Prove that for an earth satellite, the ratio of its velocity at apogee (when farthest from earth) to its velocity at perigee (when closer to earth) is in the inverse ratio of its distance at apogee and perigee.

Explanation

To prove that for an earth satellite, the ratio of its velocity at apogee (Va) to its velocity at perigee (Vp) is in the inverse ratio of its distance at apogee (r2) and perigee (r1), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- Let \( r_1 \) be the distance of the satellite from the center of the Earth at perigee.
- Let \( r_2 \) be the distance of the satellite from the center of the Earth at apogee.
- Let \( V_p \) be the velocity of the satellite at perigee.
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