Why does the mass of planets affect the gravity on their surface but the mass of objects doesn’t affect how fast they fall.

Question

Why does the mass of both objects not factor? Did I misunderstand the reason for differing gravity on other planets?

In: Physics

Answer 1

The acceleration due to gravity depends on the mass of the object that is being accelerated both as a resistance to said acceleration (inertia) and as a cause of the force. That means that there are two “opposing” effects, which cancel out perfectly. With some algebra, this can be shown very easily:

F = ma

GMm/r^2 = ma

GM/r^2 = a