Flight of an object with decreasing mass

Question

A ball with mass m is thrown upwards at a velocity $v_0$. As it travels, m decreases with time -- not because mass is being expelled outwards, as in a rocket, but simply because the ball is shrinking. What is the nature of the ball's flight? Will it land in the same time as a ball with constant mass would? Will it travel farther than a normal ball would? Assume air resistance is negligible.

I thought of this question whilst thinking about the physics of Ant-Man and now I can't stop thinking about it. I've arrived at the conclusion that the shrinking ball should follow the same path as a regular ball due to it only experiencing the gravitational force exerted on it by Earth, which is proportional to its mass. Am I correct in this logic? Is there an aspect of the problem that I've overlooked? Does the scenario violating conservation of mass preclude any analysis of it?

Answer 1

No magic is required. Nature does projectile motion with variable mass all the time - consider raindrops falling through dry air, comets, clods of dirt, etc. Raindrops evaporate, comets get their mass burned off by sunlight and blown away by solar wind, dirt clouds come apart under atmospheric drag. The mass doesn't magically appear or disappear, it just goes somewhere else that isn't part of the object we're tracking.

As long as you're talking about reality, you're correct. Neglecting slight changes because of interactions with air, and supposing that the forces that separate the projectile from its constituent parts are small and/or point in many random directions, the trajectory of a shrinking projectile is identical to the trajectory of a normal projectile.

If the mass disappears by magic, who knows. The rules of magic are up to the author.

Answer 2

As you already mentioned $a=\frac{F}{m}$. Then with $F\propto \frac{Mm}{r^2}$ acceleration $a$ is independent of mass $m$ if losing mass doesn't exert any forces on the system. And by making the assumption that losing mass doesn't interact any further with your system there's no aspect to be overlooked.
(the same goes for relativistic systems)

Answer 3

Thanks to conservation of momentum and mass (as@g s pointed out), the centre of mass of the ball always moved as though it isn't shrinking.