Satellite is revolving around earth. If its height is increased to four times the height of geostationary satellite, what will become its time period?
A geostationary satellite orbits Earth at the equator with a period of 24 hours, matching Earth’s rotation, appearing stationary.
Class 11 Physics
Gravitation
CBSE EXAM 2024-25
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According to Kepler’s law of periods, the ratio of the orbital periods of two planets is related to the ratio of their semi-major axes. Specifically, the ratio of the periods (T₂/T₁) equals the ratio of their radii raised to the power of three-halves. In this case, if the radius of the second planet is four times that of the first, the calculation shows that T₂/T₁ equals eight.
Therefore, if the orbital period of the first planet is 1 day, the orbital period of the second planet would be 8 days, demonstrating the significant impact of radius on orbital time.
According to Kepler’s law of periods,
T₂/T₁ = (r₂/r₁)³/² = (4/1)³/² = 8
T₂ = 8T₁= 8 x 1 day = 8 days