# Grav. field of spherical objects

will the gravitational field created by a point of mass m be the same than that of a spherical object of same mass (outside the volume of the object)? If so, why is this? How does the sum of the grav forces created by all the points in the sphere add up to the same as a point-mass?
Thanks,

Alex

NateTG
Homework Helper
With newtonian gravity the net gravity from a spherical shell is zero on the inside of the shell, and the same as from a point mass at the center of the shell from the outside. (I'm not sure about the shell itself.)

Proving this wihout calculus (or developing calculus as part of the proof) is pretty daunting.

I think it's called the shell theorem, maybe you can find that on google?

markci
Yes, it's the same. In other words, if the mass of the earth were compressed into a single point (ie a black hole) at the same distance from you (about 4000 miles) as the center of the earth is now, you would feel the same amount of gravity.

The reason is that some of the mass of the earth is further from you than the center and some of it is closer, and the net effect balances out that way. To prove it requires vector calculus.

It is called the Gauss' theorem