Why does the moon have a surface gravity that is 1/6 that of earth, though its mass is only 1/81 that of Earth

Answer 1

Inverse square law. You're closer to the center of the moon when you're on the surface of the moon than you are to the center of the earth when you're on the surface of the earth.

The radius of the earth over the radius of the moon is about 3.7. 3.7 squared is about 13.7. 13.5 times 1/81 is exactly 1/6. So that explains the difference, close enough for government work.

The earth spins faster, too, but centrifugal force is negligible to the degree of accuracy we're talking about.

Useful fact: A uniform solid sphere's gravitational attraction is the same as if all its mass were concentrated at a single point at its center.

Answer 2

because the potential of gravitational attraction has to do with the quantity of mass of the gravitating body and the gap at which it truly is measured. The Moon is smaller than the Earth, so the exterior is lots in route of the middle of the Moon than the exterior of the Earth is from the middle of the Earth. So in case you've been to degree the stress of gravity for the Moon vs. the Earth yet from a standardized distance from thier respective centers (presented you're "outiside' the exterior), say one hundred,000 miles, then Earth's gravity could be about a million/81th that of the Moon.

Answer 3

Because its smaller and the force of gravity is inversely proportional to your distance from the centre of the planet.
So, if the moon's radius was 4 times smaller than the earth then the force would be made 16 times greater. However, if its density was the same then its volume and mass would be 64 times less. Overall, this would make its gravity 4 times less than the earth's.

Answer 4

force = (gravitational constant)*M*m/(r^2),

where m = mass of person
M = mass of earth or moon
r = distance from surface to center (of earth or moon)

so, even though the moon is 1/81 of the mass, the radius of the moon is so much smaller than that of the earth that (and since it's squared in the denominator), it makes the force be not as small as you would imagine, because you are closer to the center of the moon on it's surface than you are to the center of the earth when you're on the earth.

Answer 5

The moon and Earth can both be treated as point particles located at their centres. Let a be the acceleration due to gravity at the surface of the Earth.

From the problem:
a_{moon} = a / 6
a = acceleration due to gravity

Newton's Law of Gravity:
F = GMm / r^2
Where M is the Earth/moon's mass, m is the mass of an object.

Newton's Law:
F = m * a

Combining the two:
a = GM / r^2

From our equality before:
GM_{Earth} / r_{Earth}^2 = 6GM_{Moon} / r_{Moon}^2

We know that G is a constant, so it cancels out. We also know:
M_{Moon} = M_{Earth} / 81

81 * M_{Earth} / r_{Earth}^2 = M_{Earth} / r_{Moon}^2
(r_{Earth} / r_{Moon})^2 = 81
r_{Earth} = r_{Moon} * 9

Therefore, we find that the stated facts can be true if the distance from the centre of the Earth to the Earth's surface is 9 times greater than the distance from the centre of the moon to the moon's surface.

Answer 6

Gravitation Force= (G (mass of 1st object)(mass of 2nd object))/ R^(2)
Newton's law of gravity says that you multiply the two objects mass with G which is a constant equalling 6.6670 x 10^(-14) and divide by the distance between the objects squared.

Answer 7

The amount of gravity on the surface of a planet has to do with the distance you are from the center of the planet, or its center of mass.

Answer 8

Because the force of gravity declines as the inverse of the mass. Don't ask me why but it just does.

Answer 9

thats a good question, but im guessing it is because the formula for gravity has either a squared root or a squared equation in it somewhere.

Answer 10

That would lead to beleive that Gravity is not a linear equation.