A satellite orbits the earth at a height of `400km` above the surface. How much energy must be expanded to rocket the satellite out of the gravitational influence of earth? Mass of the satellite is `200kg,` mass of earth `=6.0 xx 10^(24) kg,` radius of earth `=6.4 xx 10^6 m`, `G=6.67xx10^(-11)Nm^2 kg^(-2).`

Explanation

To determine the energy required to rocket the satellite out of the gravitational influence of the Earth, we need to calculate the gravitational potential energy at the satellite's current position and the energy required to escape Earth's gravitational field.

### Step 1: Calculate the distance from the center of the Earth to the satellite.
The height of the satellite above the Earth's surface is given as 400 km. We need to convert this to meters and then add the radius of the Earth to find the total distance from the center of the Earth.

\[ \text{Height of satellite} = 400 \text{ km} = 400,000 \text{ m} \]
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