An undiscovered planet, many light-years from Earth, has one moon which has a ne

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 2.43500 × 105 km and the planet has a radius of 3.300 × 103 km and a mass of 5.50 × 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.

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 2.43500 x 105 km and the planet has a radius of 3.300 x 103 km and a mass of 5.50 x 1022 kg, how long (in days) does it take the moon to make one revolution around the planet. The gravitational constant is 6.67 x10-1 N m2/kg2 Number T= days davs

Explanation / Answer

the period is calculated as follows:

T = 2pi*sqrt(r^3/(GM))

= 2pi*sqrt((2.435*10^8 + 3300*10^3)^3/(6.67*10^-11*5.50*10^22))

= 1.27*10^7 sec

= 147.13 days

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