The nature of the gravity force: Is it attractive or repulsive between positive and negative mass? [duplicate]

Question

If negative mass is rotating around fixed positive mass, then what will be the nature of force and how?

Answer 1

This is a fundamentally pointless question because negative mass doesn't exist (or so we think!), but I'll answer anyway because the answer is so unexpected.

Suppose we take our two massive bodies:

Then the gravitational force between them is repulsive because:

$$ F = \frac{G m_1 m_2}{r^2} $$

and $m_1$ and $m_2$ have different signs. But let's calculate the resulting accelerations using Newton's second law:

$$ \vec{F} = m \vec{a} $$

With normal matter the force and acceleration are in the same direction, but if the left (red) object has a negative mass then the force and acceleration point in opposite directions. That means that even though the force between our two bodies is repulsive they both accelerate in the same direction. We get a perpetual motion machine where the two bodies will accelerate away forever. And that's as good a reason as any for supposing that negative mass doesn't exist!