Why is gravity stronger on earth than the moon?

[greg5555]

If gravity is the effect of spacetime curvature, then why is it stronger on Earth than the moon? In other words, it is the curvature of space and time that gives the effect of pulling an object towards a larger object, so once that direction of pull is established why would the size of the larger object (earth) make gravity stronger? Once the direction of pull (due to curve) is established as in DOWN to the Earth or moon, why would greater mass make a difference?

I read somewhere else that if the Earth and moon were closer to the sun, that we would get pulled into the sun. That doesn't seem right. Why isn't mercury pulled into the sun too? I have only seen gravity portrayed as a 2D sheet, but we are in a 3D universe. In which direction is spacetime displaced in space, since space is not a 2D sheet? The sun is displacing spacetime in 3 dimensions, so why does one orbital plane take priority? The sun holds a large planet like Neptune in orbit due to curved spacetime, what keeps it from being pulled closer, or flying away into space?

 

[jedishrfu]

Welcome to PF!

Mercury is getting pulled toward the sun but it has sufficient orbital speed to stay in orbit. It it was a slower speed then it would spiral into th sun.

General Relativity spacetime curvature is often represented as a rubber sheet with the heavy body in the center stretching it downward and so smaller bodies follow the geometry of the sheet to reach the center. It's an analogy only and so you must imagine it in a higher dimensional space.

You should read more about it here:

http://en.wikipedia.org/wiki/Gravity

 

[ZapperZ]

If gravity is the effect of spacetime curvature, then why is it stronger on Earth than the moon? In other words, it is the curvature of space and time that gives the effect of pulling an object towards a larger object, so once that direction of pull is established why would the size of the larger object (earth) make gravity stronger? Once the direction of pull (due to curve) is established as in DOWN to the Earth or moon, why would greater mass make a difference?

Isn't this similar to asking why does a greater charge gives of a stronger electric field?

"Mass" is the source of gravity/spacetime curvature the same way "charge" is the source of electric field.

Zz.

 

[Chronos]

It's a combination of mass and distance from the center of mass. The formula for calculating acceleration due to gravity is g = GM/R^2, where g is the acceleration due to gravity, G is the universal gravitational constant, M is mass, and R is distance. Plug in the mass and radius of the moon and Earth and do the math. Note that if the moon were much denser, it would be smaller as would its radius. So, acceleration due to gravity at the moon surface could be identical to that at the surface of Earth were it small enough.

 

[JustATheory]

The reason that gravity on Earth is greater then the gravity on the Moon is because the larger the mass of an object then the higher the gravity. That is why we are orbiting the sun. Because its mass is greater then the planets that we know of in our solar system. And since the suns mass is larger than ours, the gravity is greater and is why we orbit the sun.

 

[DaveC426913]

If gravity is the effect of spacetime curvature, then why is it stronger on Earth than the moon?

The answer is quite simple: Earth has more atoms.

The gravity of any object is the sum total of the gravity of its individual components. You are being pulled toward each individual atom in the Earth by its own tiny gravitational field. The effect of gravity is cumulative.

This is true whether you look at it as a Newtonian classical gravity force, or as an Einsteinian relativistic spacetime curvature.