Answer to Question #1149 in Mechanics | Relativity for Maddie

Question

The period of a satellite is the primary way that the mass of planets is determines. The equation used for this calculation uses the fact that the gravity of the planet provides the centripetal force to keep the satellite in orbit. The distance from the Earth to the Moon is 3.8 x 10^8 m and the period of th moon is approximately 27.3 days. Use the formula derived for this purpose to calculate the mass of the Earth. M = (4π^2r^3)/(G T^2) where T is the period of the moon's orbital rotation.

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Answer 1

The period of the Moon's orbital rotation in the seconds is
T = 27.3days*24hours*60minutes*60seconds = 2,358,720 seconds,
M = (4π²r³)/(G T²) = (4*Pi²*(3.8*10⁸)³)/(6.674*10^−11*2,358,720²) = 5.83407x10²⁴ kg