Universal gravitation 6-determine strength of gravitational field

[dani123]

Homework Statement

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.

Homework 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: (T_a/T_b)²=(R_a/R_b)³

motion of planets must conform to circular motion equation: F_c=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∏²K_s)*m/R²=Gm_sm/R²

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏²K_e)m/R²=Gm_em/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=F_g=m_og, where g=9.8 N/kg
F_g=Gm_om_e/R_e²

g=Gm_e/(R_e)²

g=Gm_p/(R_p)²

determine the mass of the Earth: m_e=g(R_e)²/G

speed of satellite as it orbits the Earth: v=√GM_e/R, where R=R_e+h

period of the Earth-orbiting satellite: T=2∏√R³/GM_e

Field strength in units N/kg: g=F/m

Determine mass of planet when given orbital period and mean orbital radius: M_p=4∏²R_p³/GT_p²

The Attempt at a Solution

So for this one I did the following,

m_moon=7.34x10²²kg
R_moon=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:)

 

[grzz]

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

 

[Infinitum]

Hi dani123!

Your working is correct. Edit : I see grzz beat me by a few seconds...

 

[dani123]

Its not a matter of who replied first because both of your replies are extremely appreciated! Thank you!

 

[Nickie]

Your approach to solving this problem is correct. You correctly identified the relevant equations and used the appropriate values to calculate the strength of the gravitational field on the surface of the moon. Your answer of 1.54N/kg is also correct. Good job!