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dani123
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Homework Statement
The moon orbits the Earth at a distance of 3.84x108m from the centre of Earth. The moon has a period of about 27.3 days. From these values, determine the mass of the Earth.
Homework Equations
Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3
motion of planets must conform to circular motion equation: Fc=4∏2mR/T2
From Kepler's 3rd law: R3/T2=K or T2=R3/K
Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2
Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2
Newton's Universal Law of Gravitation: F=Gm1m2/d2
value of universal gravitation constant is: G=6.67x10-11N*m2/kg2
weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2
g=Gme/(Re)2
determine the mass of the Earth: me=g(Re)2/G
speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h
period of the Earth-orbiting satellite: T=2∏√R3/GMe
Field strength in units N/kg: g=F/m
Determine mass of planet when given orbital period and mean orbital radius: Mp=4∏2Rp3/GTp2
The Attempt at a Solution
So used mE=g(RE)2/G and i was confused as to which value to use for RE... do I use the Earth's radius or do I use the distance from the centre of the Earth to moon that is given in the problem...
If i use the value they give in the problem and g=9.8 I would obtain
mE=2.167x1028kg
Does this seem right? If someone could correct me if I am wrong here, that would be greatly appreciated... thanks so much in advance :)