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I'm trying to calculate Moon revolution period but always got 27.53 instead of 27.32.

G = 6.674e-11 (m^3 kg^-1 s^-2)

M = 5.9724e24 (kg) from http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html

R = 384400000 (m) Earth Moon distance

From 4π^2 * R^3 = GM*T^2,

got moon revolution period T = sqrt(4π^2 * R^3/(GM))

Earth day in seconds = 23*60*60 + 56*60 + 4

so moon revolution period in Earth day = 27.53

Why it is not 27.32? Is it because the orbit is not circular? But period should be same if R is the semi major axis or the orbit.

If I revise the formula and consider Moon gravitational force to the Earth,

let m be the mass of Moon

T = sqrt(4π^2 * R^3/(G(M+m)))

the moon revolution period in Earth day = 27.36, a bit closer but still some error (rounding error?)

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# I Moon revolution period 27.32, but got 27.53 from equation?

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