Mutual effects of gravity and velocity on time

[Dmstifik8ion]

The Earth takes the shape of an oblate spheroid due to its rotation and so gravity is stronger at the North/South Poles while the Equator has a velocity relative to the Poles.
When we consider General Relativity (the effect of gravity on the passage of time) together with Special Relativity (the effect of velocity on the passage of time) do these effects precisely cancel out maintaining synchronicity of clocks over the surface of a rotating oblate spheroid?

 

[DaveC426913]

The Earth takes the shape of an oblate spheroid due to its rotation and so gravity is stronger at the North/South Poles...

Don't be so quick to assume that gravity is greater at the poles because of the smaller radius. I believe this is false.

 

[pervect]

The Earth takes the shape of an oblate spheroid due to its rotation and so gravity is stronger at the North/South Poles while the Equator has a velocity relative to the Poles.
When we consider General Relativity (the effect of gravity on the passage of time) together with Special Relativity (the effect of velocity on the passage of time) do these effects precisely cancel out maintaining synchronicity of clocks over the surface of a rotating oblate spheroid?

Basically, the answer is yes. All clocks on the geoid run at the same rate. See for instance http://www.physicstoday.org/vol-58/iss-9/p12.html or http://hermes.aei.mpg.de/2003/1/article.xhtml (it's a long article, see the section above (21)).

This ignores tidal forces from the sun and moon, which have only a very small effect. (The effect does perturb the theoretical ideal, i.e. it hasn't been included in the above analysis).

One can derive this if one assumes that energy is conserved. The geoid is defined to be an equipotential surface in the rotating frame. Therfore, if energy is conserved, light measured in the rotating frame should have the same energy if it starts and stops at any two equipotential points, i.e. there should be no net red or blueshift between any two points on the geoid.

Energy conservation in GR can get tricky, but as long as one sticks to static geometries this argument works fine.

 

[Dmstifik8ion]

Basically, the answer is yes. All clocks on the geoid run at the same rate. See for instance http://www.physicstoday.org/vol-58/iss-9/p12.html or http://hermes.aei.mpg.de/2003/1/article.xhtml (it's a long article, see the section above (21)).

This ignores tidal forces from the sun and moon, which have only a very small effect. (The effect does perturb the theoretical ideal, i.e. it hasn't been included in the above analysis).

One can derive this if one assumes that energy is conserved. The geoid is defined to be an equipotential surface in the rotating frame. Therfore, if energy is conserved, light measured in the rotating frame should have the same energy if it starts and stops at any two equipotential points, i.e. there should be no net red or blueshift between any two points on the geoid.

Energy conservation in GR can get tricky, but as long as one sticks to static geometries this argument works fine.

Thanks, the links are perfect!