I Understanding the Discrepancy: Why Does the Moon Have Less Gravity Than Earth?

[Pierre Ordinaire]

TL;DR Summary

Gravity on Earth vs the Moon.

Apologies in advance if this has been touched before. If the Earth has 81 times the mass of the Moon, why the Moon has 1/6 of the gravity of the Earth?

 

[kuruman]

Do you find that strange? What do you think it ought to be instead of 1/6?

 

[Ibix]

Acceleration due to gravity increases with mass and decreases with distance squared from the center (outside spherically symmetric bodies, anyway). The moon is less massive but much smaller. If you built a tower on the moon so high that you were as far from the center as the radius of the Earth, gravity there would be 81 times weaker than the surface gravity if the Earth. But "on" the moon usually means on the surface, much closer to the center than on a huge tower.

 

[Pierre Ordinaire]

Thank you.

 

[A.T.]

Summary:: Gravity on Earth vs the Moon.

Apologies in advance if this has been touched before. If the Earth has 81 times the mass of the Moon, why the Moon has 1/6 of the gravity of the Earth?

See:
https://phys.org/news/2016-01-strong-gravity-planets.html

For example: Saturn has 95 times more mass than Earth, but about the same surface gravity:

 

[Janus]

See:
https://phys.org/news/2016-01-strong-gravity-planets.html

For example: Saturn has 95 times more mass than Earth, but about the same surface gravity:

Of course that is due to the fact that Saturn has a density that is 1/8 that of the Earth's.
In the same vein, The Moon has a lower density than the Earth. If it had the same density as the Earth and the same mass, its surface gravity would be closer to 1/4 the Earth's rather than 1/6.

 

[mjc123]

If it had the same density as the Earth and the same mass

I assume that means "the same mass as the actual Moon". Not "the same mass as the Earth" - then it would be identical. Obvious if you think about it, but at a first reading it looked wrong.

 

[Janus]

I assume that means "the same mass as the actual Moon". Not "the same mass as the Earth" - then it would be identical. Obvious if you think about it, but at a first reading it looked wrong.

Yes, I meant the moon's current mass.

 

[Meir Achuz]

g=GM/R^2. Work that out.