When Time Isn’t Based on the Sun (or, What’s a Sidereal Day?)


Here’s a New Year’s riddle! With respect to the stars, how many complete
times does the earth rotate around its axis in one full orbit of the Sun? If you answered 365, or 366 on a leap year…
you’re wrong. It’s okay through, your brain just simplified the question, changing
the complicated phrases of “rotates around its axis” to “days” and “in a full
orbit of the Sun” to “in a year”, an understandable interpretation which makes
your answer right. But the qualifying phrase “with respect
to the stars” makes the answer 366 every year. Why? I’m glad you asked! We measure days using the position of the
sun in the sky. Our 24-hour mean solar day is the average amount time it takes the sun
to come back to its highest point in the sky as the earth turns on its axis. Or more simply, it’s the average time from
noon to noon, making a day a full rotation of the Earth around its axis with respect
to the Sun. If the stars weren’t there, it’d be easy
to think that one day is also exactly one earth rotation, or even to think that the
sun revolves around us. But the stars are so far away that even though
they’re moving too, they appear fixed in their positions in sky. This makes them really
good reference points to understand what’s happening inside the solar system – like
a giant sheet of cosmic graph paper. We call this the sidereal reference frame. To see why the definition of a day and the
sidereal frame change the riddle’s answer to 366, let’s take a look at what happens
to the earth as it orbits the sun. Using the North Pole as “up”, the earth
rotates counterclockwise on its axis, and orbits the sun the same way. At the start of our example year, this point
on the earth is facing the sun. 24 hours later it’s going to face the sun again, but in
that time the earth also moves a tiny bit in its orbit. Use the stars as a reference,
we notice that the earth has had to spin a tiny bit more than a full rotation to once
again point at the sun. In fact, one full rotation, called a sidereal day, only takes
about 23 hours and 56 minutes. Over the course of a full year, these 3 minutes
and 56 seconds of extra spinning each day add up to one extra annual turn of the earth.
So even though we measure 365 complete days each trip around the sun, the earth has actually
spun on its axis 366 times. But however we label them, 366 rotations means
only one thing: Happy New Year. Don’t forget to share this video to stump
your friends. And, if you enjoyed it, consider subscribing to Tech Laboratories for monthly
videos on science and technology. See you next time!

8 thoughts on “When Time Isn’t Based on the Sun (or, What’s a Sidereal Day?)

  1. He thinks he's smart, but he's not. 1 orbit of the sun is not a year. A year is actually defined as a tropical year which is less than 1 full orbit of the sun. 365 days, 5 hours, 48 minutes, 45 seconds. This is the time between Summer Solstice to Summer Solstice. The length of 1 orbit of the sun is 20 minutes longer. Adding twenty minutes would be 365.256 days. Obviously there is one more rotation involved, so 366.256 is the correct answer. And the length of a sidereal day is 365.256/366.256 x 24 hours per solar day. = 23.934472 hours, or 23 hours, 56 minutes 4.0994 seconds.

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