Problem 1.218

Two Earth's satellites move in a common plane along circular orbits. The orbital radius of one satellite \(r=7000 \mathrm{~km}\) while that of the other satellite is \(\Delta r=70 \mathrm{~km}\) less. What time interval separates the periodic approaches of the satellites to each other over the minimum distance?

\Delta t \approx \frac{2 \pi}{\sqrt{\gamma M}} \frac{r^{3 / 2}}{3 \Delta r / 2 r+\delta}=\left\{\begin{array}{l} 4.5 \text { days }(\delta=0) \\ 0.84 \text { hour }(\delta=2) \end{array}\right.

Universal Gravitation