Gravitational attraction of bodies

[Nabeshin]

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

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!

 

[Nabeshin]

bump

 

[Mentz114]

Could you explain from whose frame reference your result applies ? For instance, your result might be correct for an observer situated in the line of sight between the bodies, and initially at rest wrt the bodies before they begin moving ( ie at t=0, nothing is moving ).

 

[Nabeshin]

The answer is with respect to either of the moving masses, actually, if that makes any sense. Although, I assumed at t=0 nothing was moving with respect to the other.