Question

An undiscovered planet, many light-years from Earth, has one moon, which has a nearly circular periodic orbit. If the distance from the center of the moon to the surface of the planet is 2.285×105 km and the planet has a radius of 3.650×103 km and a mass of 4.30×1022 kg , how long (in days) does it take the moon to make one revolution around the planet? The gravitational constant is 6.67×10−11N·m2/kg2

Answer 1

Solution Moon we have distance from center of moon moon to to surface of 91 planet 5 R' = 2.285X10 km RI Manet (م) A Radine of planet R= 3.650x 103 km R = 0.03650 X 105 km M= R+ R r 30x1022 kg Distance from both the centers of moon & & planet, 2.285 + 0.03650x com 2.3215 x 109 x (100o) m Maes of planet , M = 4.36X10 Gravitational constant, G = 6.67810*11 Nome lig 2 we use Kepler's third law to find (T) Time period make revolution around planst by moon, T2 = ut² od GM x (2.3215 x 105 x 1000) 6.67 X107 x 430 x 1022 period to 3 3 72= 4x3.44 3.14 T2 1.72040 X lolu = T= √ 1.720408 1014 1.312 8107 seconds

and I day 24 hrs 24X3600 seconds I day 86400 s I second ㅗ 86You day 7. TE 1,312x 10 days 86400 T= 151.81 days