Two satellite `S_1 and S_2` revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolutions are 1 h nd 8 h respectively. The radius of the orbit of `S_1` is `10^4 km`. When `S_2` is closet to `S_1`., find (a). The speed of `S_2` relative to `S_1` and (b). the angular speed of `S_2` as observed by an astronaut in `S_1`.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the radius of the orbit of satellite S2 using Kepler's Third Law.

According to Kepler's Third Law, the square of the period of revolution (T) is proportional to the cube of the radius (r) of the orbit:

\[
\frac{r_2^3}{r_1^3} = \frac{T_2^2}{T_1^2}
...