Tessellate - S.T.E.M.S - Physics - School - Set 2 - Problem 1

Two satellites $S_1$ and $S_2$ revolve around a planet in co-planar circular orbits in the opposite sense. The periods of revolutions are $T$ and $\eta T$ respectively. find the angular speed of $S_2$ as observed by an astronaut in $S_1$ , when they are closest to each other.

$(a)$ $\omega = \frac{2\pi(\eta^{\frac{2}{3}}-1)}{T(\eta^{\frac{2}{3}}+1)}$

$(b)$ $\omega = \frac{2\pi(\eta^{\frac{2}{3}}+1)}{T(\eta^{\frac{2}{3}}-1)}$

$(c)$ $\omega = \frac{2\pi(\eta^{\frac{1}{3}}+1)}{T(\eta^{\frac{1}{3}}-1)}$

$(d)$ $\omega = \frac{2\pi(\eta^{\frac{1}{3}}-1)}{T(\eta^{\frac{1}{3}}+1)}$

This problem is a part of Tessellate S.T.E.M.S.