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## Homework Statement

Write an expression for the gravitational field strength E at a point distance r from a planet of mass M. (In my diagram, there are two planets with mass, m and distance 2a apart)

## Homework Equations

## The Attempt at a Solution

The resultant gravitational field strength is towards the left. Using the parallelogram method to solve for the resultant vector and by the cosine rule,

[tex]|E|^2=(\frac{GM}{R^2})^2+(\frac{GM}{R^2})^2-2(\frac{GM}{R^2})(\frac{GM}{R^2})\cos 120[/tex]

[tex]|E|=\frac{GM\sqrt{3}}{(r^2+a^2)^2}[/tex]

But the answer given is

[tex]E=\frac{2GMr}{(a^2+r^2)^{\frac{3}{2}}}[/tex]