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Hypothetically, suppose there is a situation where the Earth's moon gets neatly sliced into two equal hemispheres, and the force responsible for this slicing also creates a distance between the two halves of say, half the (average) distance from the Earth to the Moon, as it originally stood.

Do the two halves revolve around each other? Do they rotate individually? Do they each still revolve around the Earth?

EDIT: The angular momentum of each half after the division is the same as the angular momentum of the moon before the division occurred.

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Unless the force also creates an angular momentum between the two halves so that one orbits around the other, the two halves fall together again and make a really big explosion. –  Peter Shor Jan 21 '13 at 18:47
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As Peter Shor hints, this problem isn't well defined. To evolve the system, you need to specify two of (energy | position | velocity | angular momentum) for each object. You've given the initial positions, but it's not clear how fast everything is moving when you are all done rearranging things. –  Chris White Jan 21 '13 at 21:16
    
Noted. Will make the necessary changes. –  chubbycantorset Jan 22 '13 at 5:50
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Do you really mean that the angular momentum of each half is the same as the original, rather than the angular velocity? If it's the angular momentum then they will each have twice the angular velocity and they will either enter highly elliptical orbits or leave the Earth altogether (I think it's the latter), whereas if it's the angular velocity then they will be in orbits similar to the original one, and the answer is given by Peter Shor's comment. –  Nathaniel Jan 22 '13 at 6:00
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Also, you probably know this, but they wouldn't stay hemispherical for very long because rock isn't strong enough to prevent gravity from re-shaping them into more spherical shapes. –  Nathaniel Jan 22 '13 at 6:04
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2 Answers 2

the moon is like a piece of chalk. If you hit a piece of chalk with a trajectory it will split in two halves, not three halves. the two halves will ultimately refuse again because of the gravity of the two halves are much greater than the gravity of the earth because earth is too far, while the two halves are too close to each other. , you can see the craters belt splicing the nearside of the moon from north pole to south pole. how could craters happen on the nearside from space astroids? it is impossible because the astroids have to come from the space side of the earth, so they will hit earth first. even if few astroids escaped collision with earth, why craters are on a line from north to south pole of nearside of moon? why not random? obviously when the two halves fused again the debris jettisoned from the impact and but moon gravity pulled them back again and that is why they hit the moon near the fusion line. You don't need scientists or even a telescope to see the craters belt. the moon dried long time ago it was a piece of chalk even 4 billion yeaars ago when the earth was still melting. the moon is a scrap from the driedup crust of the earth. thewre is no iron core in the moon. so the moon never was melting, where the iron will have the collapse momentum found on all planets. it is a piece of chalk. it's split is a matter of "Modern physics" DIY at home thing. get a piece of chalk and press on it with a pen, and vwalla, the chalk breaks in two halves. mystery solved.

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In general two moons orbiting at the same distance is an unstable configuration, so unless you choose the initial positions and velocities of the two halves very carefully they will eventually either collide, or one or both will be ejected from orbit.

There are stable configurations for two moons e.g. the two satellites of Saturn, Janus and Epimetheus, share the same orbit, but this is a special case and is rare. Also I'm not sure if this configuration would still be stable if the bodies were as large as (half of) the Moon.

There are two points, the Lagrangian points L4 and L5, where two moons could form a stable orbit, however these points are unstable to small perturbations so moons in these positions wouldn't be stable for long.

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