# Wondering about a horseshoe orbit

Since I'm not a physicist, I want to know how that system works. For instance, if there was a planet, very similar to the Earth, but with two moons, and the moons where in a horseshoe orbit, how does it work? Is it stable?
I need it explained in an easy way, and also how would the moons look like from the Earth? Thanks!

• Welcome to Astronomy Stack Exchange! Can you explain what exactly confuses you? Also, consider taking a look at Janus and Epimetheus. – HDE 226868 May 31 '17 at 14:54
• There's a nice pair of animations showing the horseshoe shaped orbit of asteroid 3753 Cruithne. I think that might be useful to you. – StephenG May 31 '17 at 19:10
• What orbits what? Normally, “moon” implies that they would orbit your Earth; but then you could only get a horseshoe orbit of one of the moons as seen from the other moon. – chirlu May 31 '17 at 19:19
• @chirlu actually, if you have a large moon and a smaller moon in horseshoe orbits to each other and you have the planet tidally locked to the large moon, then from the planet's surface the smaller moon does a horeshoe orbit, so it is possible to be observed from the planet too. Imagine the fun stories the ancient Greeks would have told about that one. :-) (the duel shadows would have made calculating the suns distance easier.) – userLTK Jun 1 '17 at 1:50

A basic orbital rule is Kepler's third law, which states that the closer the moon is to the planet, the quicker is its orbit. A body that is close to the Earth will move in orbit faster than one which is distant.

The fundamental weirdness: If a body is in orbit, and you give it a push in the direction it is moving, it will gain energy, move away from the planet, and slow down. Contrariwise, If you give it a pull back, it will drop to a lower orbit and speed up. This is fundamentally weird because we are used to the idea that if you push something it will speed up, for bodies in orbit the opposite happens. Make sure you understand why this is.

Now suppose we have two moons, a big one and a little one. The big one is in a circular orbit (and is big enough that the orbit won't change) The little one is on the opposite side of the planet, and slightly closer to the planet than the big moon (only slightly closer). The little one is also in a circular orbit, in the same direction as the big moon.

Since the little one is closer to the planet, it orbits faster than the big moon, so will slowly catch up the big moon.

As it catches up the big moon, the pull of the big moon's gravity will pull the little moon forward. Now remember the fundamental weirdness: if the little moon is pulled forward, it will move away from the planet and slow down. The big moon is also pulled, but we'll suppose the big moon is big enough for the gravity of the little moon to be negligible.

Now the little moon has slowed down. It is still going in the same direction as the big moon, but now it is going slower, so it falls behind the big moon. Eventually it falls so far behind that the big moon begins to catch it up.

Now the gravity of the big moon is pulling the little moon back, and because of the fundamental weirdness, this makes the little moon drop towards the planet, and speed up.

The process can now repeat itself, with the little moon repeatedly catching up, then falling back from the big moon. An observer on the Big moon would see the little moon slowly approach then fall back, go behind the planet, approach on the other side, then fall back again. It would appear to move in a horseshoe shape, relative to the big moon. Relative to the planet, both moons move in circles or near circles.

How stable it is depends on all sorts of things: tides, other planets, the effect of the little moon on the big. However such orbit can be stable over long periods of time. But perhaps not over the 5 billion years of the solar system.

• Thanks! It's clearer now :) I also was wondering how would like from the Earth-like planet at night (considering the cycles of each moon too)? – C. Marshall Jun 1 '17 at 2:30
• The two moons would both move in near circles around the planet. Sometimes they would be closer, other times they would be further. But the motion of each would be very similar to that our moon. – James K Jun 1 '17 at 6:16