# Homework Help: Universal gravitation 3- determine the mass of the Earth

1. Jun 14, 2012

### dani123

1. The problem statement, all variables and given/known data

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.

2. Relevant 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

3. 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 im wrong here, that would be greatly appreciated... thanks so much in advance :)

2. Jun 15, 2012

### MalachiK

Let's see, I think it's proably okay to assume that the moon is moving in a circle around the Earth at a constant speed. If that's true, do you know any formulae for the centripetal force that must be acting on a mass doing uniform circular motion? Wouldn't that be exactly equal to the size of the gravitational force between the Earth and the moon?