The radius of a planet is double that of earth but their average are the same. If the escape velocities at the planet and the earth are `v_(p)` and `v_( e)` respectively , then prove that `v_(p) = 2 v_(e)`.

Explanation

To solve the problem, we need to derive the relationship between the escape velocities of the planet and the Earth, given that the radius of the planet is double that of Earth and their average densities are the same.

### Step-by-Step Solution:

1. **Understanding Escape Velocity**:
The escape velocity \( v \) from the surface of a celestial body can be expressed as:
\[
v = \sqrt{\frac{2GM}{R}}
...