An earth satellite is revolving in a circular orbit of radius a with velocity `upsilon_(0)`. A gun in the satellite is aimed directly towards the earth. A bullet is fired from the gun with muzzle velocity `(upsilon_(0))/(2)`. Neglecting resistance offered by cosmic dust and recoil of gun, calculate maximum and minimum distance of bullet from the center of earth during its subsequent motion.

Explanation

To solve the problem, we need to find the maximum and minimum distances of the bullet from the center of the Earth after it is fired from a satellite. The satellite is in a circular orbit of radius \( a \) with velocity \( v_0 \), and the bullet is fired with a muzzle velocity of \( \frac{v_0}{2} \).

### Step 1: Establish the relationship between \( v_0 \) and gravitational force

The gravitational force provides the necessary centripetal force for the satellite's circular motion. Thus, we can equate the centripetal force to the gravitational force:

\[
\frac{mv_0^2}{a} = \frac{GMm}{a^2}
...