# Speed of a body in orbital motion [closed]

I assume I'm making a silly error somewhere but I can't see how. The question is concerning two objects $M$ and $m$ orbiting each other at a distance of $r$ apart. The first part was simply finding the magnitude of gravitational attraction between the two objects which is $$F= \frac{GMm}{r^2}$$The second part was finding the distance from mass M to the centre of mass which I calculated to $\frac{rm}{M+m}$. In the third part, it was assumed they both orbit in perfect circles and I had to find the speed of mass m.

I equated $F=\frac{GMm}{R^2}$ to $\frac{mv^2}{R}$ to get equation $$v =\sqrt{\frac{GM}{R}}$$ As in this context, $R$ is the distance from $m$ to the centre of mass which using prev question must be $\frac{rM}{M+m}$. I subbed this in to get $$v = \sqrt{\frac{G(M+m)}{r}}$$.

• If $r$ is the orbital separation, then I think that is the correct equation for the orbital velocity, since the binary orbit is circularized. Perhaps I'm missing something here – N. Steinle Sep 1 '18 at 17:34

I think you need to equate $mv^2/R$ to $GmM/r^2$ not to $GmM/R^2$.