A satellite orbits the earth at a height of 400 km, above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence ? Mass of the satellite=200 kg, mass of the earth=`6.0xx10^(24)`kg, radius of the earth=`6.4xx10(6)`m, G=`6.67xx10^(-11)Nm^(2)Kg^(-2)`.

Explanation

To find the energy required to rocket the satellite out of the Earth's gravitational influence, we can follow these steps:

### Step 1: Understand the total energy of the satellite
The total mechanical energy (E) of a satellite in orbit is given by the formula:
\[ E = -\frac{G M m}{2r} \]
where:
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