situation 1:

M100----------**X**----------M100

situation 2:

M100--**X**------------------M10

situation 3:

M100**X**--------------------m1
M=Mass (of an orbiting body).

100/10/1=Arbitrary masses of orbiting bodies.

**X**=Common centre of gravity for two body system.

Here is why the orbit of the moon would change were it replaced with an apple.

Above we have three situations. In situation 1 two bodies of mass 100 (M100) are in orbit. They do not form a system where one orbits the other. Instead they both orbit a common centre of gravity (

**X**). Just imagine each body being on the end of a T-section pole is being rotated at the red X. This rule applies in all cases.

In situation 2 the mass of the second body has been reduced (to 10). Thus the centre of gravity moves toward the larger body. The large body (

M) will orbit the centre of gravity. Being much closer to the centre its orbit will be smaller than in situation 1. The smaller body (M) will now be much farther from the centre of gravity. Thus its orbit will be larger than in situation 1.

In situation 3 the mass imbalance is very one sided. The centre of gravity for both bodies will likely be not much different from the centre of gravity for the larger body. Thus the large body will orbit a point near its own centre. This will leave it with little orbit at all. The smallest body (m) will orbit the centre of gravity and is almost as far from that centre as physically possible. Thus its orbit will be nearly the largest it could possibly be.

To model the moon/apple situation I should properly add a situation 4. This is because I somewhat overestimated the effect a change in mass from moon to apple would have. The centre of gravity for the earth/moon situation is already very close to the centre of the earth. Changing the moon to an apple would only move that centre a few thousand kilometres.

So I think it's pretty clear cut that the orbit will change if we were to replace the moon with an apple. If I am somehow incorrect then I'd appreciate an explanation of exactly how that is.