Derive the equation relating the universal gravitational constant, G and the acceleration of free fall, g, at the surface of the earth. [neglect rotation of the earth]

Question

anonymous · Answer

The general equation as given by Newton himself describing the gravitational force between two bodies is given by, $$ F=G(Mm/r^{2})$$ where m is the mass of an object and M is the mass of the Earth. Near the surface of the Earth the acceleration of free fall (g) is aproximately constant. i.e $$F=mg$$ Rearrange the equation so it is in terms of G  and dividing out the mass of the object gives the answer you are looking for. I see that James just beat me to it. :)

jamesj · Answer

(all yours!)

sasogeek · Answer

so the m's cancel out and you have g=GM/R^2

aravindg · Answer

exactly

anonymous · Answer

Right on!

aravindg · Answer

but keep in mind that g changes with height and depth

anonymous · Answer

James, you should have left your nice explaination!

aravindg · Answer

an illustrative example is that we feel more weight in the poles .could you guess why?