What Is the Lunar Mass Compared to Earth's?

[J7]

I have a problem that I've been working on FOREVER but can't figure out how to do.
Lunar Gravity at the Moon's surface is only 1/6 as strong as what we experience on Earth. Since the diameter of the Moon is about 1/4 as large as the Earth's, the lunar mass is about :
a) 3 X 10^-3 times the Earth's mass
b) 1 X 10^-2 times the Earth's mass
c) 3/8 of the Earth's mass
d) 1/3 of the Earth's mass
e) 3 times the Earth's mass

I'm just completely stuck (and very new to the physics thing!).

 

[HallsofIvy]

Do you know F= \frac{GMm}{r^2}?

Taking a fixed mass as m and M_e, r_e, M_m, r_m to mean the masses and radii of the Earth and moon, saying that the force of gravity on the surface of the moon is 1/6 that of Earth is saying that
\frac{M_m m}{r_m^2}= \frac{1}{6}\frac{M_em}{r_e^2}.

Since we are also told that the diameter of the moon is about 1/4 that of the Earth (and so the r_m= (1/4)r_e), replace r_m^2 with \frac{r_e^2}{16} and solve for \frac{M_m}{M_e}.

 

[Gokul43201]

How does the gravitational force depend on mass and distance ? Wite down the equation for Earth and for moon, and find the ratio between the forces.

Edit : Wow, when I started typing, there were no responses up yet !

 

[aekanshchumber]

It is simple,
gravitational force F = (GMm)/r^2
also F = mg clearly M=mass of earth
g = GM/r^2

Now compare it with one for moon
g(moon) = {GM(moon)}/r^2
substitute the values, get the answer.

 

[J7]

I do know that equation.. what does the second m in the numerator stand for though??

 

[Gokul43201]

The second m is the mass of the object. But to compare forces you want to be using the same object on the moon that you were using on Earth. So that m remains the same in both cases, and hence cancels out.

 

[J7]

I GOT IT! Thanks so much for all your help! On to the next question!

 

[Gokul43201]

After you get the answer, you could check it another way.

Assume the Earth and Moon have similar densities (actually, one of them with be greater, which ?). Mass is proportional to volume. Volume is proportional to the cube of the diameter. So, just using the diameters, you have an estimate for the masses of the planets. Is this estimate closer to your answer than the other choices ?

 

[Doc Al]

J7, please do not post the same question to multiple forums! https://www.physicsforums.com/showthread.php?t=46228

(Moving this to College Level Help, where it belongs.)