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## Homework Statement

There is no general analytical solution for the motion of a 3-body gravitational system. However, there do exist analytical solutions for very special initial conditions. The diagram below shows three stars, each of mass m, which move in the plane of the page along a circle of radius r.

http://spock.physast.uga.edu/res/uga/PhysicsLib/Matter_and_Interactions/Ch04/figs/3body_grav.png

Calculate the magnitude of the total gravitational force exerted on one of the stars due to the other two.

F total = ?

Period, T = ?

## Homework Equations

F= Gmm/R^2

Trig

## The Attempt at a Solution

My only attempt at a solution involved the assumption that the bodies are at 120 degrees, on the corners of an equilateral triangle, and trying to solve for the distance between the bodies in terms of r. Then using trig to solve for the y component of both forces and adding them.

Thanks in advance, guys.

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