Prove that the gravitational field inside a uniform, hollow sphere is zero.?

Answer 1

You can do the calculus if you want--here's an argument with more words and fewer equations to write:

Apply gauss' law (aka divergence law) to a spherical surface anywhere inside the physical hollow sphere. The gravitational flux through the hypothetical sphere (the integral of g dot dA around the sphere) has to be proportional to the mass enclosed by the sphere.

Therefore, the net flux through the sphere has to be zero--no mass inside the Gaussian surface.

Therefore, the symmetry of the problem ensures that the flux must be zero everywhere. QED.

Answer 2

hslayer misinterprets the Shell Theorem. Others might want to correctly be confusing this with the actual undeniable reality that the electric powered container interior of a perfectly engaging in shell is 0 (the electric powered potential is uniform). for the reason that count number number is neither an insulator nor a conductor of gravity, the gravitational stress on a mass contained in the shell is amazingly virtually a twin of the stress outdoors the mass. The equivalence to some extent-mass is valid so long because the gap to that factor isn't so small that it drives the stress to infinity. What the Shell Theorem absolutely says for the case interior the shell is that the contribution to the whole gravitational container from the shell is 0. So it really is as if the shell wasn't there. If there's a Gauss regulation proper to gravitational fields, that would want to help this interpretation of the Shell Theorem.

Answer 3

Use Gauss' theorem.

From this it follows that the surface integral of the flux of the gravitational field at a surface is -4piG times the mass enclosed by the surface, regardless of how the mass is distributed and of any mass outside.

Within a hollow sphere, the contained mass is zero. Hence the flux is zero.

Answer 4

See the "Shell Theorem" on Wikipedia. In solving the gravitation of large spherical bodies, Newton had to solve the gravitation of a hollow sphere. Wikipedia does a far better job then I can. Go to:

http://en.wikipedia.org/wiki/Shell_theorem

Answer 5

Create an equation to find the gravity at any point within the sphere. Then find the integral of all the sphere on that point so that youll get the actual gravity.

Now if you leave the variable unknown and integrate. You will still be able to find it is equal to zero.

Peace.