Problem 12.78 Determine the mass of the earth knowing that the mean radius of the moon's orbit about the earth is 238,910 mi and that the moon requires 27.32 days to complete one full revolution about the earth.

M_e = 6.04 * 10^24 kg

Explanation:

Given:

- The time period of moon orbit T = 27.32 days

- Distance from center of earth to moon r = 238,910 miles

- The gravitational constant G = 6.67408 * 10^-11

Find:

- Determine the mass of the earth

Solution:

- The mass of earth as a function of time period T and radius of orbit r is related by an expression as follows:

M_e = (2*pi / T) ^2 * (r^3 / G)

M_e = (2*pi / 27.32*24*60*60) ^2 * (238910*1609 / 6.67408 * 10^-11)

M_e = 6.04 * 10^24 kg