# Relativity and Earth's Rotation

JS357
Science 13 May '12 18:22
1. 13 May '12 18:22
Without going into too much detail:

My calculations show that if the earth is held as stationary, any object about 4.12529612e9 Km away that is directly above the equator at the same point every 24 hours is moving in an orbit around the earth at the speed of light, and anything farther away is moving faster. How is this dealt with?
2. sonhouse
Fast and Curious
13 May '12 18:58
Originally posted by JS357
Without going into too much detail:

My calculations show that if the earth is held as stationary, any object about 4.12529612e9 Km away that is directly above the equator at the same point every 24 hours is moving in an orbit around the earth at the speed of light, and anything farther away is moving faster. How is this dealt with?
In the same way as thinking about a pair of scissors 20 light years long and closing at a rate that will finish the closing in forty years so nothing moves faster than the speed of light but the place where the scissors cross moves faster than the speed of light. How is THAT possible? Same question.
3. 13 May '12 20:432 edits
Originally posted by sonhouse
In the same way as thinking about a pair of scissors 20 light years long and closing at a rate that will finish the closing in forty years so nothing moves faster than the speed of light but the place where the scissors cross moves faster than the speed of light. How is THAT possible? Same question.
From the frame of reference of the scissors, the meeting point would be moving along the axis of their meeting, at some speed s (although no matter would be moving along that axis, so there is no problem) but from the frame of reference of the meeting point, the scissors would be moving at the speed s, so matter would be moving at s>c.

In both cases (yours and mine) there is no problem from the standpoint of one frame of reference, but the problem remains from the other standpoint, because one frame allows the speed of matter s<=c, the other frame requires s>c.

I have heard that it has to do with rotatory motion being different than linear; there being no expansion of space under rotatory motion, but it still puzzles me.
4. 14 May '12 11:37
Originally posted by JS357
Without going into too much detail:

My calculations show that if the earth is held as stationary, any object about 4.12529612e9 Km away that is directly above the equator at the same point every 24 hours is moving in an orbit around the earth at the speed of light, and anything farther away is moving faster. How is this dealt with?
That's why relativity always talks about 'speed' and not 'velocity'. The relative speed is measured in a straight line between two objects and is either towards, or away from each other.
5. 14 May '12 15:561 edit
That's why relativity always talks about 'speed' and not 'velocity'. The relative speed is measured in a straight line between two objects and is either towards, or away from each other.
I'm not sure that explains it, but apparently there is empirical evidence that the frame of reference of an object cannot simply be taken to be stationary WRT the rotating object (that is, can't be taken to rotate with the object). For example, a pool of the surface of water located at and around one pole of a rotating sphere will tend toward the concave due to so-called centrifugal force, regardless of whether it is taken to be stationary to an observer who is going along for the ride. Since forces associated with rotation can be mathematically treated the same as acceleration due gravitational forces, I suspect that special relativity covers this.

http://en.wikipedia.org/wiki/Absolute_rotation
6. sonhouse
Fast and Curious
14 May '12 16:15
Originally posted by JS357
I'm not sure that explains it, but apparently there is empirical evidence that the frame of reference of an object cannot simply be taken to be stationary WRT the rotating object (that is, can't be taken to rotate with the object). For example, a pool of the surface of water located at and around one pole of a rotating sphere will tend toward the concave due t ...[text shortened]... suspect that special relativity covers this.

http://en.wikipedia.org/wiki/Absolute_rotation
Sounds like you could make a telescope mirror out of that using mercury, it should assume a parabolic shape. Not sure how that would work with small spheres though.
I think you are assuming Earth sized bodies with water at the poles, spinning.
7. 14 May '12 21:20
Originally posted by sonhouse
Sounds like you could make a telescope mirror out of that using mercury, it should assume a parabolic shape. Not sure how that would work with small spheres though.
I think you are assuming Earth sized bodies with water at the poles, spinning.
To become concave it needs a rim. Otherwise it just goes toward the equator. With enough water, it envelops the planet in an oblate ellipsoid(?) shape depending on gravity, size and rpm, I suppose.
8. 15 May '12 10:12
Originally posted by JS357
To become concave it needs a rim. Otherwise it just goes toward the equator. With enough water, it envelops the planet in an oblate ellipsoid(?) shape depending on gravity, size and rpm, I suppose.
The earth as a whole is fluid enough that it is already an oblate spheroid.