbit is inclined by 7 degrees to the plane of Earth's orbit (the ecliptic), the largest of all eight known solar planets. [100] As a result, transits of Mercury across the face of the Sun can only occur when the planet is crossing the plane of the ecliptic at the time it lies between Earth and the Sun, which is in May or November. This occurs about every seven years on average. [101]

Mercury's axial tilt is almost zero, [102] with the best measured value as low as 0.027 degrees. [103] This is significantly smaller than that of Jupiter, which has the second smallest axial tilt of all planets at 3.1 degrees. This means that to an observer at Mercury's poles, the center of the Sun never rises more than 2.1 arcminutes above the horizon. [103]

At certain points on Mercury's surface, an observer would be able to see the Sun peek up a little more than two-thirds of the way over the horizon, then reverse and set before rising again, all within the same Mercurian day. [c] This is because approximately four Earth days before perihelion, Mercury's angular orbital velocity equals its angular rotational velocity so that the Sun's apparent motion ceases closer to perihelion, Mercury's angular orbital velocity then exceeds the angular rotational velocity. Thus, to a hypothetical observer on Mercury, the Sun appears to move in a retrograde direction. Four Earth days after perihelion, the Sun's normal apparent motion resumes. [23] A similar effect would have occurred if Mercury had been in synchronous rotation: the alternating gain and loss of rotation over revolution would have caused a libration of 23.65° in longitude. [104]

For the same reason, there are two points on Mercury's equator, 180 degrees apart in longitude, at either of which, around perihelion in alternate Mercurian years (once a Mercurian day), the Sun passes overhead, then reverses its apparent motion and passes overhead again, then reverses a second time and passes overhead a third time, taking a total of about 16 Earth-days for this entire process. In the other alternate Mercurian years, the same thing happens at the other of these two points. The amplitude of the retrograde motion is small, so the overall effect is that, for two or three weeks, the Sun is almost stationary overhead, and is at its most brilliant because Mercury is at perihelion, its closest to the Sun. This prolonged exposure to the Sun at its brightest makes these two points the hottest places on Mercury. Maximum temperature occurs when the Sun is at an angle of about 25 degrees past noon due to diurnal temperature lag, at 0.4 Mercury days and 0.8 Mercury years past sunrise. [105] Conversely, there are two other points on the equator, 90 degrees of longitude apart from the first ones, where the Sun passes overhead only when the planet is at aphelion in alternate years, when the apparent motion of the Sun in Mercury's sky is relatively rapid. These points, which are the ones on the equator where the apparent retrograde motion of the Sun happens when it is crossing the horizon as described in the preceding paragraph, receive much less solar heat than the first ones described above. [106]

Mercury attains inferior conjunction (nearest approach to Earth) every 116 Earth days on average, [3] but this interval can range from 105 days to 129 days due to the planet's eccentric orbit. Mercury can come as near as 82,200,000 kilometres (0.549 astronomical units 51.1 million miles) to Earth, and that is slowly declining: The next approach to within 82,100,000 km (51.0 million miles) is in 2679, and to within 82,000,000 km (51 million miles) in 4487, but it will not be closer to Earth than 80,000,000 km (50 million miles) until 28,622. [107] Its period of retrograde motion as seen from Earth can vary from 8 to 15 days on either side of inferior conjunction. This large range arises from the planet's high orbital eccentricity. [23] Essentially because Mercury is closest to the Sun, when taking an average over time, Mercury is the closest planet to the Earth, [108] and—in that measure—it is the closest planet to each of the other planets in the Solar System. [109] [110] [d]

Longitude convention

The longitude convention for Mercury puts the zero of longitude at one of the two hottest points on the surface, as described above. However, when this area was first visited, by Mariner 10 , this zero meridian was in darkness, so it was impossible to select a feature on the surface to define the exact position of the meridian. Therefore, a small crater further west was chosen, called Hun Kal, which provides the exact reference point for measuring longitude. [111] [112] The center of Hun Kal defines the 20° west meridian. A 1970 International Astronomical Union resolution suggests that longitudes be measured positively in the westerly direction on Mercury. [113] The two hottest places on the equator are therefore at longitudes 0° W and 180° W, and the coolest points on the equator are at longitudes 90° W and 270° W. However, the MESSENGER project uses an east-positive convention. [114]

Spin-orbit resonance

For many years it was thought that Mercury was synchronously tidally locked with the Sun, rotating once for each orbit and always keeping the same face directed towards the Sun, in the same way that the same side of the Moon always faces Earth. Radar observations in 1965 proved that the planet has a 3:2 spin-orbit resonance, rotating three times for every two revolutions around the Sun. The eccentricity of Mercury's orbit makes this resonance stable—at perihelion, when the solar tide is strongest, the Sun is nearly still in Mercury's sky. [115]

The rare 3:2 resonant tidal locking is stabilized by the variance of the tidal force along Mercury's eccentric orbit, acting on a permanent dipole component of Mercury's mass distribution. [116] In a circular orbit there is no such variance, so the only resonance stabilized in such an orbit is at 1:1 (e.g., Earth–Moon), when the tidal force, stretching a body along the "center-body" line, exerts a torque that aligns the body's axis of least inertia (the "longest" axis, and the axis of the aforementioned dipole) to point always at the center. However, with noticeable eccentricity, like that of Mercury's orbit, the tidal force has a maximum at perihelion and therefore stabilizes resonances, like 3:2, enforcing that the planet points its axis of least inertia roughly at the Sun when passing through perihelion. [116]

The original reason astronomers thought it was synchronously locked was that, whenever Mercury was best placed for observation, it was always nearly at the same point in its 3:2 resonance, hence showing the same face. This is because, coincidentally, Mercury's rotation period is almost exactly half of its synodic period with respect to Earth. Due to Mercury's 3:2 spin-orbit resonance, a solar day lasts about 176 Earth days. [23] A sidereal day (the period of rotation) lasts about 58.7 Earth days. [23]

Simulations indicate that the orbital eccentricity of Mercury varies chaotically from nearly zero (circular) to more than 0.45 over millions of years due to perturbations from the other planets. [23] [117] This was thought to explain Mercury's 3:2 spin-orbit resonance (rather than the more usual 1:1), because this state is more likely to arise during a period of high eccentricity. [118] However, accurate modeling based on a realistic model of tidal response has demonstrated that Mercury was captured into the 3:2 spin-orbit state at a very early stage of its history, within 20 (more likely, 10) million years after its formation. [119]

Numerical simulations show that a future secular orbital resonant perihelion interaction with Jupiter may cause the eccentricity of Mercury's orbit to increase to the point where there is a 1% chance that the planet will collide with Venus within the next five billion years. [120] [121]

Advance of perihelion

In 1859, the French mathematician and astronomer Urbain Le Verrier reported that the slow precession of Mercury's orbit around the Sun could not be completely explained by Newtonian mechanics and perturbations by the known planets. He suggested, among possible explanations, that another planet (or perhaps instead a series of smaller 'corpuscules') might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation. [122] (Other explanations considered included a slight oblateness of the Sun.) The success of the search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place faith in this possible explanation, and the hypothetical planet was named Vulcan, but no such planet was ever found. [123]

The perihelion precession of Mercury is 5,600 arcseconds (1.5556°) per century relative to Earth, or 574.10±0.65 arcseconds per century [124] relative to the inertial ICRF. Newtonian mechanics, taking into account all the effects from the other planets, predicts a precession of 5,557 arcseconds (1.5436°) per century. [124] In the early 20th century, Albert Einstein's general theory of relativity provided the explanation for the observed precession, by formalizing gravitation as being mediated by the curvature of spacetime. The effect is small: just 42.98 arcseconds per century for Mercury it therefore requires a little over twelve million orbits for a full excess turn. Similar, but much smaller, effects exist for other Solar System bodies: 8.62 arcseconds per century for Venus, 3.84 for Earth, 1.35 for Mars, and 10.05 for 1566 Icarus. [125] [126]

Habitability

There may be scientific support, based on studies reported in March 2020, for considering that parts of the planet Mercury may have been habitable, and perhaps that life forms, albeit likely primitive microorganisms, may have existed on the planet. [127] [128]

Observation

Mercury's apparent magnitude is calculated to vary between −2.48 (brighter than Sirius) around superior conjunction and +7.25 (below the limit of naked-eye visibility) around inferior conjunction. [14] The mean apparent magnitude is 0.23 while the standard deviation of 1.78 is the largest of any planet. The mean apparent magnitude at superior conjunction is −1.89 while that at inferior conjunction is +5.93. [14] Observation of Mercury is complicated by its proximity to the Sun, as it is lost in the Sun's glare for much of the time. Mercury can be observed for only a brief period during either morning or evening twilight. [129]

Mercury can, like several other planets and the brightest stars, be seen during a total solar eclipse. [130]

Like the Moon and Venus, Mercury exhibits phases as seen from Earth. It is "new" at inferior conjunction and "full" at superior conjunction. The planet is rendered invisible from Earth on both of these occasions because of its being obscured by the Sun, [129] except its new phase during a transit.

Mercury is technically brightest as seen from Earth when it is at a full phase. Although Mercury is farthest from Earth when it is full, the greater illuminated area that is visible and the opposition brightness surge more than compensates for the distance. [131] The opposite is true for Venus, which appears brightest when it is a crescent, because it is much closer to Earth than when gibbous. [131] [132]

Nonetheless, the brightest (full phase) appearance of Mercury is an essentially impossible time for practical observation, because of the extreme proximity of the Sun. Mercury is best observed at the first and last quarter, although they are phases of lesser brightness. The first and last quarter phases occur at greatest elongation east and west of the Sun, respectively. At both of these times Mercury's separation from the Sun ranges anywhere from 17.9° at perihelion to 27.8° at aphelion. [133] [134] At greatest western elongation, Mercury rises at its earliest before sunrise, and at greatest eastern elongation, it sets at its latest after sunset. [135]

Mercury is more often and easily visible from the Southern Hemisphere than from the Northern. This is because Mercury's maximum western elongation occurs only during early autumn in the Southern Hemisphere, whereas its greatest eastern elongation happens only during late winter in the Southern Hemisphere. [135] In both of these cases, the angle at which the planet's orbit intersects the horizon is maximized, allowing it to rise several hours before sunrise in the former instance and not set until several hours after sundown in the latter from southern mid-latitudes, such as Argentina and South Africa. [135]

An alternate method for viewing Mercury involves observing the planet during daylight hours when conditions are clear, ideally when it is at its greatest elongation. This allows the planet to be found easily, even when using telescopes with 8 cm (3.1 in) apertures. However, great care must be taken to obstruct the Sun from sight because of the extreme risk for eye damage. [136] This method bypasses the limitation of twilight observing when the ecliptic is located at a low elevation (e.g. on autumn evenings).

Ground-based telescope observations of Mercury reveal only an illuminated partial disk with limited detail. The first of two spacecraft to visit the planet was Mariner 10 , which mapped about 45% of its surface from 1974 to 1975. The second is the MESSENGER spacecraft, which after three Mercury flybys between 2008 and 2009, attained orbit around Mercury on March 17, 2011, [137] to study and map the rest of the planet. [138]

The Hubble Space Telescope cannot observe Mercury at all, due to safety procedures that prevent its pointing too close to the Sun. [139]

Because the shift of 0.15 revolutions in a year makes up a seven-year cycle (0.15 × 7 ≈ 1.0), in the seventh year Mercury follows almost exactly (earlier by 7 days) the sequence of phenomena it showed seven years before. [133]

Observation history

Ancient astronomers

The earliest known recorded observations of Mercury are from the Mul.Apin tablets. These observations were most likely made by an Assyrian astronomer around the 14th century BC. [140] The cuneiform name used to designate Mercury on the Mul.Apin tablets is transcribed as Udu.Idim.Guu4.Ud ("the jumping planet"). [e] [141] Babylonian records of Mercury date back to the 1st millennium BC. The Babylonians called the planet Nabu after the messenger to the gods in their mythology. [142]

The ancients knew Mercury by different names depending on whether it was an evening star or a morning star. By about 350 BC, the ancient Greeks had realized the two stars were one. [143] They knew the planet as Στίλβων Stilbōn, meaning "twinkling", and Ἑρμής Hermēs, for its fleeting motion, [144] a name that is retained in modern Greek (Ερμής Ermis). [145] The Romans named the planet after the swift-footed Roman messenger god, Mercury (Latin Mercurius), which they equated with the Greek Hermes, because it moves across the sky faster than any other planet. [143] [146] The astronomical symbol for Mercury is a stylized version of Hermes' caduceus. [147]

The Greco-Egyptian [148] astronomer Ptolemy wrote about the possibility of planetary transits across the face of the Sun in his work Planetary Hypotheses. He suggested that no transits had been observed either because planets such as Mercury were too small to see, or because the transits were too infrequent. [149]

In ancient China, Mercury was known as "the Hour Star" (Chen-xing 辰星 ). It was associated with the direction north and the phase of water in the Five Phases system of metaphysics. [150] Modern Chinese, Korean, Japanese and Vietnamese cultures refer to the planet literally as the "water star" ( 水星 ), based on the Five elements. [151] [152] [153] Hindu mythology used the name Budha for Mercury, and this god was thought to preside over Wednesday. [154] The god Odin (or Woden) of Germanic paganism was associated with the planet Mercury and Wednesday. [155] The Maya may have represented Mercury as an owl (or possibly four owls two for the morning aspect and two for the evening) that served as a messenger to the underworld. [156]

In medieval Islamic astronomy, the Andalusian astronomer Abū Ishāq Ibrāhīm al-Zarqālī in the 11th century described the deferent of Mercury's geocentric orbit as being oval, like an egg or a pignon, although this insight did not influence his astronomical theory or his astronomical calculations. [157] [158] In the 12th century, Ibn Bajjah observed "two planets as black spots on the face of the Sun", which was later suggested as the transit of Mercury and/or Venus by the Maragha astronomer Qotb al-Din Shirazi in the 13th century. [159] (Note that most such medieval reports of transits were later taken as observations of sunspots. [160] )

In India, the Kerala school astronomer Nilakantha Somayaji in the 15th century developed a partially heliocentric planetary model in which Mercury orbits the Sun, which in turn orbits Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. [161]


What is wrong with this measurement of the synodic period of Mercury? - Astronomy

No version of Eudoxan models can account for the discrepancy between the two profoundly different invisibility periods, since the curve is essentially symmetric. At least, one would have to adjust the center of the hippopede, which would require more spheres. A 1 1/2 sign curve seems reasonable as it will capture the most important feature, the maximum elongation from the sun.

Assume that the poles of spheres 2 and 3 are 1 1/2 signs (45 degrees) apart, i.e., that the angles between the equators are 1 1/2 signs. Hence, the loops are each 1 1/2 signs in length. The maximum latitude will be 9.74 degrees, but in the wrong part of the cycle. It should be clear from the diagram that there is no retrograde motion on this model.


If, as most readers since the 6th century CE have assumed, a primary purpose was to account for retrograde motion, we can construct a model with retrograde motion. However, it will be deficient in its elongation, here 5 signs (150 degrees) and its maximum latitude will be 68.6 degrees or about 2/3 right angle.

Some modern readers have been sceptical about this assumption. Alan Bowen thinks that the primary purpose of the model was to account for latitude variation. I have suggested that invisibility periods were an important consideration. However, it is possible that the only purpose of the models for Venus and Mercury was to account for elongation.


Lunar and Solar Period Locking

The sidereal orbital period of the moon around the earth is known accurately and is 27.321661 days. (sidereal means 'relative to an observer fixed in space' i.e. 'relative to the stars').

These two figures are remarkably close, and suggest there might be some kind of tuning relationship between them.

As pointed out by Janus in another thread, it is not easy to see why there should be a relationship between the sun's apparent rotational period relative to the Earth, and the time it takes the moon to orbit the earth relative to the fixed stars.

However, there is another lunar period which is very close to the moon's synodic orbital period, and that is the moon's nodical period. The length of the nodical period is 27.2122 days, which is also very close to the solar synodic period of 27.27 days approximately. The nodical period is the period between two crossings of the ecliptic in the same direction.

Here is a feasible method here for tuning to occur, as the sun's gravity tries to pull the orbital plane of the moon into the plane of the ecliptic. Solar asymmetries or tidal effects could possibly act over long periods to tune the moon's nodical period (and thus also its sidereal period) to the solar synodic period.

(Since the sun is a fluid body, it's rotation rate varies depending on latitude, and the 'average' rate may not be directly measurable. I am not sure exactly what method is used to determine the above figure of 27.27 days, but it would seem logical to me to define it as follows: The synodic period of rotation of an equivalent rigid body of the same mass, radius, mass distribution and angular momentum as the sun. Since this 'average' period is preumably difficult to determine and conceptualise, it may only have become known relatively recently in relation to other simple orbital periods, and the co-incidence between these two periods may not have been noticed before)

Since the sun's average synodic rotational period is clearly difficult to define and deduce, the small apparent variation between 27.21 and 27.27 may be due to the methods by which it is defined and derived. The effective period for the purpose of tuning the nodic period may in fact be 27.21 days.

The following web page has a thorough discussion of the various periods of the lunar orbit:

(This thread is a continuation of a sub-discussion that arose in the "Why doesn't the Moon spin? thread". I thought it deserved its own thread)


Man's Place in the Cosmos: Observational Astronomy

The most important Greek astronomical work, Ptolemy's Almagest , was already more than 700 years old when it was translated into Arabic, In Baghdad, during the early part of the ninth century. The same work also contained the results of a host of observations that were either conducted by Ptolemy himself, or were reported by him on the authority of more ancient Greek and Babylonian sources.

These two facts alone, and especially the passage of time, can easily explain why a small observational error, or a minute approximation either intentionally or unwittingly allowed by Ptolemy, would become many centuries later easily noticeable to ninth-century Baghdad astronomers. Those same astronomers worked in a society whose major factions were reluctant to accept a foreign science that they either found incomprehensible or that contradicted and threatened to replace the traditions that they knew very well. Thus, any mistake in the original Greek texts that could be noticed by a ninth-century observer would immediately threaten the validity of that text and could easily endanger other texts associated with it. It would also threaten the persons who were importing and adopting those texts.

Some of the errors were easy to notice, while others were subtler and required good scientific training to detect. In the first instance, prescribed mathematical operations in the original Greek texts could be easily double-checked and their results verified. One such mistake, dealing with the length of the synodic lunar month, appeared to have been incorporated in the Greek text, and was silently corrected by the famous Arabic translator, al-Hajjaj Ibn Matar (flourished circa 830).

Other equally important values could not be so easily corrected. For example, the measuring unit used in the Greek texts to calculate the size of the earth was systematically given in the usual Greek unit of stadion. There were two very famous measurements in the Greek legacy: that of Ptolemy who gave the earth's circumference as being 180,000 stadions, and that of Eratosthenes, some four centuries before him, who gave the circumference as being 252,000 stadions. So either there mist have been two types of stadion, or the measure of a stadion must have changed over time.

For a ninth-century Baghdad astronomer, the measurements in this particular unit were confusing, and the stadion unit itself became essentially meaningless. It had to be "translated" into local units for there to be any hope of making sense of this data, a matter that was not so simple. For how could one translate one system of units into another if one did not have a common reference measure for comparison? No such measure existed then, and the only recourse the Baghdad astronomers had was to measure the same physical object, in this case the length of one degree of the earth's circumference, in local units.

Such a project was indeed undertaken during the reign of the Abbasid caliph al-Ma'mun (813‒833). The sources speak of a team of astronomers and mathematicians who were dispatched to the flat desert stretch in present-day northern Syria. The team was supposed to split into two groups: one group to march north along a straight line and mark the ground when the height of the North Pole star increased by one degree, and the second group to march south, in the opposite direction, along the same line and mark the ground where the height of the Pole star decreased by one degree. Incidentally, everyone concerned knew that the height of the Pole star over a specific geographic locality was equal to the geographic latitude of that locality. The north and south distances were then measured in the local Arab miles of the time, and the results were averaged in order to increase their precision. The value that emerged from this measurement was equivalent to 107.28 kilometers for the length of one degree of the earth's meridian circle. The earth's circumference could then be calculated as the product of 360 degrees and 107.28 kilometers to yield a value of 38,621 kilometers, which is rather close to the modern accepted value for the earth's circumference.

Other values, such as the rate of precession, the inclination of the ecliptic, and the position of the solar apogee were subjected to similar procedures of verification. And in all instances, the traditional Greek values were found wanting. In the case of the precession of the fixed stars, that is the apparent dislocation of the fixed stars in respect to the point of the vernal equinox, the value that was determined by Ptolemy stipulated that the dislocation would be in the order of one degree every 100 years. The positions of all those stars were measured with respect to the fixed point of the vernal equinox along the ecliptic circle, which is the middle circle of the zodiacal belt that marks the apparent yearly path of the sun. One of the famous fixed stars, in the constellation of Leo, which was called Regulus, i.e., the royal star, or the heart of the lion, happens to be very close to the ecliptic path.

Measuring its position with respect to the vernal equinox was, therefore, relatively easy. According to Ptolemy's value for precession of one degree every 100 years, this star should have been dislocated by seven degrees during the ninth century, that is, after 700 years from the time when it was observed by Ptolemy. But observers in ninth-century Baghdad, whose colleagues were measuring the size of the earth, also measured the position of Regulus and found it to have been dislocated by some 11 degrees instead of seven. After repeating this measurement several times, they finally concluded that the Greek value of one degree every 100 years was in fact too slow, and a better value to be adopted was one degree about every 70 years, a value much closer to the modern one.

Similarly, the apparent yearly path of the earth around the sun gives rise to the various seasons that all the earth's inhabitants experience. The phenomenon of seasons is caused by the inclination of the earth's axis in relation to the plane described by the earth's path. The plane of this path is the same as the plane of the ecliptic, or the plane described by the sun in its yearly path, if one were to think of the earth as being fixed and the sun moving around it―as did most astronomers of the classical Greek tradition and Islamic astronomers until very recent times. According to the Greek tradition, the inclination of the earth's axis was determined by Ptolemy to be 23 degrees, 51 minutes, and 20 seconds. And because ninth-century astronomers were in the process of double-checking these Greek values, they also tried to verify this inclination, the measurement of which is a relatively easy matter. It could also be highly precise if one used very large measuring instruments. The ninth-century Baghdad astronomers found the inclination to be around 23.5 degrees, a value that is much closer to the modern one.

The difference between the Greek value and that determined in ninth-century Baghdad is close to 0.33 of a degree, which may not appear as much of a discrepancy. But when such small numbers were multiplied by the very large astronomical numbers that gave the term "astronomical" its frightening meaning, the results could become dramatically erroneous.

The subtler determination of the position of the solar apogee, or the point along the zodiacal belt where the earth seems to be at its farthest point from the sun, was a little more intricate. It produced both a value quite at variance from the one reported in the Greek tradition and a critique of the very method of observation used by Ptolemy. Ptolemy had already determined that the point at which the sun appeared to be at its farthest from the earth or, say, the earth at its farthest distance from the sun if the sun were fixed, was located towards the beginning of the constellation of Gemini, and was fixed exactly at 5.5 degrees in that zodiacal sign. Again, 700 years later on it was easy to observe that the solar apogee had indeed moved by some 11 degrees and that it was not fixed as Ptolemy had thought. The determination of the exact location of the apogee is important as a preliminary step for the determination of other astronomical values, and thus much effort was spent in perfecting its measurement. Several questions were raised about the reasons why Ptolemy got it wrong in the first place. And after much deliberation, it became clear that Ptolemy's method for this specific measurement depended on observing the sun at four critical points of its path: at the vernal and autumnal equinoxes and at the summer and winter solstices. The determination of the time of the equinoxes is relatively easy, for at those times the day will be equal to the night. But the determination of the time of the longest and shortest days of the year was not that easy. In fact it was very difficult to determine it with any high precision. The reason for the difficulty can be easily noticed even by lay observers who can surely attest that the sun will rise every day from a slightly different point along their local horizon and will set again at the opposite point in the west. From day to day, the rising sun will slowly move to the north until it reaches its northernmost point around June 21, the longest day of the year. At that time, the rising point will reverse its direction and start moving southward until it reaches the southernmost point around December 21, the shortest day. But even a less-observant lay person can also notice that around June 21 or December 21 the sun will rise and set for several days from the same points along the local horizon, and thus it becomes very difficult indeed to determine the exact day when the sun reverses its journey.

Ninth-century Baghdad astronomers noticed this flaw in the Ptolemaic observational technique. And in their search for higher precision, they decided to abandon that method altogether and to seek an alternative one. Deploying the same mathematics used by Ptolemy and only changing the observational strategy, they decided to observe the sun during the mid-seasons, that is, when the sun was at the 15th degree of Taurus, Leo, Scorpio, and Aquarius, instead of the beginnings of the seasons as was done by Ptolemy. Their argument was that at those midpoints, the motion of the rising point of the sun along the eastern horizon and, of course, the point it reached along the meridian at high noon were much easier to observe as those positions changed noticeably from day to day. The new method they adopted was then called the fusul (seasons) method, simply because it depended on the midpoints of the seasons.

With this better observational strategy and better and larger instruments, new values for the solar apogee were determined, and the apogee was found to be moving rather than fixed, and a new solar eccentricity and solar equation were also determined as byproducts. Those values are also very close to the modem values that are still used today, while the older Greek values are now completely forgotten.For a group of astronomers working some 700 years after the Ptolemaic observations, and finding such dramatic variations between their results and those they read about in the books that were then being translated from Greek into Arabic, the only conclusion they could draw was that the Greek astronomical tradition was deeply flawed. And if the observable results that could be double-checked relatively easily were found to be so different, then what else was wrong with the astronomical Greek tradition that they were reading at the time? This and other similar questions encouraged astronomers working in the Islamic tradition to probe the imported Greek tradition more thoroughly and of course to find increasing contradictions in its very foundations. That was the point when serious research began to be conducted in order to create an alternative astronomy, and it was that very search that culminated in the total reversal of astronomical thinking during the European Renaissance in the 16th century.


Astronomy

Astronomy is the study that deals with the physics, chemistry, mathematics and the evolution of celestial objects. The objects studied are moons, planets, stars, nebular and galaxies. Astronomers also look at the phenomenon that takes place outside of the Earth’s atmosphere such as supernovae explosions, gamma ray bursts and cosmos background radiation.

Cosmology, although often related, is different than astronomy. Cosmology studies the universe as a whole. Cosmology will be discussed in a later section.

Astronomy is one of the oldest sciences. There have been astronomical artifacts found in early civilizations such as Babylonians, Greeks, Chinese, Indians, Iranians and Maya. It is evident that they performed methodical observations of the night sky. The invention of the telescope however revolutionized modern science. It allowed astronomers to be able to see further into the universe. Before telescopes, the study of the sky was conducted from tall vantage points such as tall buildings and mountains.


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