06 March 2006

Gravity on/in a Sphere

(Sorry, this is just an aside.)

For some reason this came up at work & I couldn't remember the conclusions we made at our party a while back. We were wondering:

What is the gravitational field inside of a solid homogeneous sphere?
What is the gravitational field outside of a spherical shell?
What is the gravitational field inside (i.e. between the shell and the center) of a spherical shell?

Inside a spherical shell: zero. (!) [See Feynman's lectures v. 1, 13-9, a derivation resulting in: "If the potential energy is the same no matter where an object is placed inside the sphere, there can be no force on it."

Outside a spherical shell: It's as if there were a gravitational point source at the center, or "The field outside a spherical shell is as if the mass of the shell were concentrated at its center." (link)

Inside a spherical shell: "The field due to a spherically symmetrical body at any internal point is given only by the sphere of material nearer to the centre, since shells outside that distance have no net effect." (link, "Merlyn" gravity notes)

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