How do matter and antimatter interact gravitationally? Me and my brother were watching television tonight, and he asked me a question that was somewhat along the lines of this:

What would happen if the Earth was made of matter, and the moon was made of antimatter?

I tried to answer this, saying a few things about how atoms attract, and such, but I then realized I didn't actually know the answer to this.
I'm now curious as to how matter and antimatter interact gravitationally. Do they attract? Repel? I'm specifically wondering what would happen on a planetary scale, but the nitty-gritty particle interactions would be nice too.
 A: 
What would happen if the Earth was made of matter, and the moon was made of antimatter

To start with, our elementary particle physics standard model has antiparticles which have the same mass as particles and all the quantum numbers,  charge, baryon number ...,  the opposite. What happens when a particle meets an antiparticle is that the quantum numbers annihilate  (add up to zero) and the energy of the two masses is freed to become other particles/antiparticles , from photons to electron positron  etc, as long as the total quantum numbers add to zero.
This model is validated by innumerable data. As an antiparticla has the same type of mass , i.e. positive,  the hypothesis is that antiparticles behave under the force of gravity the same as particles.
Wnen antimatter ( like antihydrogen, which has been created in the lab) meets matter (hydrogen) the same thing happens. Annihilation of quantum numbers and release of energy.
We know that the moon is composed of matter from the gross experiment of having landed on it. No explosion resulted.
Any dust, meteorite small or large, of matter hitting the moon would create explosions and thus we know it is not made of antimatter. This argument extends up to  galaxies , because we would be detecting the specific annihilation radiations if an antigalaxy or even a cluster of antigalaxies existed.
Now the same gravitational interaction is a hypothesis  and is being tested in the AEGIS experiment at CERN:

A system of gratings in the deflectometer splits the antihydrogen beam into parallel rays, forming a periodic pattern. From this pattern, the physicists can measure how much the antihydrogen beam drops during its horizontal flight. Combining this shift with the time each atom takes to fly and fall, the AEGIS team can then determine the strength of the gravitational force between the Earth and the antihydrogen atoms.
The AEGIS experiment will represent the first direct measurement of a gravitational effect on an antimatter system.

So current knowledge tells us that an antimatter moon would behave the same as a matter moon as far as gravity goes. Maybe AEGIS will find something different.
One should add that an antimatter moon in a matter planetary system, or where there exists matter and antimatter would not last long (in cosmological times) due to the explosions from matter meteorites falling on antimatter.
