What Is the Lunar Mass Compared to Earth's?

In summary, the conversation discusses the problem of calculating lunar gravity and the equation F= \frac{GMm}{r^2}. The diameter of the moon is 1/4 that of Earth, resulting in a lunar mass that is 1/6 of Earth's. The gravitational force depends on mass and distance, and this is used to compare the forces on Earth and the moon. The conversation also mentions using the densities and diameters of the planets to estimate their masses.
  • #1
J7
10
0
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!).
 
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  • #2
Do you know [tex]F= \frac{GMm}{r^2}[/tex]?

Taking a fixed mass as m and Me, re, Mm, rm 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
[tex]\frac{M_m m}{r_m^2}= \frac{1}{6}\frac{M_em}{r_e^2}[/tex].

Since we are also told that the diameter of the moon is about 1/4 that of the Earth (and so the rm= (1/4)re), replace [itex]r_m^2[/itex] with [itex]\frac{r_e^2}{16}[/itex] and solve for [itex]\frac{M_m}{M_e}[/itex].
 
  • #3
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 !
 
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  • #4
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.
 
  • #5
I do know that equation.. what does the second m in the numerator stand for though??
 
  • #6
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.
 
  • #7
I GOT IT! Thanks so much for all your help! On to the next question!
 
  • #8
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 ?
 
  • #9
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FAQ: What Is the Lunar Mass Compared to Earth's?

How does the moon's gravity affect the tides on Earth?

The moon's gravity causes the tides on Earth through the process of tidal force. As the moon orbits around the Earth, its gravitational pull creates a bulge in the ocean on the side of the Earth facing the moon. At the same time, there is another bulge on the opposite side of the Earth due to the centrifugal force of the Earth's rotation. This results in two high tides and two low tides each day as the Earth rotates through these bulges.

Why do objects weigh less on the moon compared to Earth?

The moon's gravity is much weaker than Earth's, with only about 1/6th of the strength. This means that the force pulling objects towards the moon's surface is much less, resulting in a lower weight. However, the mass of an object remains the same regardless of where it is located, so its weight will vary depending on the strength of gravity.

How does the distance between the moon and Earth affect their gravitational pull?

The distance between the moon and Earth does affect their gravitational pull, with a greater distance resulting in a weaker gravitational force. This is described by the inverse-square law, which states that the force between two objects is inversely proportional to the square of the distance between them. Therefore, as the moon moves further away from Earth, its gravitational pull decreases.

Is the gravitational interaction between the moon and Earth mutual?

Yes, the gravitational interaction between the moon and Earth is mutual. This means that the moon also exerts a gravitational force on the Earth, although it is much smaller due to the moon's smaller mass. This interaction is what keeps the moon in orbit around the Earth.

How does the moon's gravity affect the Earth's rotation?

The moon's gravity affects the Earth's rotation through tidal friction. As the moon's gravitational pull creates tidal bulges on the Earth's surface, it also causes friction between the Earth and the moon. This results in a transfer of energy from the Earth's rotation to the moon's orbit, causing the Earth to rotate slightly slower over time.

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