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## Homework Statement

Statement of the problem (quoting from my assignment):

a) write equations of motion

b) try to solve analytically

Given: m

_{1}, m

_{2}- two masses

R - distance between two masses

## Homework Equations

V=-G(m

_{1}/r + m

_{2}/(R-r))

F=-dV/dr

## The Attempt at a Solution

a) Equations of motion: v = dr/dt, a=dv/dt

b) Solution

dV/dt = G(m

_{1}/r

^{2}- m

_{2}/(R-r)

^{2})

Separating variables

dV=Gm

_{1}*1/r

^{2}dr+Gm

_{2}*1/(R-r)

^{2}dr

Integrating both sides I basically get what I started with

V=-G(m

_{1}/r +m

_{2}/(R-r))+C

So, I know what I am doing is not right. I know that somehow the equations of motions need to come into play, but don't understand the relation. My system is in equilibrium, so both velocity and acceleration are equal to 0.

I am not a physics student (I am in Math), but I'm working on a little summer project in Physics.

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