# Universal gravitation 6-determine strength of gravitational field

1. Jun 15, 2012

### dani123

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

The moon has a mass of approximately 7.34x1022kg and a radius of about 1785 km. Determine the strength of the gravitational field on or near the surface of the moon.

2. Relevant equations
I have made a list of equations that are relevant for this entire module on universal gravitation. So although there are many of them does not mean that they all apply in this circumstance. The ones relevant to this question will be placed in bold.

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

g=Gmp/(Rp)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 for this one I did the following,

mmoon=7.34x1022kg
Rmoon=1785km=1785000m
G=6.67x10-11N*m2/kg2
g=?

So I used the equation highlighted above to determine the value of g and found g=1.54N/kg

If someone could please verify my answer and let me know if I went wrong anywhere that would be greatly appreciated! Thanks so much for your time and help:)

2. Jun 15, 2012

### grzz

It is correct. But I would have started from basic equations like g = F/m & F = GMm/R$^{2}$ and derived g = GM/R$^{2}$.

3. Jun 15, 2012

Hi dani123!