A satellite is orbiting around the earth in a circular orbit and in this orbit magnitude of its acceleration is `a_1` . Now a rocket is fired in the direction of motion of satellite from the satellite due to which its speed instantaneously becomes half of initial, just after the rocket is fired acceleration of satellite has magnitude `a_2` . Then the ratio `(a_(1))/(a_(2))` is (Assume there is no external force other than the gravitational force of earth before and after the firing of rocket from the satellite)

Explanation

To solve the problem, we need to analyze the situation before and after the rocket is fired from the satellite.

### Step 1: Understand the initial conditions
The satellite is in a circular orbit around the Earth. The gravitational force provides the necessary centripetal force for the satellite's circular motion. The acceleration of the satellite in orbit, denoted as \( a_1 \), can be expressed using the formula for gravitational acceleration.

**Hint**: Remember that the gravitational force acts as the centripetal force for circular motion.

### Step 2: Calculate the initial acceleration \( a_1 \)
...