Edexcel M3 Newton's Law of Gravitation

Why F = k/x^2? The distance between them would be x + R, surely?

Makes sense
Swayum, why did you use the ULoG? For some reason, I haven't ever seen a question in the past papers requiring that, its always been separating the variables and integrating. Unless I have missed something big?!

I only ever use that in Physics...it doesn't really help M3

Makes sense
Swayum, why did you use the ULoG? For some reason, I haven't ever seen a question in the past papers requiring that, its always been separating the variables and integrating. Unless I have missed something big?!

Okay

btw... did you do the June 05 paper? It was such a *****. I only managed to do about half of it but the grade boundaries were really low, an A was at 55/75 or something.

*goes to pray he gets an easy paper*

I would prefer a "show that" and "prove that" paper, it's so much easier!

You read my mind
Ever thought of becoming a palm reader?

Assume that the Earth is a sphere of radius R and g is the acceleration due to gravity at the surface.

Prove that the magnitude of the gravitational force on a particle of mass m when it is a distance x from the centre of the Earth (x >= R) is mgR^2/x^2.

Let M be the mass of the Earth.

Newton tells us that

F = GmM/(R+x)^2

At the surface of the Earth (x = 0), we have

F = GmM/R^2 = mg

So GM/R^2 = g

What now?

Instead of arranging that last equation to find g, arrange it to find G. Then just sub it back into the original equation to get the required result.