How many hours does it take for the Earth to fully rotate?

August 23, 2024 6:36 AM

I know there are 24 hours in a day, and I always thought of that as "1 rotation of the Earth," but thinking about it more now, I realize that they're slightly different, and the more I try to figure this out, the more confused I get.

So, for simplicity's sake, I'm going to ignore the fact that the sun is also moving through the galaxy, and I'm going to ignore the tilt of the Earth. And the big thing, which some people are not going to like, is that I'm thinking in purely non-relativistic, Newtonian terms, so no "depends on the frame of reference". If it makes it easier, pretend you and I are both people living in the 18th century and we full-on believe in the aether.

So, that out of the way, let's say this white circle is the earth, and that red dot is some point on the Earth's equator.
At first blush, I assume a day is like this. The Earth does one complete rotation, and the red dot is back exactly where it started.
The problem is, if you keep doing that over and over again, three months later the situation is going to look like this. What used to be your "sunrise" is now your noon.
And then in another three months, the situation is going to look like this. The sun used to be rising at 6:00 a.m., but now it's setting at 6:00 a.m.
So the reality must be something more like this. Which means it's doing an entire rotation...and then a little bit extra. It's 24 hours with that little bit of extra added in, but the full rotation itself would just be like 23.93 hours or so, right? (24 hours of adjustment over 365 days ≅ 0.07 hours of adjustment per day)

Man, I hope I'm not coming off like time cube guy or Terrance Howard here. I don't think I've discovered anything new, I'm sure this is something that people will go "oh, yeah, that's called a periterran day, as opposed to a solar day, it's something you learn in Astronomy 101." Am I totally off-base with this? Is there a term for it, or a well-established number or something?

posted by Bugbread to Science & Nature (7 answers total)

Best answer: I think you're referring to a sidereal day, which is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars" and is 23.9344696 hours, as you correctly calculated.
posted by Mr.Know-it-some at 6:40 AM on August 23 [22 favorites]

Best answer: I may possibly be missing what you intend to be asking, but are you familiar with the synodic and sidereal days? Time of rotation relative to the sun and time of rotation relative to the stars? EDIT: I see I was slightly beaten to the punch.
posted by Whale Oil at 6:44 AM on August 23 [4 favorites]

Response by poster: That's exactly it! Thanks, both of you! (Also, that Wikipedia animation is so clear and understandable!)
posted by Bugbread at 6:53 AM on August 23 [1 favorite]

This came up last year in this post on the blue and much earlier in this one.
posted by mbrubeck at 7:20 AM on August 23

It's fantastically cool that you figured that out from first principles. If you want to keep boiling your brain in the same way, maybe look into the equation of time -- I recall drawing charts not unlike yours while trying to get a handle on that. Not sure I ever succeeded though!
posted by dick dale the vampire at 7:52 AM on August 23 [4 favorites]

If you want to see an example of this in a micro scale (and further demonstrate it for yourself), check out The SAT question everyone got wrong
posted by supercres at 8:57 AM on August 23 [5 favorites]

This concept is extemely important in astronomical observations. If you want to point your telescope at the same "place" in the sky to something you are tracking there, that will be one sidereal day later.
posted by vacapinta at 10:04 AM on August 23