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Does the spin of the earth around its axis vary at different distance from the sun?,if so how does it correspond to the length of day and night,?

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I would believe the rotation is constant (unless the Moon messes things up in a way that I can't figure out right now), but that this does imply some variation in the length of a day. See – Keep these mind Jun 4 '13 at 15:00
The moon has libration in longitude, but libration is an oscillation about an equilibrium, so I don't know if it makes sense to think of the earth as having libration in longitude. – Ben Crowell Jun 4 '13 at 21:53

No, there's no relationship between the earth's rotational speed and its distance from the sun.

The earth follows an elliptical orbit around the sun, but from the earth's frame of reference, it's in freefall. Therefore, the earth's rotation is independent of its path through space.

The earth's rotation is actually affected by tidal effects from the moon (our rotation is slowing down), but this effect is too slow to have a noticeable impact on the length of our days and nights. (We add a leap second every few years to account for this)

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thanks,but does that mean the length of day is the same through out the year at the equator,if there were no tilt,I think there ought to be a few second difference ,between various years – Derg Jun 4 '13 at 15:52
No, there really isn't. – Dmitry Brant Jun 4 '13 at 17:11
Dmitry, are you sure you can say there is absolutely no effect? For example: you agree that our rotation is slowing down due to the tidal effects of the Moon on the Earth. The Sun also causes tidal effects, smaller due to the vast distance it is away from Earth. The closer the Earth is to the Sun, the greater these effects would be, and so by the same logic you applied to the Moon-Earth system, the Sun should also affect the Earth's rotation rate, larger the smaller the Sun-Earth distance is. – Will Jun 4 '13 at 17:51
@Will Yes, technically the sun exerts a nonzero tidal force on the earth. But the strength of that effect is orders of magnitude smaller than the tidal force from the moon... – Dmitry Brant Jun 4 '13 at 18:15
"But the strength of that effect is orders of magnitude smaller than the tidal force from the moon", the tidal effect are of the same order of magnitude. That is why there are significantly larger and smaller tides over the course of the month. Near new moon and full moon the two tidal effect superimpose constructively; near either quarter moon they interfere destructively. Not that this has a any effect on the length of the day except on the time scale of tidal locking. – dmckee Oct 28 '13 at 2:16

The Sun does indirectly influence the length of day: it's not a gravitational effect, but a seasonal, as the temperature of the atmosphere changes throughout the year.

The rotation of the Earth changes over time, and in particular there are annual and semi-annual fluctuations (see wikipedia). This is caused by the exchange of angular momentum between the solid Earth and the atmosphere (and to a lesser extent, the oceans). The angular momentum of the atmosphere changes throughout the year; it is highest in January, when the temperature in the Northern Hemisphere is lowest. This causes stronger westerlies in the NH than in July, increasing the angular momentum of the atmosphere. Similarly the westerlies in the Southern Hemisphere are strongest in July and weakest in January. However, the effect is not as strong as in the Northern Hemisphere, because the larger landmass in the NH causes a higher temperature difference.

The net result is that the angular momentum of the atmosphere is larger in January than in July. However, the total angular momentum of the solid Earth + atmosphere (and oceans) is conserved: the solid Earth is spinning slower when the atmosphere is spinning faster, and vice verse. As a result, a day in January is longer than a day in July, although the difference is less than a millisecond.

Source: Atmospheric angular momentum and length of day, pag 14.

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