Question:
8.22 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.
Answer:
Mass of the Earth, M = 6.0 × 1024 kg
Radius of the Earth, R = 6400 km = 6.4 × 106 m
Height of a geostationary satellite from the surface of the Earth,
h = 36000 km = 3.6 × 107 m
Gravitational potential energy due to Earth’s gravity at height h,
= -GM / (R + h)
= - 6.67 × 10-11 × 6 × 1024 / (3.6 × 107 + 0.64 × 107)
= -9.4 × 106 J/kg.
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