As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite ? (Take the potential energy at infinity to be zero). Mass of the earth = 6.0×1024 kg, radius = 6400 km.
Given: A geostationary satellite orbits the Earth at a height of nearly 36,000 km from the surface of the earth.
The gravitational potential energy is given by,
U = − G M ( R + h )
Where, M is the mass of Earth, R is the radius of Earth and h is the height of the satellite.
By substituting the given values in the above expression, we get
U = − 6.67 × 10 − 11 × 6 × 10 24 3.6 × 10 17 + 0.64 × 10 7 = − 6.67 × 6 4.24 × 10 6 = − 9 .4 × 10 6 Jkg − 1
Hence, the potential due to earth’s gravity at the site of this satellite is − 9 .4 × 10 6 Jkg − 1 .
Given: A geostationary satellite orbits the Earth at a height of nearly
The gravitational potential energy is given by,
Where,
By substituting the given values in the above expression, we get
Hence, the potential due to earth’s gravity at the site of this satellite is
