Originally posted by kasperl
I don't entirely get Goob's "cancel eachother out" thingy
Write it out on paper. It's much easier.
I'll try to diagram it here...
M1 = Earth
M2 = Moon
F = G * M1 * M2
-----------
2
r
F = M2 * a
a = F or a = F 1
-- * --
M2 M2
a = G * M1 * M2 1
----------- * --
2
r M2
Cancel out the M2s, and you get
a = G * M1
------
2
r So no matter what M2 is, it has no effect on the gravity.
if you have two objects of identical mass distribution the effects on all the particles will average out to them acting only on the center of mass, generaly speaking this is an incredably good aproximation for all objects.
It's more than an approximation... it's the exact same thing. You can treat everything as point masses, even black holes. When you calculate the gravity on each point within the mass, and integrate over the volume of the entire mass, everything cancels out. It gives exactly the same result as doing the conventional formula and treating it as a point mass.
