Calculating the mass of the moon
Hi,
I am using this formula for two-body systems to calculate the mass of the moon.
T^(2) = (4.pi^(2) / G) * (a^(3) / (M+m))
G = 6.674 * 10^(-11) (gravitational constant)
a = 384399 km = 384399 * 10^(3) m (the semi-major axis)
T = 27.322 days = 27.322 * 24 * 60 * 60 s (orbital period)
M = 5.972 * 10^(24) kg (mass of Earth)
Rearranged to
m = (4.pi^(2) / G) * (a^(3) / T^(2)) - M
If I plug all the values, I get
m = 5.7 * 10^(22) kg
While the actual value of the mass of the moon is around 7.3 * 10^(22) kg. So even though the value that I got is in the same ballpark, it is still quite far off. I have double checked my calculations and tried using more accurate values for the known quantities (more decimal places), but the answer always remains about 5.7 * 10^(22) kg.
I am curious where this error is coming from. Am I not applying the formula correctly? Is it because Earth-Moon is not a "true" two-body system, and it is being influenced by the Sun, and so the formula needs some correction? How would you calculate the mass of the moon?