# Gravitational attraction of bodies

## Main Question or Discussion Point

Hello! The stem from this problem came to me when I was pondering how to describe the motion of two massive objects feeling the others' gravitational attraction (i.e binary star systems or something like that). Well this got ugly fast so I had to simplify a lot of things, and I finally got an answer for one.

Considering two massive bodies, initially at rest, with respective masses of m1 and m2, I derived a position-time equation of:

x(t)=$$\sqrt{x_{o}^{4}-6Gt^{2}(m_{1}+m_{2})}$$

Some notes: This isn't a true position-time equation, because I couldn't figure out how to do it with respect to an outside reference frame (i.e x-y axis), so it is merely the distance between the objects. I can add work such as the solving of the differential equation if necessary.

Can anyone confirm this result? Perhaps add a comment or two that might help with the overall goal described above? Thanks!

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