the wikipedia page on shell theorem states that
1. A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre.
2. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
and as a collary states that: A corollary is that inside a solid sphere of constant density the gravitational force varies linearly with distance from the centre, becoming zero by symmetry at the centre of mass.
I was curious about the gravitational pull of a solid sphere on an object with a density d(r) where r was the distance from the center of mass to the object, and wikipedia doesn't mention anything. it's quite useful because most objects don't have constant density, the density is usually a function
so i noticed, if you slice the sphere into infinite shells, you can ignore all the shells your object is inside according to (2) and compute the force of all the shells on the outside as a single point according to (1).
what this means in english is that if a spaceship is 100km down into the atmosphere of jupiter, and we want to find how much gravity is pulling on it, we can ignore the atmosphere above the spacecraft, and pretend all the atmosphere below is centered on a single point. seems pretty elegant.
Topic: shell theorem (Read 3322 times)
