How accurate is the “Equation of time” (mean time to actual solar time)? And how much can it vary from the average?

How accurate is the “Equation of time” (mean time to actual solar time)? And how much can it vary from the average?

At Wikipedia, they give equal values (9.87 min) for all four extremes - both troughs and both crests - caused by the obliquity of the ecliptic as seen in the graph below, where the purple dashed line is what is caused by the obliquity of the ecliptic. But the duration of the four seasons are not equal, as you can see here. So what effect does it have on the equation of time?

Also, the time from a perihelion to the next aphelion is not always the same as the time from that aphelion to the next perihelion, as seen in this almanac. As a consequence, the greatest delay of noon caused by the eccentricity of the orbit shouldn't be equal to its greatest advance. So how big can the difference be?

Also, the dates of the perihelion and aphelion, as well as the actual sun-earth distance at these events aren't the same each year, as seen in the above reference. So the actual latest and earliest noon varies from the given dates. My question is, how much can they vary?

The early Roman calendar

This originated as a local calendar in the city of Rome, supposedly drawn up by Romulus some seven or eight centuries before the Christian era, or Common Era. The year began in March and consisted of 10 months, six of 30 days and four of 31 days, making a total of 304 days: it ended in December, to be followed by what seems to have been an uncounted winter gap. Numa Pompilius, according to tradition the second king of Rome (715?–673? bce ), is supposed to have added two extra months, January and February, to fill the gap and to have increased the total number of days by 50, making 354. To obtain sufficient days for his new months, he is then said to have deducted one day from the 30-day months, thus having 56 days to divide between January and February. But since the Romans had, or had developed, a superstitious dread of even numbers, January was given an extra day February was still left with an even number of days, but as that month was given over to the infernal gods, this was considered appropriate. The system allowed the year of 12 months to have 355 days, an uneven number.

The so-called Roman republican calendar was supposedly introduced by the Etruscan Lucius Tarquinius Priscus (616–579 bce ), according to tradition the fifth king of Rome. He wanted the year to begin in January since it contained the festival of the god of gates (later the god of all beginnings), but expulsion of the Etruscan dynasty in 510 bce led to this particular reform’s being dropped. The Roman republican calendar still contained only 355 days, with February having 28 days March, May, July, and October 31 days each January, April, June, August, September, November, and December 29 days. It was basically a lunar calendar and short by 10 1 /4 days of a 365 1 /4 -day tropical year. In order to prevent it from becoming too far out of step with the seasons, an intercalary month, Intercalans, or Mercedonius (from merces, meaning wages, since workers were paid at this time of year), was inserted between February 23 and 24. It consisted of 27 or 28 days, added once every two years, and in historical times at least, the remaining five days of February were omitted. The intercalation was therefore equivalent to an additional 22 or 23 days, so that in a four-year period the total days in the calendar amounted to (4 × 355) + 22 + 23, or 1,465: this gave an average of 366.25 days per year.

Intercalation was the duty of the Pontifices, a board that assisted the chief magistrate in his sacrificial functions. The reasons for their decisions were kept secret, but, because of some negligence and a measure of ignorance and corruption, the intercalations were irregular, and seasonal chaos resulted. In spite of this and the fact that it was over a day too long compared with the tropical year, much of the modified Roman republican calendar was carried over into the Gregorian calendar now in general use.

What Are Peak Sun Hours?

Peak sun hours differ from hours of daylight the peak sun hour actually describes the intensity of sunlight in a specific area, defined as an hour of sunlight that reaches an average of 1,000 watts of power per square meter (around 10.5 feet).

Although your panels may get an average of 7 hours of daylight a day, the average peak sun hours are generally around 4 or 5 . Solar radiation peaks at solar noon, when the sun reaches the highest point in the sky.

The number of peak sun hours you get per day increases the closer you are to the equator and typically during the summer months.

How accurate is the &ldquoEquation of time&rdquo (mean time to actual solar time)? And how much can it vary from the average? - Astronomy

The accurate measurement of time by establishing accurate time standards poses difficult technological problems. In prehistory, humans recognized the alternation of day and night, the phases of the moon, and the succession of the seasons from these cycles, they developed the day, month, and year as the corresponding units of time. With the development of primitive clocks clock,
instrument for measuring and indicating time. Predecessors of the clock were the sundial, the hourglass, and the clepsydra. See also watch. The Evolution of Mechanical Clocks
. Click the link for more information. and systematic astronomical observations, the day was divided into hours, minutes, and seconds.

Any measurement of time is ultimately based on counting the cycles of some regularly recurring phenomenon and accurately measuring fractions of that cycle. The earth rotates on its axis at a very nearly constant rate, and the angular positions of celestial bodies can be determined with great precision. Therefore, astronomical observations provide an almost ideal method of measuring time. The true period of rotation of the earth, that with respect to the fixed stars, defines the sidereal day, which is the basis of sidereal time sidereal time
(ST), time measured relative to the fixed stars thus, the sidereal day is the period during which the earth completes one rotation on its axis so that some chosen star appears twice on the observer's celestial meridian.
. Click the link for more information. . All sidereal days are equal. The period of rotation of the earth with respect to the sun (i.e., the interval between successive high noons) is the solar day, which is the basis for solar time solar time,
time defined by the position of the sun. The solar day is the time it takes for the sun to return to the same meridian in the sky. Local solar time is measured by a sundial.
. Click the link for more information. . Because of the earth's motion in its orbit around the sun, the sun appears to move eastward against the fixed stars, and the earth must make slightly more than one complete rotation to bring the sun back to the observer's meridian. (The meridian is the great circle on the celestial sphere running through the north celestial pole and the observer's zenith the passage of the sun across the meridian marks high noon.) But the earth's orbital motion is not uniform, and the plane of the orbit is inclined to the celestial equator by 23 1-2°. Hence the eastward motion of the sun against the stars is not uniform and the length of the true solar day varies seasonally, but on the average is four minutes longer than the sidereal day. True solar time, as measured by a sundial, does not move at a constant rate. Therefore the mean solar day, with a length equal to the annual average of the actual solar day, was introduced as the basis of mean solar time.

Mean solar time does move at a constant rate and is the basis for the civil time kept by clocks. Actually, the earth's rotation is being slightly braked by tidal and other effects so that even mean solar time is not strictly uniform. The law of gravitation allows prediction of the moon's position in its orbit at a given time inversely, the exact position of the moon provides a kind of clock that is not running down. Time calculated from the moon's position is called ephemeris time ephemeris time
(ET), astronomical time defined by the orbital motions of the earth, moon, and planets. The earth does not rotate with uniform speed, so the solar day is an imprecise unit of time.
. Click the link for more information. and moves at a truly uniform rate. The accumulated difference between mean solar and ephemeris time since 1900 amounts to more than half a minute. However, the ultimate standard for time is provided by the natural frequencies of vibration of atoms and molecules. Atomic clocks atomic clock,
electric or electronic timekeeping device that is controlled by atomic or molecular oscillations. A timekeeping device must contain or be connected to some apparatus that oscillates at a uniform rate to control the rate of movement of its hands or the rate of
. Click the link for more information. , based on masers maser
, device for creation, amplification, and transmission of an intense, highly focused beam of high-frequency radio waves. The name maser is an acronym for microwave amplification by stimulated emission of r
. Click the link for more information. and lasers laser
[acronym for light amplification by stimulated emission of radiation], device for the creation, amplification, and transmission of a narrow, intense beam of coherent light. The laser is sometimes referred to as an optical maser.
. Click the link for more information. , lose only about three milliseconds over a thousand years. See standard time standard time,
civil time used within a given time zone. The earth is divided into 24 time zones, each of which is about 15° of longitude wide and corresponds to one hour of time. Within a zone all civil clocks are set to the same local solar time.
. Click the link for more information. universal time universal time
(UT), the international time standard common to every place in the world, it nominally reflects the mean solar time along the earth's prime meridian (renumbered to equate to civil time).
. Click the link for more information. .

Psychology of Time

As a practical matter, clocks clock,
instrument for measuring and indicating time. Predecessors of the clock were the sundial, the hourglass, and the clepsydra. See also watch. The Evolution of Mechanical Clocks
. Click the link for more information. and calendars calendar
[Lat., from Kalends], system of reckoning time for the practical purpose of recording past events and calculating dates for future plans. The calendar is based on noting ordinary and easily observable natural events, the cycle of the sun through the seasons with equinox
. Click the link for more information. regulate everyday life. Yet at the most primitive level, human awareness of time is simply the ability to distinguish which of any two events is earlier and which later, combined with a consciousness of an instantaneous present that is continually being transformed into a remembered past as it is replaced with an anticipated future. From these common human experiences evolved the view that time has an independent existence apart from physical reality.

Philosophy and Science of Time

The belief in time as an absolute has a long tradition in philosophy and science. It still underlies the common sense notion of time. Isaac Newton, in formulating the basic concepts of classical physics, compared absolute time to a stream flowing at a uniform rate of its own accord. In everyday life, we likewise regard each instant of time as somehow possessing a unique existence apart from any particular observer or system of timekeeping. Inherent in the concept of absolute time is the assumption that the simultaneity of two given events is also absolute. In other words, if two events are simultaneous for one observer, they are simultaneous for all observers.

Relativistic Time

Developments of modern physics have forced a modification of the concept of simultaneity. As Albert Einstein demonstrated in his theory of relativity relativity,
physical theory, introduced by Albert Einstein, that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference.
. Click the link for more information. , when two observers are in relative motion, they will necessarily arrange events in a somewhat different time sequence. As a result, events that are simultaneous in one observer's time sequence will not be simultaneous in some other observer's sequence. In the theory of relativity, the intuitive notion of time as an independent entity is replaced by the concept that space and time are intertwined and inseparable aspects of a four-dimensional universe, which is given the name space-time space-time,
central concept in the theory of relativity that replaces the earlier concepts of space and time as separate absolute entities. In relativity one cannot uniquely distinguish space and time as elements in descriptions of events.
. Click the link for more information. .

One of the most curious aspects of the relativistic theory is that all events appear to take place at a slower rate in a moving system when judged by a viewer in a stationary system. For example, a moving clock will appear to run slower than a stationary clock of identical construction. This effect, known as time dilation, depends on the relative velocities of the two clocks and is significant only for speeds comparable to the speed of light. Time dilation has been confirmed by observing the decay of rapidly moving subatomic particles that spontaneously decay into other particles. Stated naively, particles in motion decay more slowly than stationary particles.

Time Reversal Invariance

In addition to relative time, another aspect of time relevant to physics is how one can distinguish the forward direction in time. This problem is apart from one's purely subjective awareness of time moving from past into future. According to classical physics, if all particles in a simple system are instantaneously reversed in their velocities, the system will proceed to retrace its entire past history. This property of the laws of classical physics is called time reversal invariance (see symmetry symmetry,
generally speaking, a balance or correspondence between various parts of an object the term symmetry is used both in the arts and in the sciences. In art and design, it is often used in a somewhat loose sense, to mean a kind of balance in which the
. Click the link for more information. ) it means that when all microscopic motions of individual particles are precisely defined, there is no fundamental distinction between forward and backward in time. If the motions of very large collections of particles are treated statistically as in thermodynamics thermodynamics,
branch of science concerned with the nature of heat and its conversion to mechanical, electric, and chemical energy. Historically, it grew out of efforts to construct more efficient heat engines&mdashdevices for extracting useful work from expanding hot gases.
. Click the link for more information. , then the forward direction of time is distinguished by the increase of entropy entropy
, quantity specifying the amount of disorder or randomness in a system bearing energy or information. Originally defined in thermodynamics in terms of heat and temperature, entropy indicates the degree to which a given quantity of thermal energy is available for doing
. Click the link for more information. , or disorder, in the system. However, recent discoveries in particle physics have shown that time reversal invariance is not valid even on the microscopic scale for certain phenomena governed by the weak force of nuclear physics.

Biological Time

In the life sciences, evidence has been found that many living organisms incorporate biological clocks that govern the rhythms of their behavior (see rhythm, biological rhythm, biological,
or biorhythm,
cyclic pattern of physiological changes or changes in activity in living organisms, most often synchronized with daily, monthly, or annual cyclical changes in the environment.
. Click the link for more information. ). Animals and even plants often exhibit a circadian (approximately daily) cycle in, for instance, temperature and metabolic rate that may have a genetic basis. Efforts to localize time sense in specialized areas within the brain have been largely unsuccessful. In humans, the time sense may be connected to certain electrical rhythms in the brain, the most prominent of which is known as the alpha rhythm at about ten cycles per second.


See S. V. Toulmin and J. Goodfield, Discovery of Time (1965) S. Hawking, A Brief History of Time: From the Big Bang to Black Holes (1988).

in music: see tempo tempo
[Ital.,=time], in music, the speed of a composition. The composer's intentions as to tempo are conventionally indicated by a set of Italian terms, of which the principal ones are presto (very fast), vivace (lively), allegro (fast), moderato
. Click the link for more information. meter meter,
abbr. m, fundamental unit of length in the metric system. The meter was originally defined as 1/10,000,000 of the distance between the equator and either pole however, the original survey was inaccurate and the meter was later defined simply as the distance between two
. Click the link for more information. rhythm rhythm,
the basic temporal element of music, concerned with duration and with stresses or accents whether irregular or organized into regular patternings. The formulation in the late 12th cent.
. Click the link for more information. syncopation syncopation
[New Gr.,=cut off ], in music, the accentuation of a beat that normally would be weak according to the rhythmic division of the measure. Although the normally strong beat is not usually effaced by the process, there are occasions (e.g.
. Click the link for more information. metronome metronome
, in music, originally pyramid-shaped clockwork mechanism to indicate the exact tempo in which a work is to be performed. It has a double pendulum whose pace can be altered by sliding the upper weight up or down.
. Click the link for more information. and musical notation musical notation,
symbols used to make a written record of musical sounds.

Two different systems of letters were used to write down the instrumental and the vocal music of ancient Greece. In his five textbooks on music theory Boethius (c.A.D. 470–A.D.
. Click the link for more information. .

The dimension of the physical universe which orders the sequence of events at a given place also, a designated instant in this sequence, such as the time of day, technically known as an epoch, or sometimes as an instant.


Time measurement consists of count­ing the repetitions of any recurring phenom૞non and possibly subdividing the interval between repetitions. Two aspects to be considered in the measurement of time are frequency, or the rate at which the recurring phenomena occur, and epoch, or the designation to be applied to each instant.

Time units are the intervals between successive recurrences of phenomena, such as the period of rotation of the Earth or a specified number of periods of radiation derived from an atomic energy-level transition. Other units are arbitrary multiples and subdivisions of these intervals, such as the hour being 1/24 of a day, and the minute being 1/60 of an hour. See Time-interval measurement

Time bases

Several phenomena are used as bases with which to determine time. The phenomenon traditionally used has been the rotation of the Earth, where the counting is by days. Days are measured by observing the meridian passages of stars and are subdivided with the aid of precision clocks. The day, however, is subject to variations in duration. Thus, when a more uniform time scale is required, other bases for time must be used.

The angle measured along the celestial equator between the observer's local meridian and the vernal equinox, known as the hour angle of the vernal equinox, is the measure of sidereal time. It is reckoned from 0 to 24 hours, each hour being subdivided into 60 sidereal minutes and the minutes into 60 sidereal seconds. Sidereal clocks are used for convenience in most astronomical observatories because a star or other object outside the solar system comes to the same place in the sky at virtually the same sidereal time.

The hour angle of the Sun is the apparent solar time. The only true indicator of local apparent solar time is a sundial. Mean solar time has been devised to eliminate the irregularities in apparent solar time that arise from the obliquity of the ecliptic and the varying speed of the Earth in its orbit around the Sun. It is the hour angle of a fictitious point moving uniformly along the celestial equator at the same rate as the average rate of the Sun along the ecliptic. Both sidereal and solar time depend on the rotation of the Earth for their time base.

The mean solar time determined for the meridian of 0° longitude from the rotation of the Earth by using astronomical observations is referred to as UT1. Observations are made at a number of observatories around the world. The International Earth Rotation Service (IERS) receives these data and maintains a UT1 time scale.

Because the Earth has a nonuniform rate of rotation and since a uniform time scale is required for many timing applications, a different definition of a second was adopted in 1967. The international agreement calls for the second to be defined as 9,192,631,770 periods of the radiation derived from an energy-level transition in the cesium atom. This second is referred to as the international or SI (International System) second and is independent of astronomical observations. International Atomic Time (TAI) is maintained by the International Bureau of Weights and Measures (BIPM) from data contributed by time-keeping laboratories around the world.

Coordinated Universal Time (UTC) uses the SI second as its time base. However, the designation of the epoch may be changed at certain times so that UTC does not differ from UT1 by more than 0.9 s. UTC forms the basis for civil time in most countries and may sometimes be referred to as Greenwich mean time. The adjustments to UTC to bring this time scale into closer accord with UT1 consist of the insertion or deletion of integral seconds. These “leap seconds” may be applied at 23 h 59 m 59 s of June 30 or December 31 of each year according to decisions made by the IERS. UTC differs from TAI by an integral number of atomic seconds.

Civil and standard times

Because rotational time scales are defined as hour angles, at any instant they vary from place to place on the Earth. Persons traveling westward around the Earth must advance their time 1 day, and those traveling eastward must retard their time 1 day in order to be in agreement with their neighbors when they return home. The International Date Line is the name given to a line where the change of date is made. It follows approximately the 180th meridian but avoids inhabited land. To avoid the inconvenience of the continuous change of mean solar time with longitude, zone time or civil time is generally used. The Earth is divided into 24 time zones, each approximately 15° wide and centered on standard longitudes of 0°, 15°, 30°, and so on. Within each of these zones the time kept is the mean solar time of the standard meridian.

Many countries, including the United States, advance their time 1 hour, particularly during the summer months, into �ylight saving time.”

  1. the repeated day-to-day durພ - or ‘reversible time’ – of everyday social life
  2. the longue durພ involved in the persistence, as against the rise and fall, of social institutions and societies
  3. the ‘life span’ of the individual -‘irreversible time’.

As well as this, in social life and in sociological and historical accounts an almost infinite number of more specific ‘periodizations’ can also be noticed, e.g. ‘Victorian times’, ‘the Age of Reason’. See also CLOCK-TIME, TIME – SPACE DISTANCIATION.

Since time always exists as a fourth coordinate of time-space in specifying any event, it must obviously be an important component in any sociological account. A number of sociologists recently, however, have suggested that time has been relatively neglected in sociology, in that sociology has often been concerned with static structural models and has tended to neglect the great variety of ways in which social life is both temporally structured and, as the result of social processes occurring in time, socially transformed – see MANN (1986) and GIDDENS (1984). A resurgence of interest in time has been a feature of recent sociology and is also evident in other disciplines (e.g. see TIME-GEOGRAPHY), from which sociology has also drawn.

a basic form (together with space) of the existence of matter it consists of the regular coordination of phenomena that are occurring one after another. It exists objectively and is inseparably associated with moving matter.

Measurement. Various branches of science and technology deal with the problem of measuring time, independent of the means and system by which it is recorded. Chronometers&mdash technical means for measuring time and reproducing its units and subdivisions (clocks and other instruments)&mdashare. developed in chronometry. With the aid of special observations of celestial bodies, astronomy makes it possible to monitor the performance of time-recording devices and to determine corrections in time scales.

Even in earliest times, measurements of large and small time intervals were based on astronomical phenomena dependent on the motions of celestial bodies, especially the earth and moon. The year, which was defined by the period of the earth&rsquos orbit around the sun, began to be used as the unit for measuring large time intervals. The cycle of changes in nature is associated with this unit. The cycle of changing phases of the moon (the synodic month) began to be used as a smaller unit of time and, with slight changes, became what is now our month. The day is based on the cycle of light and dark periods and is determined by the earth&rsquos rotation. In order to record smaller intervals, the day was divided into hours originally the daylight period was divided into 12 day-time hours, and the period of darkness into 12 nighttime hours, which differed in length and whose duration throughout the year was not constant. Later, division of the day into 24 equal hours was introduced. The development of human economic activity led to greater demands on time measurement. Instruments for measuring time&mdashclocks&mdashwere perfected, which permitted the introduction of more and more accurate systems for recording time for practical and scientific purposes. In modern clocks, the system of recording time is based on various artificial periodic processes: the oscillation of a balance wheel (marine chronometers and household clocks), a pendulum (astronomical clocks), or a quartz plate (quartz clocks). In the most accurate quartz clocks, the stability of the oscillations is governed by quantum generators, whose operation is based on periodic processes occurring in atoms and molecules (atomic clocks).

The rotation of the earth about its axis relative to the stars determines sidereal time. Since the stars have motion of their own, which has been insufficiently studied, sidereal time is measured relative to the vernal equinox, whose motion among the stars is well known. The moment of its upper culmination is taken as the beginning of the sidereal day. The sidereal day is subdivided into sidereal hours, minutes, and seconds. Sidereal time is determined directly from astronomical observations and serves to coordinate the readings of clocks and chronometers with the astronomical system of recording time. Knowledge of sidereal time is essential in various astronomical observations, as well as in geodetic measurements, navigation, and other work involving observations of celestial bodies. It is impractical in everyday life, since it does not coincide with the change from day to night. For this reason, solar time is used in everyday life.

True solar time is determined by the apparent daily motion of the sun, whose upper and lower culminations are accordingly called true noon and true midnight. The interval of time between two consecutive like culminations of the center of the sun is called a true solar day. However, because of the uneven motion of the earth in its orbit and, consequently, the apparent annual motion of the sun along the ecliptic, as well as the fact that the earth&rsquos axis is not perpendicular to the plane of its orbit, the true solar day is not constant in its duration&mdashthat is, the system for recording true solar time is irregular. The system of solar time that is uniform throughout the year is called mean solar time and is based on the daily motion of the so-called mean sun, an imaginary point that moves evenly along the equator with a speed such that in its annual motion it always crosses the vernal equinox simultaneously with the true sun. The moments of upper and lower culmination of the mean sun are correspondingly called mean noon and mean midnight. The time interval between two consecutive like culminations of the mean sun is called a mean solar day, and it begins from the mean sun&rsquos lower culmination. The mean solar day is divided into mean solar hours, minutes, and seconds.

The discrepancy between mean and true solar time is called the time equation, and this varies during the year between -14 min, 22 sec, and 16 min, 24 sec. Mean solar time is checked against sidereal time by the following relationship, based on numerous observations:

(1) 365.2422 mean solar days = 366.2422 sidereal days, from which it follows that
(2) 24 hr of sidereal time = 23 hr, 56 min, 4.091 sec of mean solar time, and
(3) 24 hr of mean solar time = 24 hr, 3 min, 56.666 sec of sidereal time.

Clocks operating on mean solar time and on sidereal time are used to keep time determined by astronomical observations.

At different meridians of the earth, the moments of culmi-nation of both the vernal equinox and the true and mean sun do not occur at the same physical moment. Therefore, the time at different meridians is also different: a 15° eastward change in longitude corresponds to an increase of one hour in sidereal time, as well as in true and mean solar time. The time determined for a particular longitude is called local time (sometimes the zone time used at various points on the earth is erroneously called local time). Local mean solar time at the zero or Greenwich meridian reckoned from midnight is called universal or world time (Greenwich time). Universal time, which is the same worldwide, is extensively used in astronomy.

Local time, which is different at points with different geo-graphic longitude, causes inconvenience in its practical use in intercity and international communications. To eliminate these inconveniences, a system of zone time was adopted at the end of the 19th century in many countries of the world, whereby the entire surface of the earth was divided into 24 time zones, each 15° of longitude wide, extending along the meridians. Zone time was introduced in the USSR on July 1, 1919. To make practical use of daylight hours, clocks in some countries are advanced one hour in relation to zone time in summer. In the USSR clocks were moved ahead one hour in 1930 (so-called daylight saving time). Daylight saving time in the second time zone of the USSR is called Moscow time and is three hours ahead of universal time.

Exacting research has shown that the system for astronomical recording of time based on observations of the culminations of celestial bodies is not uniform (universal time in this system is designated UTO) this is due first to the migration of the earth&rsquos poles, which alters the longitude of observation sites, and second to unevenness in the rotation of the earth, which was discovered by using highly stable quartz and atomic clocks. The introduction of corrections in UTO to take into account the shifting of the poles results in UT1 universal time, and further corrections to account for mean seasonal changes in the period of the earth&rsquos rotation result in UT2 universal time. Even after the above corrections have been made, however, the uniform systems for recording time based on the period of the earth&rsquos rotation are not adequate for certain branches of modern science and technology.

A uniform system for recording time&mdashephemeris time&mdashis being introduced as an independent argument in the laws of celestial mechanics and is checked by observations of the rotation of the moon about the earth. Astronomical year-books are compiled on the basis of ephemeris time. This system is defined in terms of the difference between ephemeris time and mean solar time on the basis of the empirical relationship

&Deltat sec = + 24.349 + 72.318T + 29.950T 2 + 1.821B

where T is calculated in Julian centuries of 36,525 mean solar days from the date Jan. 0, 1900, at 12 o&rsquoclock universal time, and B is the deviation of the longitude of the moon computed by Braun&rsquos theory from the longitude observed at a given moment. Because of irregularities in the earth&rsquos rotation, the magnitude of a mean solar day has increased over a period of 100 years by 1.640 msec it fluctuates because of the existence of a factor dependent on B (over the past 120 years it has reached -4.8 msec in 1870 and 1.9 msec in 1911). Therefore the definition of a second in physical systems of units has now begun to be based not on the period of the earth&rsquos rotation but on the period of its orbit about the sun, which is called the tropical year and is equal to the time interval between two consecutive passages of the sun through the vernal equinox. This interval is slowly changing over the course of time and equals 365.24219879 -0.00000614(7 - 1900) mean solar days. The General Conference on Weights and Measures (Paris, 1954) gave the following definition of a second of time in the centimeter-gram-second system: &ldquoA second is 1/31,556,925.9747 of a tropical year for the moment Jan. 0, 1900, at 12 o&rsquoclock ephemeris time.&rdquo Ephemeris time defined by this second for recording large time intervals is expressed in Julian centuries of 36,525 ephemeris days from the moment Jan. 0, 1900, at 12 o&rsquoclock ephemeris time.

The development of electronics in the 1960&rsquos made it possible to obtain a system for recording time that is new in principle and independent of astronomical observations. It is based on the use of high-accuracy quartz clocks controlled by quantum generators (atomic clocks). This system of calculating time has been given the name atomic time and is designated TA1. An atomic second serves as a standard unit, and its magnitude is determined by the resonance frequency of one of the energy transitions in an atom of cesium 133.

Radio signals for exact time are broadcast by time services by means of atomic clocks in a special system for calculating TA atomic time that is coordinated with astronomical systems of timekeeping: the duration of a second of TA time is defined annually from astronomical observations. Thus, the TA time system provides a connection between universal time obtained by astronomical observations and TA1 atomic time.

All systems for calculating time are regularly compared with each other so that a shift can be made for any moment from one system to another. The results of the comparisons are published in the Bulletins of the International Time Bureau in Paris, and in the USSR also in the bulletin Etalonnoe vremia (Standard Time), published by the All-Union Scientific Research Institute of Physical Technology and Radio Measurement.

How accurate is the &ldquoEquation of time&rdquo (mean time to actual solar time)? And how much can it vary from the average? - Astronomy

Unlike Earth, the Moon is a barren, lifeless world with no liquid water and barely an atmosphere! (1.6.x) (1.4.1)

Because the Moon is nearer than any other major celestial body, it can produce dramatic "shadow events" like this! (1.6.x) (1.4.1)

The Moon's surface area is a bit less than the area of Asia, Earth's largest continent, and a bit greater than the area of Africa, Earth's second largest continent!

Eclipses occur whenever the Moon or Earth moves into or through the other's shadow. This does not happen every month, as the lunar orbit is inclined to Earth's orbit. So Earth, the Sun and the Moon produce eclipses only about every 6 months. Calendar

During Solar Eclipses the Moon moves "directly" be- tween Earth and the Sun, so the lunar shadow extends down onto Earth's surface. Solar Eclipses can only:
happen at New Moon,
last a very short time,
be seen from small areas.

WARNING! It is never safe to look directly at a Solar Eclipse with the naked eye! And looking at one, for even an instant, through a telescope or binoculars with- out adequate safeguards can cause permanent blindness! NEVER DO IT! To learn how to safely "observe" a Solar Eclipse, consult your local planetarium or observatory.

During Lunar Eclipses Earth moves "directly" between the Sun and the Moon, the Moon moving either partially or en- tirely into Earth's shadow. Lunar Eclipses:
happen at Full Moon,
can last for hours,
can be seen from over
half of our planet.

How a Solar Eclipse Looks from Space:

How a Lunar Eclipse Looks:
from the Moon


The links below open photos taken by Apollo astronauts in the 1960s and '70s, showing the various types of terrain that were encountered from landing site to landing site. The terrain chosen for suc- cessive missions became increasingly more varied, as well as more demanding.

Apollo 14 Frau Maro high-
lands, boulders #2 #3


These maps and pages show many details, including the routes taken by the Apollo astronauts as they explored the surface of the Moon. The Lunar Rovers were used from Apollo 15 onward and vastly extended the distances the astronauts could travel. So the scales of the maps vary.

Compare similar views of the traverse maps with the cool History of Apollo Landings in 3-D. Zoom, tilt and rotate the views, etc. Awesome!

And here's an informative NASA graphic comparing the Distances Traveled by Moon and Mars Rovers.

Here's a rewarding activity. First download and print out the NASA/JPL Moon Journal Worksheet . Then take a pencil and your worksheet out with you on succeeding nights and map the Moon: its phases, its surface features. Then, when the Moon is nearly Full, on the back of your worksheet sketch how it appears in a larger scale. Do it again a month later and compare your drawings. Were you able to draw a pretty good likeness of the Moon's dark areas, the maria (seas)?

Remember: it was only with the naked eye that any sky object could be observed un- til the invention of the tele- scope in the early 1600's!


Now, try mapping the Moon as you did above, this time with a pair of binoculars. Even a cheap pair will reveal much more detail. Compare your new maps with those you made when you mapped the Moon by eye alone.

Remember: until the advent of photography astronomers had to rely on the maps they drew by hand! Just like the maps you sketched above! So you're in good company.

Here's an exercise that's fun to perform with friends and other sky enthusiasts. For a few evenings each week, for two or three weeks, observe the Moon and compare its phase to the ones predicted here or on other websites.

In fact, updated for 2021, you can Make a Moon Phases Calendar and Calculator to help you! It's awesome!


Just to the right in the center column of this page, you'll see a list of the 8 kinds of Moon phases. Hover over them to find when the Moon should rise and set for each phase. Then, from the Moon Phase Calendar that you made above, find when the Moon will exhibit each of these phases in the coming month. On the day of each, confirm that the Moon does indeed rise and set when it should for each phase.


CANON has a terrific website that offers free downloads of paper models, including this cool 3-D model of the Moon. The labeled globe will quickly acquaint you with the Moon's most prominent features and many great Moon facts!


Ask your parents or a teacher to help you find a 1" diameter button (blue if possible), a #2 pencil with an eraser they'll permit you to break off, a few pieces of transparent tape, and a yardstick they'll permit you to write on.

Making your model is simple. 1.) Tape the button so its cen- ter overlaps the left edge of the yardstick. 2.) Tape the eraser so its center is 30 1/8" from the left edge of the yard- stick, and label it "Average Moon Distance". 3.) Label the button "Earth". 4.) Now, 27 7/8" inches from the but- ton's center, draw a vertical line and label it "Minimum Perigee". 5.) And to finish,
31 7/8" from the button's cen- ter, draw a vertical line and label it "Maximum Apogee".

You now have a surprisingly accurate scale model of the Earth-Moon System! More- over, you can easily take it anywhere! If permitted, you might even want to paint the yardstick black and add con- tinents to Earth and maria to the Moon!



NASA's new spacecraft will take us back to the Moon and beyond: 3-D paper model of Orion. Be the first in your neighborhood to have this model of the future!


As you go about your obser- vations, it will be easy for you to verify that the Moon rises about 50 minutes later each day. Of course, this is an average. The actual time depends on your latitude and on the Moon's very irregular orbit.


Even the ancients knew that Earth's tides were influenced by the Moon. If you live near the coastline of an ocean or other large body of water, make observations of your own. Record how the water level differs when the Moon is rising, setting, high in the sky or hidden by Earth. You can also check it at different times of the year against the graph to the right and to this Perigee and Apogee List.


Here's a cool group activity that you can suggest to your science teachers. NASA and JPL guide you through the fine points of Measuring a Supermoon!


Here's another group activity that you can suggest to your science teachers. NASA and JPL give you the recipe for making miniature Moon craters in the classroom! Great educational fun!


Use the Earth-Moon Distance diagram 2/3 of the way up the page for this. Have a conver- sation with a friend, as if he or she is on the Moon! As in- dicated to the diagram's left, click to send photons to the Moon and back for the time delay between exchanges.

For your Earth-Moon conver- sation to be accurate, you must wait for each photon to depart Earth "and" return from the Moon before you each answer one another! Of course, counting "one-one thousand, two-two thousand, three three-thousand" in be- tween your exchanges with your friend works too.

For even more fun, try it with you and your friend facing away from each other or with a partition between you. Do you think you could get used to phoning a friend on the Moon like this?

The Apollo astronauts and Mission Control had to deal with precisely this time delay whenever crews were on the Moon or in orbit around it!

The following will help you enjoy this page's 1.6.x and 1.4.1 links that run events directly in CELESTIA. If you're new to the program, these tips will also help you learn to use it.

Are you unfamiliar with our 1.6.x and 1.4.1 links? For an explanation click here.

  • After you run the links at top that display planetary orbits, Right Drag with your mouse a to get a good sense of their 3-dimensional aspects.
  • If CELESTIA's clock (i.e. the program's date and time) is not visible at the top-right of its window, press the V key until you see it. This will also turn on information text in other corners to help you keep track of several aspects of the event you're viewing. Keeping an eye on CELESTIA's clock at the top-right will help you appreciate how much time is passing in each view.
  • Pressing the "un-shifted" L key and K key respectively will speed up and slow down CELESTIA's flow of time by a factor of 10 in version 1.6.x and 1.4.1.
  • Pressing Shift+L and Shift+K respectively will speed up and slow down CELESTIA's flow of time by a factor of 2 in version 1.6.x only.
  • Pressing the J key (either shifted or "un-shifted") will reverse CELESTIA's flow of time in version 1.6.x and 1.4.1.

You'll find more information about many of CELESTIA's controls on our Learning Center page.

Physical Properties:
Equatorial Size: Compare Compare in 3-D
Radius: 1,738.1 km
Diameter: 3,476.2 km
Diameter (Earth = 1): 0.2725
View How Big Is Our Moon? video.
Compare to Other Moons


Rotational Flattening: 0.0012
Mass (Earth = 1): 0.0123
Volume (Earth = 1): 0.0203
Mean Density (Water = 1): 3.34
Mean Density (Earth = 1): 0.607
Surface Gravity (Earth = 1): 0.165
Surface Temperatures: average -23°C (-9°F)
Inclination of Axis to Orbit: 6.68°
Rotation and Revolution Period: (tidally "locked", so
the same side of Moon always faces Earth)
Synodic (in Earth days): 29.53 (cycle of Phases)
Sidereal (in Earth days): 27.3217
Note: Earth Day Lengths
Mean Solar: 24.0000 hours (24h00m00s)
Sidereal: 23.9345 hr (23h56m4.1s)
Albedo (geometric): 0.12
Magnetic Field (Earth = 1): extremely weak

More Views of Moon in 3-D:
NASA's Overview of the Moon
NASA's Moon Portal is similar but opens a few
different stories and interactive features.
History of Apollo Landings in 3-D zoom way in!
Moon-Viz gives you an appreciation for how many
satellites have studied and will study the Moon.
NASA's Moon to Mars Portal Toolkit
ESA's Lunar Exploration pages

MOON DISTANCE: General Details

Distance: (Earth diameters are "equatorial")
Mean: 384,400 km (30.13 Earth dia.)
Mean: 363,300 km
Min: 356,400 km (27.9 Earth dia.)
Mean: 405,500 km
Max: 406,700 km (31.9 Earth dia.)
Perigee and Apogee List

Mean: 3,680 km/hr
Min: 3,480 km/hr
Max: 3,950 km/hr View Earth-Moon Barycenter video

View Moon's Orbital Position & Phase video

The lunar orbit would
easily fit inside the Sun!

The Moon's path around the Sun is
often shown incorrectly with loops or
zig-zags! Actually it is nearly a circle—
always concave relative to the Sun!


Scroll image above for the actual shape of the Moon's path around
the Sun. Click on image to open it fully in a separate window.

Lunar Orbit Periods: (Months)
Sidereal: 27.32166 days (relative to background)
Synodic: 29.53059 days (relative to Sun, Phases)
Tropical: 27.32158 days (relative to equinoxes)
Anomalistic: 27.55455 (relative to perigees)
Draconic: 27.21222 (relative to nodes)


The Moon's orbit changes in complex
ways. Its plane and line of Nodes rotate "backwards" about every 18½ years! Its
line between perigee and apogee ro-
tates "forward" almost every 9 years!

And don't forget: every month
Earth and the Moon also revolve
once around their barycenter!

Long-Term Orbital Periods:
Precession of Apsides: 8.8504 years
Precession of Nodes: 18.5996 years (retrograde)
Spin-Orbit Resonance: Yes, 1 to 1
(so the same side of Moon always faces Earth)
Mean: 0.0549
Min: 0.0255
Max: 0.0775
Inclination to Ecliptic: 5.145°

A "supermoon" occurs when the Moon is full
and in the closest 10% of its distance range.

Area Component: up to 15% greater than avg
Distance Component: up to 15% greater than avg
Pairs or Triples about every 13½ calendar months

1. New Moons New Moons essentially rise and set with the Sun and reflect no sunlight toward Earth. So they do not impede Deep Sky Observing all night.

2. Waxing Crescent Moons Waxing Crescent Moons generally
rise between sunrise and "local
noon". Setting between sunset
and "local midnight", they are up
and impede Deep Sky Observing
early in the evening.

3. 1st Qtr Moons 1st Qtr Moons generally rise near "local noon". Setting near "local midnight", they are up and impede Deep Sky Observing for the first
half of the night.

4. Waxing Gibbous Moons Waxing Gibbous Moons generally
rise between "local noon" and sun-
set. Setting between "local midnight"
and sunrise, they are up and
impede Deep Sky Observing from
sunset through the early morning.

5. Full Moons Full Moons generally rise near
sunset, then set near sunrise. So
they are up and impede Deep Sky Observing all night long.

6. Waning Gibbous Moons Waning Gibbous Moons generally
rise between sunset and "local
midnight". Setting between sunrise and "local noon", they are up and impede Deep Sky Observing in the
late evening through sunrise.

7. Last Qtr Moons Last Qtr Moons generally rise near "local midnight" and set near "local noon", allowing Deep Sky Observing only during the first half of the night.

8. Waning Crescent Moons Waning Crescent Moons generally
rise between "local midnight" and
sunrise. Setting between "local
noon" and sunset, they are up and
impede Deep Sky Observing only during the early morning.


SOLAR: Total = T , Annular = A LUNAR: Total = T , Partial = P

Click on months for Phases

2021 Phase List plus more Astronomical Events

Old Format Previous Months' Phase Calendars:
2014: Jan 2013: Dec Nov Oct Sep Aug Jul Jun May Apr Mar Feb

ECLIPSE "SEASONS" 2019 - 2030


W A R N I N G ! It is never safe to look directly at the Sun with the naked eye! Moreover, looking at it—even for an instant—through either a telescope or binoculars without adequate safeguards can cause permanent blindness! NEVER DO IT! To learn how to safely "observe" the Sun and a Solar Eclipse, consult your local planetarium or observatory.

NASA's 5 Millenia of Eclipses: Solar Lunar

View of Moon (from Sun's direction in CELESTIA):
With Location Labels ON: (1.6.x) (1.4.1)
With Location Labels OFF: (1.6.x) (1.4.1)

Partial Information Source: NASA Fact Sheets

"pertaining to the Moon"

lunar (from Latin: Luna)
selenian (from Greek goddess, Selene)


Like the Sun, every day the Moon generally rises in the east, moves westward across the sky, then sets in the west. Also like the Sun, the Moon has an "apparent" motion independent of the daily-rotating background of fixed stars. This independent motion was much more obvious to the ancients than the Sun's motion, for the Moon moves through the background stars much faster —on average about 13&frac13 times faster—than the Sun! Always staying within the band of the Zodiac, the Moon moves generally eastward through the background stars, each hour moving a distance roughly equal to its own diameter . The SkyMarvels&trade video directly below shows the Moon's motion for the full year of 2014.

On average, this motion makes the Moon visible in the sky for about 12½ hours each day, not 12, because the Earth has to rotate a little further to "catch up" with the moving Moon! On average the Moon also therefore rises and sets about 50 minutes later each day, completing one circuit of the heavens in about 27&frac13 days relative to the stars and in about 29½ days relative to the Sun. These two periods are known respectively as a sidereal month and a synodic month, and they are only averages due to the Moon's quite-irregular orbit.

For the 50th anniversary of human- kind's first walk on another world, check out these awesome interac- tive adventures: First Men on the Moon, Apollo 11 in Real-Time and Mapping the Mission. Then view the Command Module in 3-D, its interior and the LEM on the Moon in 3-D! Sadly, the awesome "We Choose the Moon", an excellent recre- ation written in Flash, can no longer be found on the net. Truly a great loss.

That's how the Total Solar Eclipse of 21 August 2017 is described. That Monday the Moon's shadow whisked across the United States, gracing it with an outstanding sky marvel! NASA Page PDF HMNAO Page HMNAO Visibility Tool

Awesome online app and animations from NASA:

APOLLO Missions: high resolution posters

Here's a link to a nice NASA page: Timeline of Lunar Exploration Missions. Lots of good background info here!

Here's a link to a nice Lunar Panorama from Apollo 17 in color. Yes, that's a barren-looking place! Can you find the Rover?

Apollo Landing Sites shows Moon phases during missions.

Lunar Clementine Moon Spin. Video Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio

Clementine Lunar South Pole. Video Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio

Lunar Prospector Hydrogen Concentration - South Pole. Video Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio

© 2007- by Gary M. Winter. All rights reserved.

Interested in political cartoons and humor?
Check out The HIPPLOMATS™.

Current Sunsize vs Moonsize, SUN and MOON Current Apparent Sizes, Current Geocentric Apparent Sizes of the Sun and Moon. GREAT AMERICAN ECLIPSE! BEST ECLIPSE IN AMERICAN HISTORY! BEST ECLIPSE IN U.S. HISTORY! BEST ECLIPSE IN US HISTORY! SkyMarvels, Sky Marvels,, MOON Info, THE MOON! View its Current Distance, Current Apparent Size, Current Phase, Current Position in Orbit, Eclipses, Eclipse Calendar, Interactive Eclipse Seasons Calendar, Eclipse Seasons, Upcoming Eclipses and much more! Supermoons & Extreme Perigean Tides 2020-2021! celestia4all, celestiaforall, CELESTIA, astronomy, space, simulations, animations, downloadable astronomy posters, stars, planets, Inner Planets, Outer Planets, Inferior Planets, Superior Planets, moons, asteroids, comets, Oort Cloud, galaxy, galaxies, Milky Way, Andromeda, globular clusters, binaries, quasars, black holes, supermassive black holes, telescope, telescopes, planetarium, software, freestuff, satellites, add-ons, addons, scripts, eclipses, Solar Eclipses, Lunar Eclipses, Solar Eclipse Finder, Lunar Eclipse Finder, mutual eclipses, transits, occultations, Solar System, CELES-TOOLS, celeSTARrium, CELX, CELX programming, Freebies, Bonuses, multiple views, atronomical unit, light year, parsec, meteors, meteor showers, Perseids, Geminids, Leonids, barycenter, time, Time Zones, tides, alignments, conjunctions, oppositions, seasons, apogees, perigees, aphelion, perihelion, Earth, Luna, Mercury, Venus, Mars, Jupiter, Galilean Moons, Io, Europa, Ganymede, Callisto, Saturn, Titan, rings, Uranus, Neptune, Triton, E-MSpectrum, electromagnetic spectrum, astronaut, equinoxes, solstices, precession, rotation, spin, inclination, tilt, Ecliptic, orbits, ellipse, parabola, hyperbola

"Our Moon is the greatest influence on Earth's tides."

Earth's & our Moon's motion around their barycenter helps produce Earth's tides.

K E E P S A F E! It is never NEVER safe to
look directly at the real Sun with the naked
eye! Moreover, looking at it—even for an instant—
through a telescope, binoculars, camera or similar
instrument without adequate safeguards can cause
permanent blindness! NEVER DO IT! To learn how
you can safely "observe" the Sun, consult the pro-
fessionals at your local planetarium or observatory.

Donate safely with: Pay Pal --> Pay Pal

and receive one or more
Sky-Gifts. Your support is greatly appreciated!

NOTE: you do not need a Pay Pal account to donate.

What is the Earth's average temperature?

Earth Observation of sun-glinted ocean and clouds. Credit: NASA

Earth is the only planet in the solar system where life is known to exists. Note the use of the word "known", which is indicative of the fact that our knowledge of the solar system is still in its infancy, and the search for life continues. However, from all observable indications, Earth is the only place in the solar system where life can – and does – exist on the surface.

This is due to a number of factors, which include Earth's position relative to the sun. Being in the "Goldilocks Zone" (aka. habitable zone), and the existence of an atmosphere (and magnetosphere), Earth is able to maintain a stable average temperature on its surface that allows for the existence of warm, flowing water on its surface, and conditions favorable to life.

The average temperature on the surface of Earth depends on a number of factors. These include the time of day, the time of year, and where the temperatures measurements are being taken. Given that the Earth experiences a sidereal rotation of approximately 24 hours – which means one side is never always facing towards the sun – temperatures rise in the day and drop in the evening, sometimes substantially.

And given that Earth has an inclined axis (approximately 23° towards the sun's equator), the Northern and Southern Hemispheres of Earth are either tilted towards or away from the sun during the summer and winter seasons, respectively. And given that equatorial regions of the Earth are closer to the sun, and certain parts of the world experience more sunlight and less cloud cover, temperatures range widely across the planet.

However, not every region on the planet experiences four seasons. At the equator, the temperature is on average higher and the region does not experience cold and hot seasons in the same way the Northern and Southern Hemispheres do. This is because the amount of sunlight the reaches the equator changes very little, although the temperatures do vary somewhat during the rainy season.

The average surface temperature on Earth is approximately 7.2°C, though (as already noted) this varies. For instance, the hottest temperature ever recorded on Earth was 70.7°C (159°F), which was taken in the Lut Desert of Iran. These measurements were part of a global temperature survey conducted by scientists at NASA's Earth Observatory during the summers of 2003 to 2009. For five of the seven years surveyed (2004, 2005, 2006, 2007, and 2009) the Lut Desert was the hottest spot on Earth.

However, it was not the hottest spot for every single year in the survey. In 2003, the satellites recorded a temperature of 69.3°C (156.7°F) – the second highest in the seven-year analysis – in the shrublands of Queensland, Australia. And in 2008, the Flaming Mountain got its due, with a yearly maximum temperature of 66.8°C (152.2°F) recorded in the nearby Turpan Basin in western China.

Meanwhile, the coldest temperature ever recorded on Earth was measured at the Soviet Vostok Station on the Antarctic Plateau. Using ground-based measurements, the temperature reached a historic low of -89.2°C (-129°F) on July 21st, 1983. Analysis of satellite data indicated a probable temperature of around -93.2 °C (-135.8 °F 180.0 K), also in Antarctica, on August 10th, 2010. However, this reading was not confirmed by ground measurements, and thus the previous record remains.

All of these measurements were based on temperature readings that were performed in accordance with the World Meteorological Organization standard. By these regulations, air temperature is measured out of direct sunlight – because the materials in and around the thermometer can absorb radiation and affect the sensing of heat – and thermometers are to be situated 1.2 to 2 meters off the ground.

Comparison to other planets:

Despite variations in temperature according to time of day, season, and location, Earth's temperatures are remarkably stable compared to other planets in the solar system. For instance, on Mercury, temperatures range from molten hot to extremely cold, due to its proximity to the sun, lack of an atmosphere, and its slow rotation. In short, temperatures can reach up to 465 °C on the side facing the sun, and drop to -184°C on the side facing away from it.

Venus, thanks to its thick atmosphere of carbon dioxide and sulfur dioxide, is the hottest planet in the solar system. At its hottest, it can reach temperatures of up to 460 °C on a regular basis. Meanwhile, Mars' average surface temperature is -55 °C, but the Red Planet also experiences some variability, with temperatures ranging as high as 20 °C at the equator during midday, to as low as -153 °C at the poles.

On average though, it is much colder than Earth, being just on the outer edge of the habitable zone, and because of its thin atmosphere – which is not sufficient to retain heat. In addition, its surface temperature can vary by as much as 20 °C due to Mars' eccentric orbit around the sun (meaning that it is closer to the sun at certain points in its orbit than at others).

Since Jupiter is a gas giant, and has no solid surface, an accurate assessment of it's "surface temperature" is impossible. But measurements taken from the top of Jupiter's clouds indicate a temperature of approximately -145°C. Similarly, Saturn is a rather cold gas giant planet, with an average temperature of -178 °Celsius. But because of Saturn's tilt, the southern and northern hemispheres are heated differently, causing seasonal temperature variation.

Uranus is the coldest planet in the solar system, with a lowest recorded temperature of -224°C, while temperatures in Neptune's upper atmosphere reach as low as -218°C. In short, the solar system runs the gambit from extreme cold to extreme hot, with plenty of variance and only a few places that are temperate enough to sustain life. And of all of those, it is only planet Earth that seems to strike the careful balance required to sustain it perpetually.

Variations Throughout History:

Estimates on the average surface temperature of Earth are somewhat limited due to the fact that temperatures have only been recorded for the past two hundred years. Thus, throughout history the recorded highs and lows have varied considerably. An extreme example of this would during the early history of the solar system, some 3.75 billion years ago.

At this time, the sun roughly 25% fainter than it is today, and Earth's atmosphere was still in the process of formation. Nevertheless, according to some research, it is believed that the Earth's primordial atmosphere – due to its concentrations of methane and carbon dioxide – could have sustained surface temperatures above freezing.

Earth has also undergone periodic climate shifts in the past 2.4 billion years, including five major ice ages – known as the Huronian, Cryogenian, Andean-Saharan, Karoo, and Pliocene-Quaternary, respectively. These consisted of glacial periods where the accumulation of snow and ice increased the surface albedo, more of the sun's energy was reflected into space, and the planet maintained a lower atmospheric and average surface temperature.

These periods were separated by "inter-glacial periods", where increases in greenhouse gases – such as those released by volcanic activity – increased the global temperature and produced a thaw. This process, which is also known as "global warming", has become a source of controversy during the modern age, where human agency has become a dominant factor in climate change. Hence why some geologists use the term "Anthropocene" to refer to this period.

Thanks to increasing concentrations of CO² and other greenhouses gases, which are generated by human activity, average surface temperatures have been steadily increasing since the mid-20th century. For the past few decades, NASA has been charting average surface temperature increases through the Earth Observatory.

Internal Temperatures:

When talking about the temperatures of planets, there is a major difference between what is measured at the surface and what conditions exist within the planet's interior. Essentially, the temperature gets cooler the farther one ventures from the core, which is due to the planet's internal pressure steadily decreasing the father out one goes. And while scientists have never sent a probe to our planet's core to obtain accurate measurements, various estimates have been made.

The Earth has been through five major ice ages in the past 2.4 billion years, including the one we are currently living in. Credit: NASA Goddard’s Scientific Visualization Studio

For instance, it is believed that the temperature of the Earth's inner core is as high as 7000 °C, whereas the outer core is thought to be between 4000 and 6000 °C. Meanwhile, the mantle, the region that lies just below the Earth's outer crust, is estimated to be around 870 °C. And of course, the temperature continues to steadily cool as you rise in the atmosphere.

In the end, temperatures vary considerably on every planet in the solar system, due to a multitude of factors. But from what we can tell, Earth is alone in that it experiences temperature variations small enough to achieve a degree of stability. Basically, it is the only place we know of that it is both warm enough and cool enough to support life. Everywhere else is just too extreme!

NASA Map Gives Most Accurate Space-Based View of LA’s Carbon Dioxide

This animation shows the accumulation of data from NASA’s OCO-3 instrument used to create a map of carbon dioxide (CO2) concentrations that covers about 50 square miles (80 square kilometers) of the Los Angeles metropolitan area. The highest concentrations are in yellow.Credits: NASA/JPL-Caltech

Such detailed maps could help policymakers choose the most effective ways of cutting carbon emissions.

Using data from NASA’s Orbiting Carbon Observatory 3 (OCO-3) instrument on the International Space Station, researchers have released one of the most accurate maps ever made from space of the human influence on carbon dioxide (CO2) in the Los Angeles metropolitan area. The map shows tiny variations in airborne CO2 from one mile of the giant L.A. Basin to the next.

The highest CO2 readings, in yellow on the map, are on the west side of downtown L.A. – a densely populated area with congested freeways and CO2-emitting industries. Yellow indicates atmospheric CO2 elevated by five or more molecules out of every million molecules of air, or five parts per million. That’s equivalent to the amount that global atmospheric CO2 is rising globally on average every two years

The animation shows five adjoining swaths of data the OCO-3 instrument collected over the metropolitan area to create a map of CO2 concentrations that covers about 50 square miles (80 square kilometers). Each pixel is about 1.3 miles (2.2 kilometers) the color indicates how much higher the concentration of CO2 is in that spot than in clean desert air north of the city (measured at NASA’s Armstrong Research Center, upper right).

Most of the increasing CO2 in the global atmosphere comes from humans burning fossil fuels for energy, and 70% of that comes from cities. Los Angeles has set goals for cutting its carbon emissions. This type of data can help decision makers choose the most effective policies to reach those goals and to measure the effectiveness of new regulations. Data from ground level provides critical local measurements, but satellite data is equally necessary because it covers a wider area and also measures CO2 throughout the entire depth of the atmosphere.

The International Space Station, which hosts the OCO-3 instrument, circles Earth between 52 degrees north and 52 degrees south latitudes – about the latitudes of London and Patagonia. Almost all cities on Earth come within its view on average once every three days. The OCO-3 team at NASA’s Jet Propulsion Laboratory in Southern California schedules measurements at up to 40 locations a day. Most of these targets are high-CO2-emitting cities.

The instrument consists of a telescope and three spectrometers, a kind of instrument that analyzes wavelengths of the electromagnetic spectrum of sunlight to find the spectral “fingerprint” of carbon dioxide. The telescope swivels rapidly to collect as many adjoining swaths of data as possible over a targeted location within two minutes. OCO-3 usually collects a single swath of data as it orbits, like its predecessor the OCO-2 mission (which is still operating), but it’s designed to create snapshot maps like this one to give researchers a more complete picture of emissions from cities and other areas of interest.

The maps were published this week in a paper in the journal Remote Sensing of Environment.

Jane J. Lee / Ian J. O’Neill
Jet Propulsion Laboratory, Pasadena, Calif.

6. EGM2008 Model Products

[138] The primary product of the EGM2008 model development is the set of estimated spherical harmonic coefficients, to degree 2190 and order 2159. From these coefficients the user may compute the values of various functionals of the gravitational potential such as gravity anomalies, height anomalies, deflections of the vertical, etc., on or above the physical surface of the Earth, using harmonic synthesis. Holmes and Pavlis (2006) made available a FORTRAN computer program called HARMONIC_SYNTH, which may be used to perform such harmonic synthesis tasks in various modes, e.g., for randomly scattered geographic locations, or for grids of point and/or area-mean values. This program, accompanied by test input and output files, and associated documentation is freely available from:

[139] In Table 13 we list the estimated values and their standard deviations of the EGM2008 zonal spherical harmonic coefficients of the gravitational potential to degree 10.

Degree (n)
2 −0.484165143790815D-03 0.7481239490D-11
3 0.957161207093473D-06 0.5731430751D-11
4 0.539965866638991D-06 0.4431111968D-11
5 0.686702913736681D-07 0.2910198425D-11
6 −0.149953927978527D-06 0.2035490195D-11
7 0.905120844521618D-07 0.1542363963D-11
8 0.494756003005199D-07 0.1237051133D-11
9 0.280180753216300D-07 0.1023487582D-11
10 0.533304381729473D-07 0.8818400481D-12

[140] For height anomaly and geoid computations, the user should also pay attention to some important issues related to the Permanent Tide, and the Geodetic Reference System (GRS) to which the computed values refer. For example, in applications involving ellipsoidal heights obtained from space techniques like the Global Positioning System, the user should be aware of the fact that the International Earth Rotation and Reference Systems Service (IERS) reports positions with respect to a conventional “Tide-Free” crust (also known as “Non-Tidal”). Therefore, in order to maintain consistency, geoid undulations and/or height anomalies involved in computations that use positions derived from space techniques, should be computed in the same Tide-Free system. In contrast, in applications involving satellite altimetry, the “Mean Tide” system is commonly used. Therefore, geoid undulations that are to be subtracted from altimetry-derived sea surface heights, in order to estimate the dynamic ocean topography, should also be computed in the Mean Tide system. The definition of the three systems in use with regards to the Permanent Tide (Tide-Free, Mean Tide, and Zero Tide), and the relationships between the geoid undulations expressed in different systems is also discussed by Lemoine et al. [1998 , chapter 11]. This chapter is available online from:

[141] In the same chapter [ Lemoine et al., 1998 , chapter 11], the issue of expressing the geoid undulations and/or height anomalies with respect to a specific GRS is discussed. In the case of EGM2008, the conversion from an “ideal” mean-Earth ellipsoid, whose semi-major axis remains numerically unspecified, to the WGS 84 GRS in the Tide-Free system, involves the application of a zero-degree height anomaly, denoted byζzin equation 11.2–1 of the above chapter from Lemoine et al., equal to −41 cm. The zero-degree height anomaly,ζz, that was computed when the WGS 84 EGM96 geoid was released was equal to −53 cm [ Lemoine et al., 1998 , chapter 11]. The main reason for the change in the numerical value of ζzfrom the EGM96 days to the current best estimate, is the discovery by Ouan-Zan Zanife (CLS, France) of an error in the Oscillator Drift correction applied to TOPEX altimeter data [ Fu and Cazenave, 2001 , p. 34]. The erroneous correction was producing TOPEX sea surface heights, biased by approximately 12 to 13 cm. Due to the fact that the height anomaly to geoid undulation conversion terms do not average to zero globally, the −41 cm ζzvalue results in a −46.3 cm zero-degree geoid undulation value (N0). N0 depends not only on ζz, but also on the formulation and the data used to compute the height anomaly to geoid undulation conversion terms.

[142] Under: user can find a modified version of the HARMONIC_SYNTH program, specifically designed to compute geoid undulations at arbitrarily scattered locations, in the Tide-Free system, with respect to the WGS 84 GRS. In the same web site, the user can also find pre-computed global grids of these geoid undulations, at both 1 and 2.5 arc-minute grid-spacing, as well as a FORTRAN program to interpolate from these grids. The interpolation error, i.e., the difference of interpolated values from those obtained via harmonic synthesis, associated with the use of the 1 arc-minute grid and of the interpolation program provided does not exceed ±1 mm. This error rises to ±1 cm with the use of the 2.5 arc-minute grid.

[143] Several other products of the EGM2008 model development can be found under: These include the spherical harmonic coefficients of the Dynamic Ocean Topography model DOT2008A, complete to degree and order 180, as well as grids of height anomalies and of the DOT, computed with oceanographic applications in mind. In addition, grids of pre-computed gravity anomalies and deflections of the vertical, as well as grids of the propagated errors implied by EGM2008 in gravity anomalies, geoid undulations and deflections of the vertical (ξ, η) are available from the same web site.

3 Methods

3.1 EAGEL (Ecliptic Cut Angles From GCS for ELEvoHI)

In this section, we present a newly developed Interactive Data Language (IDL™) tool called EAGEL (Ecliptic cut Angles from GCS for ELEvoHI). EAGEL allows any user to determine the propagation direction, ϕ, and the half width, λ, within the ecliptic plane, based on GCS reconstruction of a CME. To perform GCS reconstruction, coronagraph images from at least two vantage points (STEREO and/or LASCO) are required. EAGEL provides the routines to download the required coronagraph images, combines all the functions to perform GCS reconstruction, and produces a cut in the ecliptic plane. Standard preprocessing of the images is implemented in EAGEL to make the CME features clearly visible to the user, who can decide between using background-subtracted, running-difference, and base-difference images. The user can then perform GCS reconstruction using the IDL SolarSoft procedure rtsccguicloud. The top row of Figure 1a shows the coronagraph images (from left to right: STB/COR2, LASCO/C2, STA/COR2) for event #5. The bottom row additionally shows the GCS wire frame (green mesh). In its current version, ELEvoHI is a 2D prediction model giving results only in the ecliptic plane. Therefore, EAGEL calculates the ecliptic part of the GCS wire frame and selects the boundaries of the ecliptic cut (see red and green line in Figure 1b). The boundaries are defined to be the outermost points of each side of the ecliptic cut with respect to the apex direction from GCS reconstruction. This gives λ and ϕ, where the latter is defined to be exactly in between the two boundaries. A plot is shown to the user (Figure 1b) and, if needed, the boundaries can be changed manually. Once the user approves the selection, λ and ϕ relative to Earth and to the two STEREO spacecraft are stored and can be used by ELEvoHI.

GCS reconstruction (left) and ecliptic cut of the wire frame (right) for event #5. (a) Top row from left to right: STB/COR2, LASCO/C2, STA/COR2. Bottom row: same as top row but with the GCS wire frame overlaid. (b) Ecliptic cut (black) of the GCS wire frame. Red and green lines show the boundaries selected by either EAGEL or the user. The yellow line defines the ecliptic propagation direction with respect to Earth, ϕEarth, of the CME. The half width, λ, is the angle between one boundary and ϕEarth. The blue arrow indicates the direction to Earth.

In Table 2, we list the time (Date) of the STEREO coronagraph images used to get λ and ϕ for each event. EAGEL then selects the SoHO coronagraph images closest in time to the quoted date. Each CME is fitted once based on the three different viewpoints (STA, STB, LASCO). However, for event #1 no LASCO data are available, so GCS reconstruction is based on STEREO images only. For all the events, the times of the images are selected in such a way that the CME front is clearly visible in the coronagraph images of all the viewpoints. Furthermore, we try to fit the CME at times when the front is already far out in both STA and STB COR2 images. Table 2 additionally contains the GCS parameters (Lon, Lat, TA, AR, HA). Also the half width, λ, and the CME ecliptic propagation angle, ϕ, relative to Earth (ϕEarth), and relative to the two STEREO spacecraft (ϕSTA and ϕSTB) obtained from EAGEL are given. Lon is the longitude (here given in Stonyhurst coordinates) and Lat the latitude of the apex of the idealized hollow croissant shaped model. The tilt angle (TA) defines the tilt of the croissant, calculated with respect to the solar equator. The half angle (HA) represents the angle between the center of the foot points and the aspect ratio (AR) is the ratio of the CME size in two orthogonal directions.

GCS parameter EAGEL results
No. Date Lon (°) Lat (°) TA (°) AR (°) HA (°) λ (°) ϕEarth (°) ϕSTA (°) ϕSTB (°)
1 February 03, 2010, 15:54 355 −17 −1 0.33 30 36 −4 67 68
2 March 19, 2010 17:39 23 −12 −7 0.29 19 30 22 44 93
3 April 03, 2010, 12:39 7 −19 15 0.39 30 38 9 58 81
4 April 08, 2010 06:39 1 −10 −20 0.28 30 31 −2 70 69
5 May 23, 2010 20:39 6 2 −15 0.48 18 35 −6 65 76
6 October 26, 2010 14:39 18 −35 −28 0.51 30 18 −11 95 69
7 January 30, 2011 21:24 351 −18 −20 0.33 12 24 −11 97 82
8 February 15, 2011 04:08 10 −10 27 0.87 29 49 10 77 104
9 September 06, 2011 23:39 29 20 −90 0.49 30 26 29 74 124
10 January 23, 2012 04:39 19 41 64 0.77 55 37 9 99 123
11 June 14, 2012 14:54 360 −28 11 0.90 30 53 1 116 117
12 July 12, 2012 17:54 8 −12 68 0.46 30 26 14 106 129
  • Note. Date: time set in EAGEL to perform the reconstruction. Lon: longitude (Stonyhurst coordinates), Lat: latitude, TA: tilt angle, AR: aspect ratio, HA: half angle from GCS. The remaining values are based on the ecliptic cut from EAGEL: λ: half width of the CME, ϕEarth, ϕSTA, ϕSTB: propagation direction with respect to Earth, STA, STB, respectively.

When comparing Lon (longitude from GCS reconstruction) and ϕEarth (longitude relative to Earth from the ecliptic cut), it can be seen that the propagation direction obtained from the ecliptic cut is quite comparable to (within 5° of) the propagation direction from the GCS reconstruction. Only for events #6 and #10 we find differences of about 30° and 10°, respectively. The reason can be found in the combination of low/high latitude and large tilt angle. Therefore, the part within the ecliptic plane does not correspond well to the main propagation direction resulting from GCS reconstruction for these two CMEs.

3.2 WSA/HUX Model

In the following paragraph, we summarize the main characteristics of the numerical framework used here for modeling the physical conditions in the evolving ambient solar wind flow. For this study, we make use of the framework shown in Reiss et al. ( 2019 , 2020 ), but the components of this framework were developed by Wang and Sheeley ( 1995 ), Arge et al. ( 2003 ), Riley and Lionello ( 2011 ), and Owens and Riley ( 2017 ). Specifically, we use magnetic maps of the photospheric field from Global Oscillation Network Group (GONG) provided by the National Solar Observatory (NSO) as input to magnetic models of the solar corona. Using the Potential Field Source Surface model (PFSS Altschuler & Newkirk, 1969 Schatten et al., 1969 ) and the Schatten current sheet model (SCS Schatten, 1971 ) we compute the global coronal magnetic field topology. While the PFSS model attempts to find the potential magnetic field solution in the corona with an outer boundary condition that the field is radial at the source surface at 2.5 R, the SCS model in the region between 2.5 and 5 R accounts for the latitudinal invariance of the radial magnetic field as observed by Ulysses (Wang & Sheeley, 1995). From the global magnetic field topology, we calculate the solar wind conditions near the Sun using the established Wang-Sheeley-Arge (WSA) model. To map the solar wind solutions from near the Sun to Earth, we use the Heliospheric Upwind eXtrapolation model (HUX). This model simplifies the fluid momentum equation as much as possible, by neglecting the pressure gradient and the gravitation term in the fluid momentum equations as proposed by Riley and Lionello ( 2011 ). The HUX model solutions match the dynamical evolution explored by global heliospheric MHD codes fairly well while having low processor requirements. An example of the ambient solar wind, modeled by WSA/HUX combination, is shown in Figure 2.

Ambient solar wind speed provided by the WSA/HUX model for event #5. The white box defines the area that is used to calculate an estimate of the ambient solar wind speed for the ensemble member of ELEvoHI corresponding to the minimum propagation direction (ϕSTA = 56°) with the maximum half width (λ = 50°). The black box indicates the total area based on all the ensemble members of ELEvoHI for this event. The longitude of 0° corresponds to the longitude of Earth. WSA/HUX, Wang-Sheeley-Arge/Heliospheric Upwind eXtrapolation ELEvoHI, ELlipse Evolution model based on Heliospheric Imager observations.

3.3 ELEvoHI Ensemble Modeling

ELEvoHI uses HI time-elongation profiles of CME fronts and assumes an elliptical shape for those fronts to derive their interplanetary kinematics (detailed information about the underlying Ellipse Conversion method can be found in Rollett et al. ( 2016 ). The tracking of each CME was done manually using ecliptic time-elongation maps (j-maps Davies et al., 2009 Sheeley et al., 1999 ), generated by extracting ecliptic data from STA and STB HI images. Transients, like CMEs, appear as a bright feature in the j-maps. To extract the time-elongation profiles, we use the SATPLOT tool implemented in IDL™ SolarSoft. It allows any user to measure the elongation, which is defined as the angle between the Sun-observer (STA or STB) line and the CME front. ELEvoHI converts the resulting time-elongation profiles to time-distance profiles, assuming an elliptic frontal shape using the ELEvoHI built-in procedure ELlipse Conversion (ELCon Rollett et al., 2016 ).

ELEvoHI accounts for the effect of the drag force exerted by the ambient solar wind, which is incorporated in the model. The drag force is an essential factor influencing the dynamic evolution of CMEs in the heliosphere. Within ELEvoHI, the time-distance track is fitted using a drag-based equation based on the drag-based model (DBM) given in Vršnak et al. ( 2013 ). The user has to define the start-point and end-point for the DBM fit (usually around 30 − 100 R) in the time-distance profile. In order to account for the de-/acceleration of the CME due to drag, an estimate of the ambient solar wind speed is needed. Here, we make use of the WSA/HUX model (see Section 3.2), which provides the ambient solar wind conditions for a full Carrington rotation (see Figure 2). We only consider the part of the full map according to the start-point and end-point selected by the user, and the CME propagation direction and half width from EAGEL. From this area, surrounded by the white box in Figure 2, we take the median of the solar wind speed and define the uncertainties to be ±100 km s −1 , based on a study by Reiss et al. ( 2020 ). They considered 9 years (mid-2006 to mid-2015) and report a mean absolute error of the WSA solar wind speed prediction with respect to the in situ speed of 91 km s −1 . The obtained ambient solar wind speed with its uncertainty is split into steps of 25 km s −1 , which gives nine different input speeds to ELEvoHI. For each of the nine input speeds, DBM fitting is performed. ELEvoHI then selects the combination of drag parameter and ambient solar wind speed that best fits the time-distance profile for each ensemble member (for a detailed description see Rollett et al., 2016 ). The selected drag parameter and solar wind speed are assumed to be valid for the full CME front during the propagation in the heliosphere.

Since ELEvoHI is a 2D model, we are only interested in the propagation of a CME in the ecliptic plane. ϕ and λ, in this plane, are provided by EAGEL (see Section 3.1). The inverse ellipse aspect ratio, f, defines the shape of the assumed CME front in the ecliptic plane, where f = 1 represents a circular front, while f < 1 corresponds to an elliptical CME front (with the semimajor axis perpendicular to the propagation direction).

To run ELEvoHI in ensemble mode, we vary ϕ, λ, and f. A details description can be found in Amerstorfer et al. ( 2018 ) and the code is available online (see Section 6). ϕ and λ vary over a range of ±10° from their values obtained from EAGEL, with a step size of 2° and 5°, respectively. This range is defined based on a study by Mierla et al. ( 2010 ), who report an uncertainty in the parameters when different users manually perform GCS reconstruction. Note that the propagation direction and the half width obtained from EAGEL are rounded to even numbers and to whole tens, respectively. For f we set a fixed range from 0.7 to 1.0 (0.1 step size). Thus, we get a total of 220 ensemble members for one ELEvoHI event (i.e., 11 values of ϕ, 5 values of λ, and 4 values of f). For each ensemble member we select a different sector from the ambient solar wind provided by the WSA/HUX model combination according to the propagation direction, half width, start-point, and end-point. In Figure 2, the WSA/HUX model results for event #5 are shown. The white box indicates the area from which the ambient solar wind speed for one individual run of ELEvoHI is computed. Shown is the area for the minimum propagation direction, ϕSTA of 56° with a λ of 50°. For each ensemble member, the area surrounded by the white box is slightly different according to ϕ and λ. The black box plotted indicates the total area based on all ELEvoHI ensemble members for this event.

Running ELEvoHI in ensemble mode enables us to calculate a mean and a median predicted CME arrival time and also to define an uncertainty. In addition, we can give a probability for whether a CME is likely to hit Earth or not. When all of the 220 ensemble members predict an arrival at Earth, we assume the predicted likelihood of an Earth hit to be 100%.