Why does gravity rotate with the Earth?

[Gfoxboy]

Okay, relativity and gravity don't seem to like getting along even with the General Theory. Think about this: Obviously everyone knows the simple way of thinking of gravity as a force pulling you toward a mass. The force is inversely proportional to the distance with 1/4 in there somewhere (I don't remember exactly ). Now if you think of your 3D coordinate cube as rotating with the Earth then in order to stay still with the coordinate plane you would have to stay still with the surface of the earth. In this way we can describe the veolocity required to orbit the Earth at a certain distance. My question is why gravity rotates with the earth. Let's say that the coordinate plane does not rotate with the Earth and the 0,0,0 point is at the center. Also you are at the perfect distance at which you fly at such a speed that if a line was drawn from you to the Earth's surface, you would remain over the same point. According to our new coordinate plane you are moving fast enough to orbit the earth, but according to the Earth's surface you would fall. And if you changed direction you would fly away from the Earth because you would be moving two times as fast as you needed in order to orbit. Should this not bring into account the Earth's rotation in the explanation of gravity?? I personally dont' think the mere bending of space time is enough to account for this, considering the relativity of motion. This kind of stuff makes my head hurt... :yuck:

 

[Nenad]

the difference in gravity is $$\frac {1}{d^2}$$

 

[HallsofIvy]

Gravity DOESN'T "rotate with the earth". Gravity is rotationally invariant.

 

[Gfoxboy]

If gravity doesn't rotate with the Earth then you could potentially orbit the Earth at a critical velocity but not move at all compared to the ground. And in that case it would take no energy to stay airborne. Gravity has to rotate with the earth.

 

[pervect]

If gravity doesn't rotate with the Earth then you could potentially orbit the Earth at a critical velocity but not move at all compared to the ground. And in that case it would take no energy to stay airborne. Gravity has to rotate with the earth.

Sounds like a geostationary satellite over the equator?

 

[mee]

Gravity DOESN'T "rotate with the earth". Gravity is rotationally invariant.

Then how could the new devices hinted at in the new scientific american measure different gravitational variances that are stable over parts of the earth. If these variances are stable then they have to be location specific on the Earth and thus rotate with it?

 

[Nenad]

there is a variance by elevation, not by rotation. And also, it depends on the time. If it is day ouside, you are facing the sun and the suns gravity on you is pulling on you, making gravity on Earth seem less (very samll, but noticable). If it is night, then the gravities of Earth and the sun add up vectorially, and make gravity larger. This is what I could think of variation. Theres probably more causes.

 

[jcsd]

Doesn't the rotation of the Earth cause 'frame-dragging'?

 

[selfAdjoint]

Yes. It's called the Lense-Thirring effect. For the Earth it's very small, but they're trying to test it now.