A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km . Then, the time period of a sky satellite orbiting a few 100 km above the earth's surface R = 64000 km will approximately be

Question

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km . Then, the time period of a sky satellite orbiting a few 100 km above the earth's surface R = 64000 km will approximately be, 1 2 h, 1 h, 2 h, 4 h

MARKS App · Accepted Answer

By Kepler's law of planetary motion, T 2 ∝ r 3 , hence T 1 2 ∝ r 1 3 Similarly T 2 2 ∝ r 2 3 ∴ T 1 2 ∝ 36000 3 T 2 2 ∝ 6400 + h 3 Therefore, T 2 2 = T 1 2 6400 + h 36000 3 > T 1 2 6400 3600 3 > 24 2 8 45 3 ∴ T 2 > 24 × 8 × 8 45 × 45 > 1 . 8 h So, T 2 ≅ 2 h

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