An object with negative mass accelerates in the opposite direction to the force applied to it, since F=ma.

So, which way will an object with negative mass fall under gravity?

Since F=GMm/r^2 (where m is the mass of the less massive object). If m is negative (which G also is) the force is positive. Positive forces repel and negative forces attract. Therefore the force would be acting away from the Earth, pushing the object upwards.

But the negative mass accelerates in the opposite direction to the force, so should still fall down.

This makes sense when you consider the fact that objects have the same acceleration due to gravity regardless of mass.

So, which way will an object with negative mass fall under gravity?

Since F=GMm/r^2 (where m is the mass of the less massive object). If m is negative (which G also is) the force is positive. Positive forces repel and negative forces attract. Therefore the force would be acting away from the Earth, pushing the object upwards.

But the negative mass accelerates in the opposite direction to the force, so should still fall down.

This makes sense when you consider the fact that objects have the same acceleration due to gravity regardless of mass.