A `400 kg` satellite is in a circular orbit of radius `2 R_(E)` around the Earth. How much energy is required to transfer it to a circular orbit of radius `4 R_(E)`? What are the changes in the kinetic and potential energies?
Given `g = 9.81 m^(-2) , R_(E) = 6.37 xx 10^(6) m`.

Explanation

To solve the problem, we need to calculate the energy required to transfer a satellite from a circular orbit of radius \(2 R_E\) to a circular orbit of radius \(4 R_E\). We will also determine the changes in kinetic and potential energies during this transfer.

### Step 1: Calculate the Gravitational Potential Energy (PE)

The gravitational potential energy (PE) of a satellite in orbit is given by the formula:

\[
PE = -\frac{GMm}{R}
...