A satellite is nine times closer to Earth than the Moon. If the Moon's orbital period is 27 days, the satellite's orbital period is:
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A satellite is nine times closer to Earth than the Moon. If the Moon's orbital period is 27 days, the satellite's orbital period is:

G1 Physics · Accepted Answer

By Kepler's third law, T²∝r³. If r s = r m / 9 , r_s=r_m/9, r s ​ = r m ​ /9 , then T s / T m = ( 1 / 9 ) ( 3 / 2 ) = 1 / 27. T_s/T_m=(1/9)^(3/2)=1/27. T s ​ / T m ​ = ( 1/9 ) ( 3/2 ) = 1/27. Hence T s = 27 / 27 = 1 T_s=27/27=1 T s ​ = 27/27 = 1 day.