Moon's unusual gravity
We know that the Moon's gravity is about one-sixth that of Earth. Then I recently read that the mass of the Moon is about one-eightieth the mass of Earth. Since gravity depends on the mass of the 2 objects, shouldn't the Moon's gravity be one-eightieth the gravity of Earth? Is the Moon extra dense?
Do you know the formula for determining the gravitational force between two masses?
@Alchemista: If the Moon had its current mass but was the size of the Earth -- and was therefore enormously less dense -- then it would have 1/80th of the surface gravity. But the Moon is not the size of the Earth, and that matters. I asked if the original poster knew the formula as a nudge towards thinking about the fact that the distance between centers of the masses is just as important a factor as the masses.
I get it. If the Moon had its same mass, but with a radius the same as Earth, then the surface gravity would be 1/80th. The distances would correspond, and mass would be the only variable. The Moon's smaller radius from center to surface gives us the 1/6 instead of 1/80th. No wonder it's so hard to split an atom.
@JohnCanon: The difficulty of splitting an atom is not due to the gravitational force holding it together, but that belongs on physics.se Gravity is truly negligible at that scale.
@John I find it more helpful to think if it had the same density, it would have the 1/ (the cube root of 80) the surface gravity. That's a bit less than a quarter.
As you said, the mass of the Moon is 1.2 percent that of the Earth.
Now, if you mean the gravitational acceleration at the surface, it is calculated like this $G\frac{M}{R^2}$, where $M$ is the mass, and $R$ is the radius of the celestial body. The moon's mass is a hundred times smaller, but the radius is four times smaller, meaning its surface gravity will be $100/16 \approx 6$ times smaller. Considering the factor is mass over radius to the power of two here, density alone does not help you determine the ratio of surface accelerations.
On a side note, the moon's density is around 60 per cent that of the Earth.... and that 60% density value should derive directly from knowledge of the radius and gravitational force at that radius :-)
Low density because Theia drops most of its iron core onto proto-Earth) at collision time. Still the 2nd densest moon in the solar system; only Io is denser
@DavidTonhofer that must mean Io is worth more, since it has a higher metal content. How do we go about trading?
@corsiKa That's easy. I give you \$10 for a bit of the Moon and you give me \$50 for the same amount of Io.
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Content dated before 7/24/2021 11:53 AM
Parrotmaster 2 years ago
The moon being made from other stuff than the Earth probably factors into this. A lot fewer liquids there.