A satellite of mass $M$ is in a circular orbit of radius $R$ about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:
Answer: (A) In an elliptical orbit
The satellite moves tangentially with the orbital speed $v$; the meteorite moves radially with the same speed. Conserving momentum for the combined mass $2M$:
$$\vec{V} = \frac{v}{2}\hat{t} + \frac v2\hat{r},\qquad V = \frac{v}{\sqrt2}$$
The speed is less than the escape speed $\sqrt2v$, so the body stays bound; and the velocity has a radial component, so the orbit is not circular. It moves in an elliptical orbit.
Solution by Sreeraj P, M.Sc Physics