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## Homework Statement

Two spheres of mass m and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass m4 is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is M in terms of m? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere?

## Homework Equations

Fnet = F1,4 + F2,4 + F3,4

F = GMm/r

^{2}

## The Attempt at a Solution

F1,4 = GMm/r

^{2}

F2,4 =Gm

^{2}/r

^{2}

F3,4 =Gm

^{2}/r

^{2}

Fnet = 0 = F1,4 + F2,4 + F3,4

0 = GMm/r

^{2}+ Gm

^{2}/r

^{2}+Gm

^{2}/r

^{2}

0 = Mm + 2m

^{2}

Mm = -2m

^{2}

M = -2m

this is not correct. please help me figure out what I'm doing wrong. thanks.