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

AI Thread Summary
The calculation for the Moon's revolution period typically yields 27.53 days using the formula T = sqrt(4π^2 * R^3/(GM)), based on the distance from Earth and the mass of the Earth. However, the expected value is 27.32 days, leading to questions about potential discrepancies. Factors such as the elliptical nature of the Moon's orbit and the Earth's movement during the Moon's revolution may contribute to this difference. Adjusting the formula to include the Moon's mass results in a period of 27.36 days, which is closer but still not exact. The discussion highlights the complexity of orbital mechanics and the influence of multiple factors on calculated periods.
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Hello,

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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