A geostationary satellite is orbiting the Earth at a height of 6 R above the surface of the earth, R being the radius of the Earth. The time period of another satellite, at a height of 2.5 R from the surface of the Earth, is

Question

A geostationary satellite is orbiting the Earth at a height of 6 R above the surface of the earth, R being the radius of the Earth. The time period of another satellite, at a height of 2.5 R from the surface of the Earth, is, 6 2 hour, 6 hour, 5 2 hour, 10 hour

MARKS App · Accepted Answer

A geostationary satellite has a time period of T = 24 h r . From Kepler's law, T 2 ∝ R 3 ⇒ T 2 2 T 1 2 = R 2 3 R 1 3 ⇒ T 2 2 24 2 = R + 2.5 R 3 R + 6 R 3 T 2 = 24 × 24 8 = 6 2 h r .

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