
#1
Dec3012, 06:53 AM

P: 40

hi, i can calculate the distance of moon from the earth and its diameter  but i could't get the formula by which i can calculate the mass of the moon  although i can calculate the mass of the moon by assuming it has same average density that of earth 




#2
Dec3012, 08:11 AM

Mentor
P: 10,840

The orbital period of the moon depends on its distance and the sum of masses of earth and moon  if you can determine this sum with sufficient precision, you can subtract the mass of earth and get the mass of moon.
Satellites orbiting the moon are a better way to determine its mass  they give direct access to the gravitational acceleration at a specific distance, together with the gravitational constant this can be used to calculate its mass. 



#3
Jan213, 11:37 AM

P: 40

but how do i calculate the sum of earth and moon mass?




#4
Jan213, 11:59 AM

Mentor
P: 10,840

mass of the moon?
Measure distance, orbital period and the gravitational constant.
##M+m=\frac{4\pi^2a^3}{GT^2}## with the semimajor axis a (for a circular orbit, this would be the distance) 



#5
Jan413, 07:28 PM

Sci Advisor
HW Helper
P: 2,275

I'm curious as to how you calculated the distance between the Moon and Earth. That distance might not be the semimajor axis of the Moon's orbit. It might be the sum of the Moon's semimajor axis and the Earth's semimajor axis, as measured from their combined center of mass. (The 'a' in the previous equation is actually the sum of the semimajor axes, or the distance you most likely calculated.)
In practice, calculating the mass and the semimajor axis of planets was an almost impossible task even after Newton turned Kepler's Third Law into a formula. You had a formula containing three unknown variables (the universal gravitational constant, the mass, and the semimajor axis) and the only known was the orbital period. In fact, that's why the Earth's semimajor axis for it's orbit around the Sun was measured in astronomical units, with one AU being the distance between the Sun and the Earth. You could measure Jupiter's semimajor axis in AU's, but had no way to convert that into a more traditional measure such as kilometers. 


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