Two satellites have mistakenly been put in identical Earth orbits of radius R. Satellite A with mass "m" is orbiting clockwise while satellite B with mass "2m" is orbiting counterclocwise. The two satellites have a head on collision and move as one body after the collision. In terms on the given quantities, what orbit radius would the collided objects have to possess in order to move in a circular path?
2. Homework Equations /Attempt
I believe that since the satellites are orbiting at the same radius, the are orbiting at the same speed so
Va = - Vb
I can get a quarter of it but I'm not even sure if it's right:
(3m)(vf)²/(Rf) = ?
using the collision formula to get vf
mVa + 2mVb = 3m Vf
Vf = (Va - 2Vb)/3
so (3m)[(Va - Vb)/3]/Rf = ?
I'm very stuck. Help!