A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius (1.02)R. The period of the second satellite is larger than the first one by approximately

Question

A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius (1.02)R. The period of the second satellite is larger than the first one by approximately, 0.7%, 1.0%, 1.5%, 3.0%

MARKS App · Accepted Answer

from kepler's law, T 2 ∝ R 3 ⇒ T ∝ R 3 2 ⇒ T = k R 3 2 ; k k is some constant . for radius = R T = k R 3 2 d T d R = 3 2 k R 1 2 when radius = 1.02 R ; d R = 1.02 R − R = 0.02 R d T d R = 3 2 k R 1 2 ⇒ d T = 3 2 k R 1 2 × d R ⇒ d T = 1.5 k R 1 2 × 0.02 R % change = d T T × 100 = 0.03 T T × 100 = 3

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