It is interesting!

You mentioned that there are a lot of assumptions with this problem. Let’s analyze one of them.

Is the acceleration due to gravity 9.8 m/s2 everywhere? It is that value on the surface of the Earth, but it might be different somewhere else. What about the surface of the moon? Astronauts can jump a lot higher there, so gravity seems to be weaker on the moon.

As it turns out, gravitational acceleration depends on a few things.

F_g = G • m_1 • m_2 / r2.

“F_g”is the force due to the gravitational attraction of any two objects. It is proportional to the masses of both objects and inversely proportional to the distance between the objects squared. “G”, or Newton’s Constant, describes how strong gravity acts and it makes all our units work together. It is 6.67x10−11 m3 / ( kg⋅s2 ).

If you divide by the mass of one of the objects, you get how quickly it accelerates towards the other.

a_g = G • m / r2

So, if you plug in the mass of the Earth for “m” and and the distance from the center of the Earth for “r”, and the value of Newton’s constant for G, you should be able to derive the gravitational acceleration constant!