Two satellites `S_1` and `S_2` revolve around the earth at distances `3R` and `6R` from the centre of the earth. Find the ratio of their (a) linear speeds and (b) angular speeds.

Explanation

To solve the problem, we need to find the ratio of the linear speeds and the angular speeds of two satellites \( S_1 \) and \( S_2 \) revolving around the Earth at distances \( 3R \) and \( 6R \) from the center of the Earth, respectively.

### Part (a): Ratio of Linear Speeds

1. **Understanding Linear Speed**:
The linear speed \( v \) of a satellite in orbit can be derived from the formula:
\[
v = \sqrt{\frac{GM}{r}}
...