Two identical satellites are moving around the Earth in circular orbits at heights 3R and R respectively where R is the radius of the Earth. The ratio of their kinetic energies is x. Find x.

Explanation

To find the ratio of the kinetic energies of two identical satellites moving around the Earth in circular orbits at heights 3R and R, we can follow these steps:

### Step 1: Understand the relationship between gravitational force and centripetal force
The gravitational force acting on a satellite in orbit provides the necessary centripetal force to keep it in circular motion. The gravitational force \( F_g \) can be expressed as:
\[ F_g = \frac{GMm}{(R + h)^2} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, and \( h \) is the height of the satellite above the Earth's surface.
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