If the earth had a second moon, could the moons ever cross? How and when?

May 30, 2012 2:12 PM

Imagine that the earth is hit by another Mars-ish sized object causing a second moon to be formed. If the second moon were orbiting the Earth inside or outside of the orbit of The Moon, and assuming it was not orbiting the Earth parallel to The Moon, the two moons would have to cross each other at some point, right? A sort of moon-over-moon eclipse thing. How would you calculate how often this would occur? What would it look like? Does this happen on planets with more than one natural satellite? Does the premise of this question make no sense because my knowledge of astrophysics is basically nil? Explain to me like I am in fifth grade, please.

As I understand it, the moon orbits around the earth where it does based on a common center of gravity. So if this second moon were to be larger or smaller, would the second moon be able to orbit inside or outside of The Moon's orbit?

If so, then could it orbit Earth on a plane that wasn't parallel to The Moon's orbit?

If both of those things happened, then ostensibly the moons would have cross each other at some point, right? Is there a name for this? How would you calculate how often/when this would occur?

If this happened, what would it look like? If the moon is reflecting light from the sun, would one moon crossing over the other just block out the light reflecting from the farther moon?

Are there any other weird things (like weird tidal things or the like) that would drastically change by having a second moon?

Does this not make any sense whatsoever because I've gotten some basic premise about gravity and mass and orbits mixed up?

Please explain to me like I don't know much about how the movements of celestial bodies work, because I don't.

Thank you Metafilter.

posted by Lutoslawski to science & nature (7 answers total)

This sort of thing happens in planetary systems with multiple moons, such as Jupiter's. You would calculate the orbits using calculus.
posted by longsleeves at 2:35 PM on May 30, 2012

A collision between the Earth and a Mars-sized object didn't create a moon -- it created a cloud of debris, some of which fell back to Earth and some of which escaped Earth's gravity, and some of which was moving fast enough to fall into an orbit, creating a ring. One theory I heard is that the moon's core is the core of the colliding planet, which swept up the debris, making such a large moon for such a small planet. Otherwise, varying speeds and collisions means, over many millions of years, the Moon was created through collisions and aggregation of those bits that didn't fall back to Earth and didn't reach escape velocity.

So, if this happened with a Moon already in existence, it's really unlikely we'd get two Moons. What would probably happen is that the initial impact would create a huge debris cloud around the Earth, and the new mass of the Marslike would change the center of gravity a bit. The gravity of the Earth would increase due to the added mass of the Marslike, and the existing Moon would sweep up the debris cloud, adding to its mass. Earth would get bigger, the Moon would get bigger. Because there's two massive objects already orbiting here, another massive Moon would be likely to crash into either of the existing planets long before ending up in its own stable orbit.

Now, depending on the energy involved, sweeping up debris, in theory, slows down the Moon due to collisions. The new mass increases the gravity of both. Gravity is a function of speed -- you're falling fast enough to keep "missing" colliding with the Earth. A slower Moon, with higher gravity, might mean another collision on the way. It's also possible that the Marslike impact moves the Earth or the Moon far enough that it keeps the orbit in something stable, preventing a Moon-crash, we hope.

So, that's not to say there won't be more than one 'moon', just not another Moon. As I said, orbit is a function of speed, so if something is going fast enough to not crash into the Moon and not crash into the Earth, but also not reach escape velocity and leave the system, then it will be a new natural satellite, a small moon like the ones Mars has. It would have to be going pretty fast, and be pretty small, to exist in between the current Earth and Moon, or be very slow and be outside of the Moon's orbit. Yes, there'd be new eclipses for both the Moon and the Sun, but it's unlikely that this new moon will have the same size-to-distance ratio that our Moon has with the Sun, causing complete eclipses.
posted by AzraelBrown at 2:35 PM on May 30, 2012 [1 favorite]

If you set aside the whole "collision" part and just magic a new moon into existence, we can still address the remaining questions:

So if this second moon were to be larger or smaller, would the second moon be able to orbit inside or outside of The Moon's orbit?

Orbits can be large or small, independent of the mass of the orbiting object (basically the smaller the orbit the faster the thing has to be moving to avoid falling into the center.) So the new moon could be anywhere: inside the existing moon's orbit, or outside it. Or it could be in a different plane, or on some funky elliptical shape, or whatever. (Planets and moons tend to all be in the same plane in real life, but IIRC this is a result of how the solar system formed, it's not a necessary result of orbital mechanics.)

Technically the moons and earth would be orbiting around the point which is the center of gravity for all three objects considered together; if the moons were close in mass to the earth, or were close enough together that this center point would move around substantially during the orbits, this would get Very Complicated To Figure Out. But for a moon-sized moon (1/80th the mass of the earth) you can basically ignore that and just pretend it's all orbiting around the center of the earth, because close enough.

ostensibly the moons would have cross each other at some point, right?

By "cross" I assume you mean as in an eclipse: the earth, the moon, and the new moon all arranged in a straight line, right?

Assuming the new moon is on the same plane as the old one, then yes, this would happen regularly because each moon would have to be traveling at different speeds. How often would depend on the particular orbits. (For circular orbits, the math for how often would look like this. For elliptical orbits, it would be more complicated.)

If the new moon is in a different plane, then they wouldn't necessarily ever line up like this.

If this happened, what would it look like?

It'd pretty much just look like one moon moving behind the other in the sky.

Are there any other weird things (like weird tidal things or the like)

Yeah, tides would be really complicated -- there'd be extremely high and low tides when the moons line up, and a bunch of irregular-seeming mini-tides the rest of the time instead of the regular pattern we're used to, as each moon pulls in different directions.
posted by ook at 3:01 PM on May 30, 2012 [1 favorite]

This sort of thing happens in planetary systems with multiple moons, such as Jupiter's. You would calculate the orbits using calculus.

longsleeves, Jupiter's moons (and pretty much every other known multi-satellite system) operate with the moons all rotating the same direction in a single plane - which is how I interpret the OP's "orbiting the Earth parallel to The Moon". So, this isn't what happens. A non-coplanar satellite would add a lot of instability to the system, and eventually probably lead to collision.

An exception is Pluto, which is slightly canted w.r.t. the rest of the planetary plane - but it's small and faaaar out, so it has minimal effects. In fact, it's "eccentricity" is part of how it was discovered, due to the gravitational effects on Uranus.

Also, since the three-body gravitational problem doesn't have a known solution, we don't actually calculate the orbits with calculus. We calculate them with (a sort of fancy) piecewise approximations.
posted by IAmBroom at 3:46 PM on May 30, 2012 [1 favorite]

Mars has two small moons, Phobos and Deimos, both much smaller than Earth's moon, and much closer-- Phobos is so close to Mars that you can't see half of Mars from its surface.

Phobos orbits in less than 8 hours, while Deimos takes over a day, and the ratio of their periods is almost exactly 4:1. (Using Earth days here, but the Martian Day is 24 hours, 41 minutes, so...) The reason for the "almost" can be credited to the orbit of Mars around the Sun and a few other things.

When you have multiple bodies in orbit, the ones that stay in orbit are the ones that're harmonically balanced with everything else that influences it. As described above, the debris that formed the moon must've initially been in a cloud around the young Earth, but the cloud was swept out-- some of it had a motion that was repetitively amplifed by other objects in space (i.e. the sun, Jupiter, maybe Mars) while others had orbits that were damped by same. That which is amplified or damped generally doesn't survive in orbit, but those bits whose orbits struck a balance, they can stay around to coalesce into things. That is to say, Nature tried every possible orbit (or at least covered the spread very well), and only the crap that formed a stable system is left today, because the unstable crap long ago paid the consequences of even the tiniest instabilities in orbits.

Likewise, the Asteroid belt between Mars and Jupiter is constantly stirred by those bodies, so the belt can continue to exist in its volume, but it can't coalesce for the same reason. In fact, what applies to the planets applies to the solar system, which was once all gas and dust at one point-- the Sun was just the heavy thing in a big spinning clot of gas and crap that formed after whatever hot young stars predated our own. The planets coalesced from that gas and dust (initially called a planetary nebula) just as the sun coalesced from the heavy center (and consumed most of the matter).

As to the particular case of adding a moon to the Earth-Moon system, yes, a smaller moon (or, god forbid, a larger one) could orbit inside Moon's orbit, but not just any size, and not just any orbit would work in a stable system.
posted by Sunburnt at 4:30 PM on May 30, 2012

Are there any other weird things (like weird tidal things or the like) that would drastically change by having a second moon?

The drastic change would be that both the earth and moon would feel a gravitational force from the new, third body. A gravitational system of three or more bodies is inherently unstable, unless certain limiting conditions are met. In particular, planets are able to sustain more than one moon because the masses of the moons are much smaller than the mass of the planet. This is also what makes the sun/earth/moon system stable -- the masses of the earth and moon are much smaller than the mass of the sun. The technical term for these systems is restricted three body problems. The key restriction is that one or more of the masses must be negligibly small compared to the largest mass, but there are other restrictions (the orbits must be close to circular and lie more or less in the same plane).

The general three body problem, in which masses are arbitrary, and orbits are neither circular nor co-planar, is known to be highly chaotic and unstable. So if a second moon were to orbit the earth, any of these three conditions might cause the entire system to quickly destabilize:

1. The mass of the new moon is comparably large to the mass of the earth (our original moon already meets this criteria).
2. The orbit of the new moon is eccentric (non-circular).
3. The orbit of the new moon is not co-planar to the old moon.

Again, the key criteria is the mass of the new moon. Satellites meet the small mass criteria and orbit the earth just fine, in several different planes (I don't know how eccentric their orbits get). Strictly speaking, you could have a large second mass orbit the earth, but it would have to meet criteria 2 and 3 to such an exacting degree that such an event is highly unlikely (i.e. impossible in the scenario you describe).

Finally, the inevitable result of an unstable three body system consisting of the earth and two large moons is either a collision or a decoupling (earth/moons flung into deep space).
posted by grog at 6:54 PM on May 30, 2012

I can't comment on the likelihood of getting to satellites in coplanar enough orbits for this to happen. But if it did happen it would look a little something like this.
posted by cirrostratus at 9:18 AM on May 31, 2012