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## Homework Statement

Four masses m are arranged at the vertices of a tetrahedron of side length a. What is the gravitational potential energy of this arrangement?

(answer is -6Gmm/a)

## Homework Equations

gravitational potential energy = -Gmm/r

## The Attempt at a Solution

One mass is "a" away from another mass. So the gravitational potential energy there is -Gmm/a. But it is attracted to two other masses, so the gravitational potential energy of this one mass is -3Gmm/a. So for all four masses, the total potential energy should be -12Gmm/a, right? So why is this not the answer? Thanks