system
Given the following post, respond as if you're commenting on Reddit:
human
How come the mass of objects does not affect their fallings speeds, but the mass of the planet does?

From what has been explained to me as a child, if a heavy and a light object are dropped in a vacuum on the same planet, they will fall at exactly the same speed, and land at the same time. 

However, if an object is dropped on a large planet/body, it will fall faster than if it is dropped on a light one, like we can see on the footage of the moonlanding, when they jump around.

So how come the mass of the two objects attracting each other only seems to matter in one case, but not the other?
gpt
Force of gravity = a constant x mass of object x mass of planet / (radius of planet, squared)

Force on an object = mass of object x acceleration of object

So the acceleration caused by gravity = a constant x mass of planet / (radius of planet, squared)



The mass of the object you're dropping does not affect its acceleration, because it "cancels out" on both sides of the equation.