Why the Earth's gravitational acceleration is the same for every body?

Question

As i understand forces gives bodys acceleration. And mass resist this acceleration. So why does every body, regardless of their mass, gains the same acceleration when they are in earths gravitational field? Shouldnt then more massive objects resist that acceleration and fall slower to earth than a lighter object?

Answer 1

The gravitational force is proportional to the objects mass, the acceleration is indirect proportional to the objects mass, so they cancel each other out. As an equation:

$$F_\mathrm{grav} = G\frac{mM}{r^2} = ma \rightarrow a = GM/r^2 $$