Recall that F=ma, a=F/m. Assuming that you have a negative mass, acceleration for an object will have to be in the reverse of the force excerted. You push a -m object left, it accelerates right.
Now, also recall that force of gravity Fg m1*m2 at any given radius. Now, assuming that m1 and m2 are positive, you will get a positive force, which means towards each other.
But now let's throw in one negative mass object. You'll then get a negative Fg, right? Which you'd think would mean that the objects fly apart, but remember that a negative mass object will go in the opposite direction of a force that's applied. That means that the negative mass object will be move towards the positive mass object, and the positive mass object will move away from the negative mass object. These will cancel out if the masses are the same. However, if, for example, you were on the earth with a small negative-mass object (let's give it a mass of 1kg, and it's on the surface), you would have:
Fg=-9.8 N
"dropping" the -1kg mass would result in the earth accelerating away from the negative mass at virtually 0m/s/s, while the -1kg mass would accelerate TOWARDS the earth at a rate of 9.8m/s/s
That said, the -1kg mass would indeed fall DOWN.
Using the same math and logic, it would follow that:
If the negative mass object is less massive than the positive, the objects would be pulled together.
If the negative mass object is more massive than the positive, the objects would fly apart.
If the negative mass object were more massive than the positive mass object, the objects would fall apart
If the masses are the same, no acceleration would be observed.
