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 2.07500 × 105 km and the planet has a radius of 3775 km and a mass of 6.40 × 1022 kg, how long (in days) does it take the moon to make one revolution around the planet. The gravitational constant is 6.67 × 10-11 N·m2/kg2.

Answer 1

The distance from the center of the moon to the surface of the planet r ' = 2.07500 × 10⁵ km

the planet has a radius R = 3775 km

The distance from the center of the moon to the center of the planet r = r ' + R

        r = 211275 km

          = 2.11275 x10 ⁵ km

          = 2.11275 x10 ⁸ m

mass M= 6.40 × 10²² kg

Time take the moon to make one revolution around the planet T = ?

The gravitational constant G = 6.67 × 10^-11 N·m²/kg².

We know T = 2(pi) [ r ³ / GM ] ^1/2

                  = 2(22/7) [ (9.43 x10 ²⁴)/(4.2688 x10 ¹²)] ^1/2

                  = 2(22/7) (1.486x10 ⁶ )

                  =9.338x10 ⁶ s

                  = [(9.338 x10 ⁶ ) / (24 x3600)] days

                  = 108 days