How Long is a Day?

"How long is a day?" - Question prompted by another question that I'll get to later.

A loose definition of an astronomical body's "day" is the time it takes to rotate once.

But relative to what? A "solar day" is the time it takes for a body to rotate such that a point on its surface ends up with the Sun in the same position in the sky. For example, if you were to stand on the meridian line at the Greenwich observatory at noon (the point at which the Sun is highest in the sky) and stay there until the Sun returns to that position once more, you'd have stayed there for one solar day.

A "stellar day" is the same idea*, but the basis for your measurements is not the Sun but the distant background of stars. "Sidereal days" are measured relative to the vernal equinox. Here are the lengths of a day on Earth from solar, stellar and sidereal points of view:

 - Solar day: 86,400 seconds (exactly 24 hours, but that's not surprising as that's how we have historically defined the second. It may be interesting or infuriating (depending on who you are) to note that the "SI" second is slightly shorter than an "apparent" second due to the Earth's slowing rotation).
 - Stellar day: 86,164.10004 seconds (that's 23 hours, 56 minutes and 4.10004 seconds)
 - Sidereal day: 86,164.09164 (23 hours, 56 minutes and 4.0916 seconds).

As you can see, stellar and sidereal time are pretty close together (about 0.0084 seconds in it), but a bit less than 4 minutes shorter than the 24 hours that we colloquially call "a day".

I'll stop there, I think, and avoid mentioning that these values aren't all constant - some 'wobble' a bit.

* No, it doesn't just mean "a really particularly good day".


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