Astronomy

As the Moon and the Earth are predicted to get into tidal lock, how slow would the Earth rotate?

As the Moon and the Earth are predicted to get into tidal lock, how slow would the Earth rotate?

This answer to Will the Earth ever be tidally locked to the Moon? supports the widely held thinking that during the Sun's red giant phase or later the Earth and the Moon should be tidally locked to each other. The Earth is said to have a slower rotation then.

Do we have any idea how long a sidereal day and the mean solar day on Earth would be in several billion years?


The last part of the answer you linked to actually says (right at the end) that tidal locking will never be achieved, with reasoning similar to what I gave in this answer.

That said, even though the Moon and the Earth will never actually achieve tidal synchronization, we can still do the thought experiment and ask, "If there were enough time for the current Earth-Moon system to achieve tidal synchronization, what would the length of the day be at which the rotation of the Earth and the orbit of the Moon would be synchronized?"

To do this, we can assume that the Moon spirals outward due to an exchange of angular momentum between the Earth's rotation and the Moon's orbit. The Earth's spin slows down as it loses angular momentum, and the Moon moves into a larger (and thus higher angular momentum) orbit as it gains that same angular momentum. The rotation of the Moon would presumably stay locked to the Moon's orbital period, so it would slow down as well.

So, using $L$ to represent angular momentum, the key equation is

$$ L_{ m now} = L_{ m then} $$

where "then" is some time in the future when lock is achieved. The total angular momentum in the system is constant.

The angular momentum of any object is $L = Iomega$, where $I$ is the moment of inertia, and $omega = frac{2pi}{P}$ is the orbital frequency, related to the orbital period $P$. For a constant-density sphere of mass $M$ and radius $R$ rotating on its axis, $I = 0.4 M R^2$. The Earth and the Moon are somewhat more centrally condensed, so their moments of (rotational) inertia are a little smaller than the 0.4 for a uniform sphere. The leading coefficient is 0.33 for the Earth, and 0.39 for the Moon.

For the Moon orbiting the Earth, it's a good approximation to just treat it as a point mass (since its size is small compared to its distance from Earth), so it has $I = M_{ m Moon}R_{ m Earth-Moon}^2$.

Putting all three of these motions (Earth rotation, Moon orbit, Moon rotation) together, we get

$$L_{ m now} = 2pi left( frac{0.33 M_oplus R_oplus^2}{P_oplus} + frac{0.39 M_{ m Moon} R_{ m Moon}^2}{P_{ m Moon}} + frac{M_{ m Moon} R_{ m Earth-Moon}^2}{P_{ m Moon}} ight) $$

All of the values there represent current, known values, i.e. $P_oplus = 1$ day, and $P_{ m Moon} = 1$ month = 27.3 days. Similarly, at some point in the (hypothetical) future, we would have

$$ L_{ m then} = 2pi left( frac{0.33 M_oplus R_oplus^2}{P_{ m then}} + frac{0.39 M_{ m Moon} R_{ m Moon}^2}{P_{ m then}} + frac{M_{ m Moon} R_{ m Earth-Moon, then}^2}{P_{ m then}} ight) $$

or

$$ L_{ m then} = frac{2pi}{P_{ m then}} left(0.33 M_oplus R_oplus^2 + 0.39 M_{ m Moon} R_{ m Moon}^2 + M_{ m Moon} R_{ m Earth-Moon, then}^2 ight) $$

Notice that there's just a single period here, since everything is now assumed to be synchronized. So we could set this equal to $L_{ m now}$ and solve for $P_{ m then}$ - except that we have a second unknown in the equation, $R_{ m Earth-Moon, then}$, the new orbital distance of the Moon from the Earth. Fortunately, we can use Kepler's third law to relate this distance to the orbital period:

$$ P_{ m then}^2 (M_oplus + M_{ m Moon} ) = frac{4 pi^2 }{G} R_{ m Earth-Moon, then}^3 $$

To make life a little easier when we substitute into the equation, we could write this as a proportion with the current values, which makes some of the constants cancel:

$$ frac{P_{ m then}^2}{P_{ m Moon}^2} = frac{R_{ m Earth-Moon, then}^3}{R_{ m Earth-Moon}^3} $$

which means that

$$ R_{ m Earth-Moon, then}^2 = R_{ m Earth-Moon}^2 left(frac{P_{ m then}}{P_{ m Moon}} ight)^{4/3} $$

Substituting that into our expression for $I_{ m then}$, we finally end up with

$$L_{ m then} = frac{2pi}{P_{ m then}} left(0.33 M_oplus R_oplus^2 + 0.39 M_{ m Moon} R_{ m Moon}^2 + M_{ m Moon} R_{ m Earth-Moon}^2 left(frac{P_{ m then}}{P_{ m Moon}} ight)^{4/3} ight) $$

So in principle, we're done - we set this equal to $L_{ m now}$ and solve for $P_{ m then}$. It's not a simple equation to solve analytically, but not hard to solve numerically.

Symbolically there's a lot going on, but we know most of these values, so if we plug in numbers for everything we know and simplify, this becomes

$$ P_{ m then} = 0.16809413 {mathrm d} + 0.27626727 {mathrm d}^{-1/3} P_{ m then}^{4/3} $$

where the "d" represents units of days. Solving this equation gives a period of 46.9 days, so that is how long the day, the month (i.e. the orbital period of the Moon), and the rotation period of the Moon would be if all were to become tidally locked to each other.

If you want to see the calculation done in Python, I've posted the code in a gist here. It's a nice example of the usefulness of Python's quantities and astropy's constants.


This is a gravitational phenomenon known as tidal lock. It is closely related to the phenomenon of tides on Earth, hence the name.

Tidal locking is an effect caused by the gravitational gradient from the near side to the far side of the moon. (That is, the continuous variation of the gravitational field strength across the Moon.) The end result is that the Moon rotates around its own axis with the same period as which it rotates around the Earth, causing the face of one hemisphere always to point towards the Earth.

Begin by imagining that the moon isn't quite a perfect sphere. One side is just a little bigger than the other. As the moon rotates, the heavier face will swing around towards the earth a little faster, and it will swing away from the earth a little slower, since it feels a stronger gravitational attraction via its larger mass.

Since gravity is a conservative force, you might think that this continues forever - but it doesn't! The moon isn't totally rigid rocks can slide around both on the surface and even inside the moon. The heavier lump actually slides through the moon to try to stay facing the earth, which causes friction inside the moon. That friction heats up the rocks, but the heat is slowly lost into space.

Now we have a conservation of energy problem: the rotational energy of the moon is being converted to thermal energy in the rocks, and that thermal energy is being slowly leaked out of the system. The only resolution is that the rotation slowly stops over many millions of years.

Finally, let's return to our assumption of a small mass imbalance. Is this true? Almost certainly - all we need is the fact that the moon isn't a truly perfect sphere.


The moons' spiraling oribts

It is most likely that the resulting particulates in the ring are individually too dense to be torn apart any further by tidal forces. As such, they are stable. However, they have so little mass that other moons, etc. end up perturbing them and throwing them out of the system. The rings slowly dissipate over time.

I'll take a shot at some of these. The condition in which we currently find our moon is a situation astronomers refer to as being "tidally locked". It is a result of the tidal forces the earth exerts on the moon (of course, it could just be a huge coincidence, but what are the odds?). And yes, these same forces are slowing the rotation of the earth, but our planet's rotation is slowing down to synchronize with the moon, not the sun, because the moon has a much stronger tidal effect on the earth than the sun does.

AFAIK, the direction in which the moon orbits a planet is not a factor in whether or not that moon will break up. The only true deciding factor here is whether the moon is in a decaying orbit (one that brings it closer and closer to the planet). It just happens that the best example we have in our solar system of a moon with a decaying orbit is also the only moon that orbits in retrograde (the opposite direction from all the other orbits in the solar system). But these two properties of Neptune's moon Triton are probably effects of a common cause Triton is probably not a moon that formed around Neptune, but rather a Kuiper Belt object that get trapped by the planet's gravitation.

Cause of all of this is tides.

Let's look first at why the Moon always presents one side to the Earth.

The Earth exerts a tidal force on the moon which tends to strecth it out along the line joining the Moon and Earth. This create "tidal" bulges. When the moon was rotating faster, different parts of the moon would pass through these tidal bulges, this created a friction which caused the moon to slow its rotation until it reached the state it is now in. This is known as being in tidal lock.

The Earth undergoes the same with the Sun, But for the Earth, this is only part of the picture. The Moon also creates tidal bulges on the Earth, and because of the proximity of the Moon these are larger than those of the Sun,

This causes two things to happen One, the Earth slows in its rotation, and two, the Earth tends to drag the tidal bulges along with its rotation.

The draging of the tidal bulges pulls them slightly out of alignment with the moon, Causing a "forward" pull on the Moon, The Earth transfers some of its rotational energy to the moon. Adding Energy to the Moon causes it to move into a higher orbit. This will continue until the Earth rotates at the same rate as the moon orbits.

If the moon orbited the Earth in the opposite direction than the Earth rotated, this mis-alignment would pull counter to its orbital direction, the Moon would fall into a lower and lower orbit.

So it really depends on whether the moon and planet rotate in the same direction as to which direction(in or Out) the Moon will spiral.

If in, the Moon will get closer and closer. As it does so, the tidal forces on it get stronger. If the moon is large enough that it is primarily holds its shape due to gravity, it will eventually reach a point where the tidal forces exeed those holding it together and it will break apart. This distance is the Roche Limit.

Once a ring sytem is formed, there will be no more tendancy for the components to continue spiraling. It was the fact that the intact moon pulled all in one direction that caused the tidal bulge which lead to the spiral, with a ring system, all the components are pulling in different directions, canceling each other out.

As far as the planets go, they all revolve around the Sun in the same direction as the Sun rotates, so there is no tendancy for them to spiral inwards toward the sun.


The Moon Comes Around Again

As the moon wheels around Earth every 28 days and shows us a progressively greater and then stingier slice of its sun-lightened face, the distance between moon and Earth changes, too. At the nearest point along its egg-shaped orbit, its perigee, the moon may be 26,000 miles closer to us than it is at its far point.

And should the moon happen to hit its ever-shifting orbital perigee at the same time that it lies athwart from the sun, we are treated to a so-called supermoon, a full moon that can seem embraceably close — as much as 12 percent bigger and 30 percent brighter than the average full moon.

If the weather is good where you are, please, go out Monday or Tuesday night and gawk for yourself: A supermoon will be dominating the sky. It’s the last of this summer’s impressive run of three supermoons, and the final one of the year.

Some astronomers dislike the whole supermoon hoopla. They point out that the term originated with astrology, not astronomy that perigee full moons are not all that rare, coming an average of every 13 ½ months and that their apparently swollen dimensions are often as much a matter of optical illusion and wishful blinking as of relative lunar nearness. The superstar astronomer Neil deGrasse Tyson grumbled archly on Twitter that the “perennially hyped” term debases the legacy of Superman, supernovas and the video game character Super Mario.

Still, astronomers concur that whatever the reason, yes, you should look at the moon early and often, whether it’s waxing or waning, gibbous or crescent, and appreciate the many features that set our moon apart from the other 100-plus moons of the solar system, and even celebrate our loyal satellite as a planet in its own right.

“I know it goes contrary to the nomenclature currently used,” said David A. Paige, a professor of planetary science at the University of California, Los Angeles, referring to the definition of a planet as the dominant gravitational object in its orbit. “But where I come from, anything that’s big enough to be round is a planet.” Unlike most moons of the solar system, ours has the heft to pull itself into a sphere.

Sparks of Discovery

Scientists say that while the public may think of the moon as a problem solved and a bit retro — the place astronauts visited a half-dozen times way back before Watergate and then abandoned with a giant “meh” from mankind — in fact, lunar studies is a vibrant enterprise that is yielding a wealth of insights and surprises.

One research group reported new evidence that the moon was born violently, in an act of planetary suicide that left faint but readable fingerprints. Another team proposed that the moon’s cataclysmic origins could explain the mysterious lunar features we know as the man in the moon.

Partly on the basis of data from NASA’s Lunar Reconnaissance Orbiter, a multi-instrument spacecraft that has been orbiting, mapping and analyzing the moon since 2009, researchers have found that the moon is a place of thermal lunacy, of searing heat crossed with sub-Plutonic cold, and of pockets that may be the most frigid spots in the entire solar system. Recent measurements taken inside impact craters at the lunar poles, where no solar light is thought to have penetrated for a billion years or more, showed temperatures of about 30 degrees Celsius above absolute zero, Dr. Paige said.

Andrew Jordan of the University of New Hampshire and his colleagues have calculated that these temperature extremes could give rise to a novel form of sparkiness, tiny bolts of lightning that dance silently through the moon’s airless landscape and fluff up the soil as they flash.

Reporting in The Journal of Geophysical Research: Planets, the researchers proposed that charged particles from the sun could be getting trapped at slightly different depths of the frigid lunar surface, forming electric fields. Those fields would gradually build up strength until, zap, serious sparks start to fly, which in turn would vaporize particles of soil.

Sparking events, the researchers said, could explain the foamy appearance of soil recently detected by NASA’s orbiter. The lunar surface “may be far more active than we thought,” Dr. Jordan said. “It’s amazing to have this kind of natural laboratory almost in our spatial backyard.”

Image

At an average distance of 238,855 miles, the moon is indeed on Earth’s patio: string together just 11 round trips from New York to Tasmania, and you’re there. The moon is not the largest satellite in the solar system — three moons of Jupiter and one of Saturn are bigger — but with a diameter almost 30 percent of Earth’s, it is by far the largest relative to its planet. Jupiter’s Ganymede, for example, which tops the lunar size chart, measures just 4 percent the diameter of its gas-giant sponsor.

Old Moon, New Surprises

A Violent Birth

Another outstanding feature of the moon is its origin. Most of the other moons in the solar system are thought to be celestial passers-by that were pulled into a planet’s orbit, or to have formed contemporaneously with their planet from an initial starter disc of dust, gas and rock. The moon, by contrast, is thought to have a bloodier past.

According to the reigning hypothesis, about 4.5 billion years ago, shortly after Earth had accreted down into a sphere from its little slub of circumsolar material, another newborn planet, still shaky on its feet, slammed obliquely into Earth with terrifying force.

That “giant impactor,” Theia, who in Greek mythology was mother to the goddess of the moon, is thought to have been roughly the size of Mars and to have been pulverized in the encounter, along with a good chunk of proto-Earth. From that fiery cloud of all-Theia and part-Earth, the scenario goes, our moon soon condensed.

The impactor hypothesis made sense and comported with computer models, but hard evidence for it proved elusive. If the moon was partly the offspring of a non-Earth body — Theia — there should be chemical fingerprints attesting to the foreign parentage. Astronomers who have analyzed a wide array of extraterrestrial material have determined that the many residents of the solar system differ measurably in their isotope ratios, the forms of the chemical elements they carry. (Heavy oxygen or light? Titanium with more neutrons or fewer?) But when researchers checked the isotope content in rocks from the moon, the ratios looked identical to rocks on Earth. Where were the traces of Theia?

Now it looks as if the evidence has arrived. This summer, Daniel Herwartz, a geochemist working at the University of Göttingen in Germany and his colleagues reported in the journal Science that they had detected isotopic ratios of oxygen in lunar rocks that were unlike the forms of oxygen found on Earth. It is, Dr. Herwartz said, “the difference between Earth and moon predicted by the impact theory.”

The researchers stumbled to victory accidentally, he said. As geochemists, they had developed new techniques for more precisely measuring oxygen isotopes to address Earth-based geological problems. “When that succeeded,” Dr. Herwartz said, “we thought we’d have a look at the moon question again.”

Initial efforts foundered. “NASA doesn’t hand out Apollo samples to everybody,” he said, referring to rocks brought back decades ago by astronauts. So the scientists tried to work with meteorite fragments, which proved too disturbed to be useful.

They then persuaded the space agency to hand over a baby aspirin’s worth of pure Apollo rock, and, sure enough, there was Theia’s isotopic thumbprint.

Emerging From the Darkness

Other signs of the fiery collision may linger in the moon’s familiar patchwork of dark and light splotches that has long been likened, dubiously, to a man’s face. It’s the only side of the moon we ever see from home base, a result of Earth’s having yanked its satellite into a so-called tidal lock: The time it takes the moon to rotate once on its axis is the same as the four weeks it takes to orbit Earth, which means the same side is always turned toward us.

“It’s the minimum energy configuration, the most stable configuration the two can take,” said Arpita Roy, a doctoral student in astronomy and astrophysics at Penn State who is also an author of a new report in The Astrophysical Journal Letters.

Ever since the dawn of the space age, when astronomers glimpsed the first photographs of the far side of the moon, they’ve wondered why it differed visibly from the near side, particularly in its absence of the dark flat plains called maria, from the Latin for seas. In the new paper, the researchers applied insights from the study of exoplanets that circle close to their stars and, like the moon, are tidally locked, with one half facing ever sunward.

In the immediate aftermath of the giant impact, Ms. Roy said, the Earth would have been as hot as a small sun, which means the half of the moon that faced us would have remained hot as well, while the opposite side had a chance to cool down. Some metals and silicates from the dust cloud surrounding the young orb would preferentially settle onto the cool side, thickening that portion of the crust.

As a result, future meteor impacts on the far side would fail to puncture below the crust, while those hitting the thin-crusted near side would expose the moon’s soft inner layers. “The craters would fill with the gooey stuff underneath,” Ms. Roy said.

That goo then hardened into maria, the seas we see when we have the good sense to look up and lock eyes with the moon.


8 Scientific Facts Everyone Should Know About Leap Day

Once every four years, at least under most circumstances, humanity inserts an extra day into our calendar year to help keep time: Leap Day. February 29 is a date that only rarely graces our lives, but plays an enormously important role: to keep our annual calendar and the passing of the seasons aligned over very long timescales. Despite a bizarre historical origin and a series of urban legends surrounding it, Leap Day exists for scientific, not superstitious, reasons.

Without a Leap Day, the physics of planet Earth would quickly cause the seasons to move out-of-phase with our annual calendar, and the equinoxes and solstices would drift around the days, months and seasons. In fact, if we did Leap Day every four years without fail, things wouldn’t line up very well, either. Only if we properly account for our planet’s axial rotation and revolution around the Sun can we keep our calendar correct, and that’s what Leap Day is all about. Here are eight scientific facts everyone should know.

1.) There are not really 24 hours in every day. The Earth’s motion has two basic parts: our rotational motion around our axis and our revolutionary motion around the Sun. Typically, we think about our rotation as lasting 24 hours, which is why a day is 24 hours, and our revolution as requiring 365 days, which is why a year is 365 days long.

Only, these effects are inseparable, as both motions are always occurring. If Earth were totally stationary, remaining in the same position, then a full rotation through all 360° would equate to a day. But that full 360° rotation isn’t a day: it’s slightly less by two metrics. First, it only takes the Earth 23 hours, 56 minutes and 4 seconds to rotate through 360°. But secondly, because the Earth moves through space in its orbit around the Sun, it has to rotate a little bit extra to position the Sun in the same relative location as it was in the previous day. That extra bit of required motion is what makes days, on average, 24 hours.

2.) Some days are actually longer than others. Have you ever wondered why the earliest sunrise and latest sunset don’t occur on the summer solstice, and why the latest sunrise and earliest sunset don’t line up with the winter solstice? It’s because the Earth orbits the Sun in an ellipse, which means when the Earth is closest to the Sun (perihelion) it moves at its fastest, and when it’s farthest from the Sun (aphelion), it moves most slowly.

Combine that with the fact that perihelion/aphelion doesn’t line up with either the solstices or equinoxes, and you’ll find that some days have less than 24 hours while others have more. The 24 hour day that we’re used to is just an average of all the days throughout the year, and even at that, they don’t line up perfectly.

3.) The Earth completing one revolution around the Sun doesn’t add up to a calendar year. In astronomy, as in mathematics, a complete revolution is defined as when the Earth returns to the same position it occupied in space a full 360° orbit ago. In astronomy, this is what we call a sidereal (sigh-DEER-ee-ul) year, or the amount of time it takes the Earth to return to the same relative position it occupied earlier with respect to the Sun.

But a sidereal year is not the same as a calendar (also known as a tropical) year. The Earth rotates on its axis while it revolves around the Sun, and that axis precesses over time, which means that the Earth is oriented slightly differently with respect to the Sun when it completes one astronomical revolution versus the year prior. The difference between a sidereal and a tropical year is small only about 20 minutes but that means a calendar year, which is what you need to make the seasons line up, is actually 20 minutes shorter than a full revolution around the Sun.

4.) The combined effects of Earth’s axial rotation, orbital revolution, and precession give an uneven number of days in the year. Now we’re getting to the fun stuff. If you do the math to the best of our knowledge, you wind up figuring out that there are 365.242188931 days in a true calendar year. This is not an even number. If we had 365 days in a year each year, each passing century would throw our calendar out of whack by almost a full month.

If we put a single Leap Day every four years, we’d account for 365.25 days on an annual basis, which is very close but not quite right. In fact, this is what the old Julian Calendar, which we followed for

1,600 years, did to account for the years. By the late 1500s, this difference was so apparent (our calendar was off by about 10 too many days), that the calendar needed to be revised.

In Italy, Poland, Spain, and Portugal, the dates October 5 through 14, in 1582, never existed. Other countries skipped those 10 days at a later date Isaac Newton was born on Christmas Day in England only because they hadn’t skipped those dates by 1642. Elsewhere in the world, Newton was born in January 4, 1643.

5.) The Gregorian calendar accounts for Leap Days extraordinarily well. The way we make up for the mismatch of our calendar year with the demands of Earth’s combined motions is brilliant and relatively simple:

  • every year that is divisible by 4 is a leap year,
  • unless it’s also divisible by 100 but not 400, in which case it’s not a leap year.

This means that 2004, 2008, 2012, 2016, 2020, etc., will all be leap years, because they’re all divisible by 4. But if your year marks the turn-of-the-century, it’s only a leap year if it’s also divisible by 400. The year 2000 was a leap year, but 1900 wasn’t and 2100 won’t be. All told, the adoption of the Gregorian calendar gives us 365.2425 days in a year, which means we won’t be off by even a single day until more than 3,200 years have gone by, at which time we might want to skip another Leap Day down the road.

If we excluded every year that’s divisible by 3200 from having a Leap Day, we wouldn’t be off by a single day until

6.) Over the long term, we’ll need to change our calendar yet again. If everything were constant ⁠ — our rotation rate, our axial tilt’s orientation, and our orbital motion around the Sun ⁠ — this calendar would be practically perfect, but only for now. Every time there’s an earthquake, our rotation rate slightly speeds up, but that effect is swamped by the gravitational effects of the Sun and Moon on the Earth, which slow us down.

The slow-down effect is known as tidal braking, and clocks in at an average of 14 microseconds per year. That might seem negligible, but over time, it really adds up. If we examine the daily patterns that the tides imprinted on our soil from long ago, known as tidal rhythmites, we can calculate what Earth’s rotation rate used to be. 620 million years ago, just before the Cambrian explosion, our day was a little under 22 hours long, which means that back when Earth first formed, our day was only 6-to-8 hours long. The lengthening days mean that, as time goes on, we’ll need fewer and fewer days to complete a tropical year.

7.) In four million years, Leap Days will be unnecessary. This extraordinarily slow effect of tidal braking will start to become important as the millennia continue to tick by. While right now, we’re only adding a single leap second every 18 months or so to accommodate it, the day continues to lengthen. After another 4 million years go by on Earth, the day will lengthen by another 56 seconds: the exact amount necessary for a tropical year to require exactly 365 days.

At that point approaches, we’ll want to first reduce the number of Leap Days and later get rid of them altogether, as they’ll become completely unnecessary. If humans are still around and keeping calendars at that point, we’ll want to think about further transitions, as we’re going to need to begin skipping days (in a reverse-Leap Day scenario) in order to keep our seasons aligned with our calendar.

8.) The ultimate fate of the Earth-Moon system will be wildly different from what we experience today. As the effect of tidal braking continues, not only will Earth’s rotation slow down, but the Moon will slowly spiral away from the Earth. In a few hundred million (but less than one billion) years, the Moon will be so distant from Earth that there will no longer be any total solar eclipses they will all be annular instead.

Assuming we survive the Sun’s transformation into a red giant and planetary nebula/white dwarf combination, a day on Earth and the Moon’s orbital period will both lengthen until they match: until they both take about 47 of our modern days, which will occur

50 billion years in the future. Instead of the same face of the Moon always pointing towards the spinning Earth, the Moon and Earth will be mutually locked, just as Pluto and Charon are with one another today.

We should all appreciate the need for Leap Days without them, the Earth’s seasons, equinoxes, and solstices would all shift over time, rather than falling on the same date year after year. But, simultaneously, we should also appreciate that the length of a day is not constant, just as the number of days in a year is not constant. As time goes on and the Earth’s rotation continues to slow, we’ll need fewer and fewer days to make up a full calendar year, which will mean we’ll require a constantly changing calendar system.

But for now, particularly on the scale of a human lifetime, the Gregorian calendar — where Leap Days occur every 4 years but not on centuries that aren’t also divisible by 400 year intervals — will do just fine. Enjoy your extra day this year however you see fit, and remember that without these Leap Days, our calendar simply wouldn’t add up.


Highest tides for 18.6 years set for the UK this week

Many places along the UK coastline will experience the highest tide for 18.6 years between the 19th and 30th of September, as a result of the co-incidence of a series of astronomical factors.

This unusually large spring tide is due to the moon and sun becoming aligned directly over the equator at the same time as the moon's 'nodal cycle' reaches a stage favourable to high tides.

Tides are controlled by well-known astronomical cycles. Every fortnight -- at new moon or full moon -- the Earth, Sun and moon are in a straight line, which causes an increase in tidal ranges. These higher than average tides are called spring tides. The word is thought to derive from the German or Anglo-Saxon word to "leap up."

Yet some spring tides are higher than others. Tidal forces are strengthened if the moon is closest to Earth in its elliptical orbit. Tide generating forces are also enhanced when the Sun and the moon are directly overhead at the equator. For the Sun this happens on or around the equinoxes, which happen on 21 March or September. Spring tides are always higher at these times of year. The moon's orbit also takes it above and below the equator over a period of 27.2 days. Just as with the Sun, the tide generating forces are greatest when the moon is directly overhead at the equator.

The high tides predicted for 2015 are due to a very slow change in the moon's orbit, which is inclined to the plane in which Earth orbits the Sun. The moon's orbit cuts this surface at an angle of approximately 5 degrees. Over 18.6 years the moon's orbit slowly rotates around so it cuts through the solar orbit in a different place. This so-called nodal cycle has the effect of changing how far above or below the equator the moon can reach in its orbit.

In 2015 the moon's orbital excursion above or below the equator takes the minimum value of 18 degrees. This slightly increases the chances of the moon being directly overhead at the equator coinciding with the other factors that contribute to extreme tidal forces.

In some places, these extreme tidal conditions can cause water levels to be 0.5m higher than a normal spring tide. But it is important to remember that stormy weather has a greater impact than exotic tides. Storm surges, due to low pressure and high winds, can raise sea levels by up to 3m around the UK coastline.

Professor Kevin Horsburgh, from the National Oceanography Centre (NOC), said: "NOC scientists continue to lead the world in the study of tides and all factors contributing to sea level change. The 18.6 year cycle is a fascinating result of heavenly motions. Whilst many features of tides have been known for centuries we are still making new discoveries -- for instance we recently showed how slow changes in global sea level can affect the ocean tides."

Details of the highest tides each year can be found on the website of the National Tidal and Sea Level Facility.


8 Scientific Facts Everyone Should Know About Leap Day

February 29, which occurs on a Saturday in 2020, is known as Leap Day. But it doesn't occur every . [+] four years as some think, and it holds tremendous importance for keeping our calendar and the Earth-Sun system aligned over centuries and millennia.

Once every four years, at least under most circumstances, humanity inserts an extra day into our calendar year to help keep time: Leap Day. February 29 is a date that only rarely graces our lives, but plays an enormously important role: to keep our annual calendar and the passing of the seasons aligned over very long timescales. Despite a bizarre historical origin and a series of urban legends surrounding it, Leap Day exists for scientific, not superstitious, reasons.

Without a Leap Day, the physics of planet Earth would quickly cause the seasons to move out-of-phase with our annual calendar, and the equinoxes and solstices would drift around the days, months and seasons. In fact, if we did Leap Day every four years without fail, things wouldn't line up very well, either. Only if we properly account for our planet's axial rotation and revolution around the Sun can we keep our calendar correct, and that's what Leap Day is all about. Here are eight scientific facts everyone should know.

To travel once around Earth's orbit in a path around the Sun is a journey of 940 million kilometers. . [+] The extra 3 million kilometers that Earth travels through space, per day, ensures that rotating by 360 degrees on our axis won't restore the Sun to the same relative position in the sky from day to day. This is why our day is longer than 23 hours and 56 minutes, which is the time required to spin a full 360 degrees.

Larry McNish at RASC Calgary Centre

1.) There are not really 24 hours in every day. The Earth's motion has two basic parts: our rotational motion around our axis and our revolutionary motion around the Sun. Typically, we think about our rotation as lasting 24 hours, which is why a day is 24 hours, and our revolution as requiring 365 days, which is why a year is 365 days long.

Only, these effects are inseparable, as both motions are always occurring. If Earth were totally stationary, remaining in the same position, then a full rotation through all 360° would equate to a day. But that full 360° rotation isn't a day: it's slightly less by two metrics. First, it only takes the Earth 23 hours, 56 minutes and 4 seconds to rotate through 360°. But secondly, because the Earth moves through space in its orbit around the Sun, it has to rotate a little bit extra to position the Sun in the same relative location as it was in the previous day. That extra bit of required motion is what makes days, on average, 24 hours.

The equation of time is determined by both the shape of a planet's orbit and its axial tilt, as well . [+] as how they align. During the months nearest the June solstice (when the Earth nears aphelion, its farthest position from the Sun), it moves the most slowly, and that’s why this section of the analemma is pinched, while the December solstice, occurring near perihelion, is elongated.

Wikimedia Commons user Rob Cook

2.) Some days are actually longer than others. Have you ever wondered why the earliest sunrise and latest sunset don't occur on the summer solstice, and why the latest sunrise and earliest sunset don't line up with the winter solstice? It's because the Earth orbits the Sun in an ellipse, which means when the Earth is closest to the Sun (perihelion) it moves at its fastest, and when it's farthest from the Sun (aphelion), it moves most slowly.

Combine that with the fact that perihelion/aphelion doesn't line up with either the solstices or equinoxes, and you'll find that some days have less than 24 hours while others have more. The 24 hour day that we're used to is just an average of all the days throughout the year, and even at that, they don't line up perfectly.

Over the course of a 365-day year, the Sun appears to move not only up-and-down in the sky, as . [+] determined by our axial tilt, but ahead-and-behind, as determined by our elliptical orbit around the Sun. When both effects are combined, the pinched figure-8 that results is known as an analemma. The Sun images shown here are a selected 52 photographs from César Cantú's observations in Mexico over the course of a calendar year. Note that if we did not account for time properly, the analemma would shift position year after year.

3.) The Earth completing one revolution around the Sun doesn't add up to a calendar year. In astronomy, as in mathematics, a complete revolution is defined as when the Earth returns to the same position it occupied in space a full 360° orbit ago. In astronomy, this is what we call a sidereal (sigh-DEER-ee-ul) year, or the amount of time it takes the Earth to return to the same relative position it occupied earlier with respect to the Sun.

But a sidereal year is not the same as a calendar (also known as a tropical) year. The Earth rotates on its axis while it revolves around the Sun, and that axis precesses over time, which means that the Earth is oriented slightly differently with respect to the Sun when it completes one astronomical revolution versus the year prior. The difference between a sidereal and a tropical year is small only about 20 minutes but that means a calendar year, which is what you need to make the seasons line up, is actually 20 minutes shorter than a full revolution around the Sun.

Just 800 years ago, perihelion and the winter solstice aligned. Due to the precession of Earth's . [+] orbit, they are slowly drifting apart, completing a full cycle every 21,000 years. 5,000 years from now, the spring equinox and the Earth's closest approach to the Sun will coincide. This is a small, subtle effect that creates another minor departure from 24 hours being the exact length of a day, but it's negligible when compared to Earth's rotational motion on its axis and its orbital motion around the Sun.

Greg Benson at Wikimedia Commons

4.) The combined effects of Earth's axial rotation, orbital revolution, and precession give an uneven number of days in the year. Now we're getting to the fun stuff. If you do the math to the best of our knowledge, you wind up figuring out that there are 365.242188931 days in a true calendar year. This is not an even number. If we had 365 days in a year each year, each passing century would throw our calendar out of whack by almost a full month.

If we put a single Leap Day every four years, we'd account for 365.25 days on an annual basis, which is very close but not quite right. In fact, this is what the old Julian Calendar, which we followed for

1,600 years, did to account for the years. By the late 1500s, this difference was so apparent (our calendar was off by about 10 too many days), that the calendar needed to be revised.

In Italy, Poland, Spain, and Portugal, the dates October 5 through 14, in 1582, never existed. Other countries skipped those 10 days at a later date Isaac Newton was born on Christmas Day in England only because they hadn't skipped those dates by 1642. Elsewhere in the world, Newton was born in January 4, 1643.

Although a great many countries first adopted the Gregorian calendar in the year 1582, it wasn't . [+] until the 18th century that it was adopted in England, with many countries making the transition even later.

English Language Wikipedia

5.) The Gregorian calendar accounts for Leap Days extraordinarily well. The way we make up for the mismatch of our calendar year with the demands of Earth's combined motions is brilliant and relatively simple:

  • every year that is divisible by 4 is a leap year,
  • unless it's also divisible by 100 but not 400, in which case it's not a leap year.

This means that 2004, 2008, 2012, 2016, 2020, etc., will all be leap years, because they're all divisible by 4. But if your year marks the turn-of-the-century, it's only a leap year if it's also divisible by 400. The year 2000 was a leap year, but 1900 wasn't and 2100 won't be. All told, the adoption of the Gregorian calendar gives us 365.2425 days in a year, which means we won't be off by even a single day until more than 3,200 years have gone by, at which time we might want to skip another Leap Day down the road.

If we excluded every year that's divisible by 3200 from having a Leap Day, we wouldn't be off by a single day until

The Moon exerts a tidal force on the Earth, which not only causes our tides, but causes braking of . [+] the Earth's rotation, and a subsequent lengthening of the day. The asymmetrical nature of Earth, compounded by the effects of the Moon's gravitational pull, causes the length of a day on Earth to lengthen over time, and for the Moon to spiral outward from the Earth.

Wikimedia Commons user Wikiklaas and E. Siegel

6.) Over the long term, we'll need to change our calendar yet again. If everything were constant ⁠— our rotation rate, our axial tilt's orientation, and our orbital motion around the Sun ⁠— this calendar would be practically perfect, but only for now. Every time there's an earthquake, our rotation rate slightly speeds up, but that effect is swamped by the gravitational effects of the Sun and Moon on the Earth, which slow us down.

The slow-down effect is known as tidal braking, and clocks in at an average of 14 microseconds per year. That might seem negligible, but over time, it really adds up. If we examine the daily patterns that the tides imprinted on our soil from long ago, known as tidal rhythmites, we can calculate what Earth's rotation rate used to be. 620 million years ago, just before the Cambrian explosion, our day was a little under 22 hours long, which means that back when Earth first formed, our day was only 6-to-8 hours long. The lengthening days mean that, as time goes on, we'll need fewer and fewer days to complete a tropical year.

Tidal rhythmites, such as the Touchet formation shown here, can allow us to determine what the rate . [+] of Earth's rotation was in the past. During the time of the dinosaurs, our day was closer to 23 hours long, not 24. Back billions of years ago, shortly after the formation of the Moon, a day was closer to a mere 6-to-8 hours, rather than 24.

Wikimedia Commons user williamborg

7.) In four million years, Leap Days will be unnecessary. This extraordinarily slow effect of tidal braking will start to become important as the millennia continue to tick by. While right now, we're only adding a single leap second every 18 months or so to accommodate it, the day continues to lengthen. After another 4 million years go by on Earth, the day will lengthen by another 56 seconds: the exact amount necessary for a tropical year to require exactly 365 days.

At that point approaches, we'll want to first reduce the number of Leap Days and later get rid of them altogether, as they'll become completely unnecessary. If humans are still around and keeping calendars at that point, we'll want to think about further transitions, as we're going to need to begin skipping days (in a reverse-Leap Day scenario) in order to keep our seasons aligned with our calendar.

While approximately half of all eclipses today are annular in nature, the increasing Earth-Moon . [+] distance means that in approximately 600-700 million years, all solar eclipses will be annular in nature.

Wikimedia Commons user Kevin Baird

8.) The ultimate fate of the Earth-Moon system will be wildly different from what we experience today. As the effect of tidal braking continues, not only will Earth's rotation slow down, but the Moon will slowly spiral away from the Earth. In a few hundred million (but less than one billion) years, the Moon will be so distant from Earth that there will no longer be any total solar eclipses they will all be annular instead.

Assuming we survive the Sun's transformation into a red giant and planetary nebula/white dwarf combination, a day on Earth and the Moon's orbital period will both lengthen until they match: until they both take about 47 of our modern days, which will occur

50 billion years in the future. Instead of the same face of the Moon always pointing towards the spinning Earth, the Moon and Earth will be mutually locked, just as Pluto and Charon are with one another today.

A model of the Pluto/Charon system shows the two main masses orbiting one another. The New Horizons . [+] flyby showed that there were no moons of Pluto or Charon that were interior to their mutual orbits, and confirmed the mutual tidal lock between their faces.

Wikimedia Commons user Stephanie Hoover

We should all appreciate the need for Leap Days without them, the Earth's seasons, equinoxes, and solstices would all shift over time, rather than falling on the same date year after year. But, simultaneously, we should also appreciate that the length of a day is not constant, just as the number of days in a year is not constant. As time goes on and the Earth's rotation continues to slow, we'll need fewer and fewer days to make up a full calendar year, which will mean we'll require a constantly changing calendar system.

But for now, particularly on the scale of a human lifetime, the Gregorian calendar — where Leap Days occur every 4 years but not on centuries that aren't also divisible by 400 year intervals — will do just fine. Enjoy your extra day this year however you see fit, and remember that without these Leap Days, our calendar simply wouldn't add up.


Ask Ethan: Why Are The Moon And Sun The Same Size In Earth’s Sky?

Total solar eclipses are possible on Earth, and occur whenever the Moon aligns with the Earth-Sun . [+] plane during a new Moon phase, and is close enough for its shadow to fall on Earth. This has happened

3 billion times in Earth's history, but won't happen for much longer.

In our Solar System, there’s one overwhelming source of mass that all the planets orbit around: our Sun. Each planet has its own unique system of natural satellites that exist in stable orbits around it: moons. Some moons, like Saturn’s Phoebe or Neptune’s Triton, are captured objects that were once comets, asteroids, or Kuiper belt objects. Others, like Jupiter’s Ganymede or Uranus’s Titania, formed from an accretion disk at the same time the planets of the Solar System formed. But from the surface of Earth, we have just one Moon — likely formed from an ancient, giant impact — and it just so happens to be practically identical in angular size to the Sun. Is that just a wild coincidence, or is there some reason behind this fact? That’s what Brian Meadows wants to know, asking:

“From a scientific point of view, what are the chances that the Moon and the Sun would appear the same size in the sky?”

It’s a great question, and one that still has great uncertainties surrounding it. Here’s what we know so far.

Voyager 1 took this photo of Jupiter and two of its satellites (Io, left, and Europa) on Feb. 13, . [+] 1979. The four Galilean moons of Jupiter, along with most moons around the gas giants, likely formed from the initial circumplanetary disk that they each possessed in the early Solar System. (Universal History Archive/Universal Images Group via Getty Images)

Universal Images Group via Getty Images

As far as moons of the Solar System go, there are four known ways that they naturally form.

  1. From the initial material that formed the objects of the Solar System this is where most of the large moons around our gas giant planets come from.
  2. From collisions between a planet and another large body in space that kick up debris, where that material then coalesces into one or more moons around the planet.
  3. From other objects traversing the Solar System that become gravitationally captured by a parent planet.
  4. Or from material in a ring system around a planet that accretes to form a moon all on its own.

When we examine the moons found in our Solar System, we find strong evidence of all four types.

The planet Neptune and its largest moon Triton, as photographed by the Voyager 2 space probe in . [+] August 1989. Although it requires a very strong telescope to be able to see Neptune's largest moon, Triton, Neptune itself can be seen with an off-the-shelf pair of binoculars, if you know where to look. With 1846-level technology, discovering its presence was easy and unambiguous, once its location was known. Triton is the largest captured object in the known Solar System.

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But three of those types of moons — the ones that form from the initial Solar System material, the ones that get gravitationally captured, and the ones that form from accreted ring systems — are only found around the gas giant worlds in our Solar System. The moons that we find around smaller, terrestrial worlds, including Earth, Mars, and even objects like Pluto, Eris, and Haumea, are all consistent with their moons arising from one source and one source alone: ancient impacts between a large, massive, fast-moving body and the major world itself.

We didn’t always think this was the case, but an enormous suite of evidence now exists to support it. The Apollo missions returned samples of the lunar surface to Earth, where analysis confirmed that the material composing the Moon’s and the Earth’s crust have a common origin. Measurements of the composition and orbital parameters of Mars’s moons not only point to their creation from an impact, but indicate that a third, larger, inner moon was created, and has since fallen back to Mars. And most recently, measurements by New Horizons support a picture that Charon, Pluto’s giant moon (and likely the other, outer moons) all originated from a giant impact as well.

Rather than the two Moons we see today, a collision followed by a circumplanetary disk may have . [+] given rise to three moons of Mars, where only two survive today. This hypothetical transient moon of Mars, proposed in a 2016 paper, is now the leading idea in the formation of Mars's moons.

LABEX UNIVEARTHS / UNIVERSITÉ PARIS DIDEROT

So if you’re asking a question like, “what are the odds that an Earth-like planet would have a Moon that’s approximately the same angular size as the Sun as seen from that same planet,” here are the facts we have to consider.

  • The only way that we know of, so far, to get a moon around a rocky planet like Earth is to have some sort of giant impact in the planet’s past.
  • We’ve only ever detected moons around rocky worlds in our Solar System, never around rocky exoplanets, as the technology to do so isn’t there yet.
  • Of the rocky planets, Mercury and Venus have no moons, Earth has just the one of this “miracle” size, while Mars’s two surviving moons both appear much smaller than the Sun.

And yet, when we consider the parameters of Earth’s moon with respect to how we observe it compared to the Sun, we experience a remarkable set of circumstances that no other known system possesses.

When the Earth, Moon, and Sun perfectly align during the new Moon, a solar eclipse will result. But . [+] whether that's annular, total, or hybrid depends on the Moon's distance from Earth.

NASA'S SCIENTIFIC VISUALIZATION STUDIO

Here on Earth, the Moon orbits our planet in almost exactly the same plane that the Earth rotates on its axis: another piece of evidence that points to our Earth and Moon having a common origin from a giant impact. When the Moon happens to pass directly between the Earth and the Sun, and all three bodies are perfectly aligned, we experience a phenomenon known as a solar eclipse. This is common to all worlds with moons that cross the planet-Sun plane, but Earth and our Moon are unique in a very exciting way.

On Earth, we can experience three different types of solar eclipse with a perfect alignment:

  1. Total solar eclipse — where the Moon appears to entirely block out the disk of the Sun.
  2. Annular solar eclipse — where the Moon fails to block out the Sun’s disk, creating an annulus (or ring) of visible Sun circumscribing the eclipsing Moon.
  3. Hybrid solar eclipse — where the Moon fails to block the entire Sun for a portion of the eclipse, but does successfully block the entire Sun for a different portion.

Right now, the largest (perigee) full Moon appears bigger than the Sun at all times of the year. . [+] However, over time, the Moon will migrate away, causing its angular diameter to shrink. When the perigee full Moon is smaller than the aphelion Sun, no total solar eclipses can occur anymore.

EHSAN ROSTAMIZADEH OF ASTROBIN

Earth only experiences all three types of solar eclipse because the Moon, in its elliptical orbit around the Earth, can appear either larger or smaller than the Sun does due to Earth’s elliptical orbit around the Sun. This is no doubt a rarity neither of Mars’s moons is ever large enough to eclipse the Sun totally, as every eclipse from Mars is annular. Moreover, if Mars did have a third, larger, inner moon at one point, its eclipses would have always been total eclipses annular or hybrid eclipses would have been impossible.

But there’s another point to consider: these three possibilities weren’t always what Earth experienced, and they won’t always be what Earth experiences, either. The story of our Solar System, as best as we can reconstruct it, tells a tale of an ever-changing relationship between the Earth, Moon, and the Sun. It began some 4.5 billion years ago, where our ancient protoplanetary disk, which gave rise to all the planets, began to fragment into clumps that grew, interacted, and both merged and ejected one another. There were two types of survivors: large, massive planets that held onto hydrogen and helium envelopes, and smaller, less-decisive victors, which become planets and dwarf planets.

The Solar System formed from a cloud of gas, which gave rise to a proto-star, a proto-planetary . [+] disk, and eventually the seeds of what would become planets. The crowning achievement of our own Solar System's history is the creation and formation of Earth exactly as we have it today, which may not have been as special a cosmic rarity as once thought.

These early planets, planetoids, and planetesimals interact and sometimes collide, and those collisions — when they occur — tend to kick up large amounts of debris that surround the major planet. This shroud of post-impact material around the planet is known as a synestia, and although it’s short-lived, it’s incredibly important. Most of that material winds up falling back to the parent planet, while the rest coalesces into one or more moons. In general, the innermost moon will be the largest and most massive, and then you’ll have smaller, less massive moons that can exist at greater distances.

These moons exert differential forces on the planet: they gravitationally attract the portion of the planet that’s closer to the moon with a greater force than the portion that’s farther away. This not only creates tides on the planet, but it also results in what we call tidal braking, which causes the main planet to slow its rotation and the moon(s) to spiral away from the planet. Of course, there’s a competing effect: the planet’s atmosphere can create a drag force on the moon, drawing it closer to the planet. Depending on how the moons initially form, either effect can win.

A synestia will consist of a mixture of vaporized material from both proto-Earth and the impactor, . [+] which forms a large moon inside of it from the coalescence of moonlets. This is a general scenario capable of creating one single, large moon with the physical and chemical properties we observe ours to have. It is more general that the Giant Impact hypothesis, which involves a collision between Earth and a hypothesized co-orbiting protoplanetary world: Theia.

S. J. Lock et al., J. Geophys Research, 123, 4 (2018), p. 910-951

In the case of Mars, the drag force appears to have won, drawing the innermost moon in over time, the next moon, Phobos, will eventually fall back onto Mars as well. In the case of Pluto, tidal braking is complete, and the Pluto-Charon system is now a binary planet, where Pluto and Charon are both tidally locked to one another, surrounded by four additional, outer, smaller moons.

But the Earth-Moon system is fascinating. The current thought is that, early on, the Moon was very close to Earth, and there may have been a number of smaller, outer moons beyond our own. Earth, back more than 4 billion years ago, may have been rotating incredibly rapidly, completing a 360° rotation in just 6-to-8 hours. A year, back in Earth’s early history, may have had as many as 1500 “days” in it.

But over time, the tidal friction of the Moon slowed that rotation tremendously, an act which transfers angular momentum from the spinning Earth to the orbit of the Moon. Over time, this causes the Moon to spiral away from the Earth.

The asymmetrical nature of Earth, compounded by the effects of the Moon's gravitational pull, causes . [+] the length of a day on Earth to lengthen over time. To compensate and conserve angular momentum, the Moon must spiral outwards.

WIKIMEDIA COMMONS USER ANDREWBUCK, MODIFIED BY E. SIEGEL

For billions of years, until only a few hundred million years ago, all of the solar eclipses on Earth were total eclipses the Moon was close enough that it always blocked out the Sun from our perspective. In 570 million years, Earth will experience its final total solar eclipse, and in another 80 million years, its final hybrid solar eclipse. After that, all of Earth’s solar eclipses will be annular.

This means that when we look from Earth at the Moon today, and compare its angular size to that of the Sun today, we see three different types of solar eclipses, but that this is a temporary situation. The evidence indicates that, early on, the Moon was much larger in angular size than the Sun was, and that there may have been additional moons farther out. Over time, our Moon has spiraled away, and if there were smaller, more distant moons, they’ve been ejected. In the far future, the Moon will spiral out even farther, and will become eternally smaller in our sky than the Sun will ever be, for the remainder of its lifetime.

While approximately half of all eclipses today are annular in nature, the increasing Earth-Moon . [+] distance means that in approximately 600-700 million years, all solar eclipses will be annular in nature.

WIKIMEDIA COMMONS USER KEVIN BAIRD

When you ask the question, “what are the odds that an Earth-like planet will have a Moon that’s comparable in angular size to the Sun,” you’re really asking what the odds are of:

  • having an Earth-like planet, which is an Earth-sized planet at the right distance from its star for liquid water on its surface,
  • that experienced a giant impact in its early history, creating a synestia,
  • where the planet itself winds up rotating rapidly after that collision,
  • where a large, inner moon gets created but won’t fall back onto the planet,
  • and then spirals away as angular momentum gets transferred from the planet to the Moon.

It’s remarkable that science, despite only having information about moons around terrestrial planets in our Solar System alone, has uncovered the ingredients necessary to create the situation we have today. If you assume you get an Earth-like planet, our best estimates have enormous uncertainties, but may lead to a total probability in the range of around 1-10%. To really know the answer to this question, however, we’ll need more and better data, and for that, we’ll need to wait for the next generation of astronomical observatories.

The answers are out there, written on the face of the Universe itself. If we want to find them, all we have to do is look.


Why are most moons tidally locked?

With the exception of Pluto's smaller moons, all the moons in the Solar System are, to my knowledge, tidally locked with their respective planets. Why is this?

Most major moons in the Solar System, the gravitationally rounded satellites, are tidally locked with their primaries, because they orbit very closely and tidal force increases rapidly (as a cubic function) with decreasing distance.

But I don't honestly have any idea what any of this means.

Tides are a small bulge induced by gravity differences when two astronomical bodies interact. You can see that with the sea, but it also works on rocks. It is less noticeable, but has been detected on earth (most notably with the large hadron collider).

When the smaller body is not tidally locked with the larger one, the bulge is not always in the same place (as are our sea tides). The rotation of those moons induce a small shift on where the bulge is compared to where it would be if the moon was tidally locked (as much as sea takes time to go up and down, so do the rocks). Gravity pulls on the misaligned bulge, acting as a break on the small body's rotation until it is in step with its rotation around the bigger one.

The closer you are to the bigger body, the stronger its influence on the smaller one.

Does this mean the planets in the solar system will on day become tidally locked with the sun?

Gravity pulls on the misaligned bulge, acting as a break on the small body's rotation until it is in step with its rotation around the bigger one.

This is not always true as it depends on the sign of the difference of spin and orbital frequencies. That is the tidal evolution can result in a spin up or spin down of either of the bodies in the system.

The vast majority of the moons are not tidally locked.

Most major moons in the Solar System

This is an important keyword here. The big moons tend to be tidally locked. They formed with the planet and close to it, they experience large tidal forces if they are not locked which makes them tidally locked over time. But most moons are small and in distant and irregular orbits around the gas or ice giants, these are not tidally locked.

Some of the other comments are close, but dancing around what actually causes the rotation to slow. To change the rate of rotation there must be a net torque (moment if you're an engineer) acting on the object. A torque occurs whenever a force is exerted at some distance from the axis of rotation with the force directed not exactly toward or away from the axis.

So how do we get a torque from gravity? First of all, gravity exerts a stronger force on the near side of the moon than the far side, because it's closer to the planet and gravity decreases with distance. This difference in force, as others have said, is known as a tidal force and it stretches the moon into a bit of a bulged shape, known as an ellipsoid, sort of like an egg.

However, because the egg shaped moon is rotating and it takes time for this deformation of the moon to move around the moon as it rotates, the result is that the long axis of the ellipsoid doesn't point directly at the planet, but ends up rotated slightly ahead of a line pointing directly at the planet.

Now, the moon is rotating about its center of mass, which is in the geometric center of the moon. However, the net effect of gravity is exerted, not at the center of mass, but at the center of gravity, which is the average lcoation of all the gravitational pulls on all the bits of mass that make up the moon. On earth, where the gravitational field is basically constant, your center of mass and center of gravity are pretty much in the same place, but remember gravity is stronger on the near side of the moon than the far side, because the moon is much larger than you. This means that the center of gravity of the moon is moved from the geometric center a bit closer to earth along the long axis o fthe ellipsoid. Which means that the net pull of gravity is at this point, which is in a different location than the axis the moon rotates around as it runs through the center of mass.

So we have met the first condition for a torque, in that the net force isn't at the axis of rotation. And since there is the time delay for the bulge to move around, making the long axis of our ellipsoid/egg-shaped moon not directly aligned toward the planet, that means that net gravitational pull isn't quite directed out from the geometric center of the moon either. Thus we have also met the second condition for torque, creating a torque caused by gravity that acts to slow the moon's rate of rotation.


Question of the Week: All the Planets Spin West To East, Except One. Why Does It Spin In the Opposite Direction?

Question of the Month Submitted by Michael Dole, Covina, Calif., and answered by Peter Goldreich, Lee A. DuBridge Professor of Astrophysics and Planetary Physics at Caltech.

You're undoubtedly thinking of Venus as the planet that spins east to west. In other words, if you arrived on Venus in the morning, the sun would be in the west and would set in the east. The only thing is that it would set about four Earth-months later! That's because a day on Venus lasts for 243 of our Earth-days.

Actually, you should probably add Uranus to your list of planets in retrograde (or "backward") rotation, because it is tipped more than 90 degrees. The day would be a short one, because Uranus completes a rotation on its axis every 17 hours, which is a pretty typical time for all the gas giants. The Uranian year is 84 Earth years. Over that time there are large seasonal variations at the poles as they alternately point toward and away from the sun.

As a rule, the inner planets (the solid ones) have much longer spin periods. Mercury completes three rotations every time it goes around the sun once because it is in a tidal lock with the sun, in a manner similar to the tidal lock that causes the moon to always face Earth. A day there lasts about 30 Earth-days.

Mars has the same spin period as Earth, but the angle between its spin axis and the axis of its orbital angular momentum is predicted to vary chaotically between about 11 and 44 degrees on a time scale of millions of years. This is due to the gravity of the sun and other planets. So if you go to Mars now, the sun would rise in the east southeast if you landed at a Southern California latitude during the summer. But if you wait a few million years, the planet might be so tilted that the sun would come up a few degrees north of east each morning while you were at that same latitude at the same time of year.

To get back to your question, nobody knows why the planets have the spins they have. It's plausible that the spin rates date back to the formation stage of the solar system, which began about 4.6 billion years ago and lasted about half a billion years. Because fairly big bodies were being gobbled up by the planets that we observe today, the inclinations of the axes as well as the spin rates are probably relics of these collisions.

Probably, both Venus and Uranus originally rotated from west to east, just like the other seven planets. Perhaps the collisions of other bodies with these two planets flipped them over permanently. In the case of Venus, the tidal effect of the sun's gravity also undoubtedly had a profound effect.