Assume that the force of gravitation `F prop 1/(r^(n))` . Then show that the orbital speed in a circular orbit of radius r is proportional to ` 1/(r^((n-1)//2))` , while its period T is proportional to ` r^((n+1)//2)`

Explanation

To solve the problem, we need to show how the orbital speed \( v \) and the period \( T \) of an object in a circular orbit are related to the radius \( r \) when the gravitational force is given by \( F \propto \frac{1}{r^n} \).

### Step-by-Step Solution:

1. **Understanding the Gravitational Force**:
The gravitational force \( F_g \) acting on a satellite of mass \( m \) in a circular orbit of radius \( r \) is given by:
\[
F_g = \frac{K}{r^n}
...