A spaceship approaches the Moon along a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of the maximum approach the brake rocket was fired for a short time interval, and the spaceship was transferred into a circular orbit of a Moon satellic. Find how the spaceship velocity modulus increased in the process of braking.

Explanation

To solve the problem, we need to analyze the situation of the spaceship approaching the Moon and transitioning from a parabolic trajectory to a circular orbit. Here’s a step-by-step solution:

### Step 1: Understand the Initial Conditions
The spaceship is approaching the Moon along a parabolic trajectory, which means it is not in a stable orbit but is on a path that will bring it close to the Moon's surface. At the point of maximum approach, we denote the velocity of the spaceship as \( V_1 \).

### Step 2: Apply Energy Conservation for Parabolic Trajectory
For a parabolic trajectory, the total mechanical energy is zero. The kinetic energy (KE) and gravitational potential energy (PE) at the point of maximum approach can be expressed as:
\[
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