Satellite of mass 200 kg is revolving in a circular orbit of radius `4R_(E)` around the earth. Calculate orbit of radius `8R_(E)`. Also find the changes in kinetic and potential energies `g = 9.8 m//s^(2), R_(E) = 6,400 km` (radius of earth)

Explanation

To solve the problem, we will calculate the change in kinetic and potential energies of a satellite of mass 200 kg revolving in circular orbits at radii of \(4R_E\) and \(8R_E\) around the Earth. We will use the following values:
- Gravitational acceleration, \(g = 9.8 \, \text{m/s}^2\)
- Radius of the Earth, \(R_E = 6400 \, \text{km} = 6.4 \times 10^6 \, \text{m}\)

### Step 1: Calculate the initial potential energy (PE) at \(4R_E\)

The formula for gravitational potential energy is:
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