# Clocks lose 4 min a day relative to the sun...why doesn't the sun rise at 6pm after 180 days?

partly inspired by a response in this thread that the earth make one rotation in 23.97 hours

If the earth rotates once every 23 hours 56 minutes it is rotating faster than our clocks which are set for 24 hours. So it seems that everyday our clocks are off by 4 minutes. After 180 days they will be off by 720 minutes or 12 hours.
Why don’t we see the sun rising progressively 4 min earlier than predicted everyday, such that after 180 days the sun is rising at 6pm instead of 6am?
I’m going to guess…
This discrepency is countered by the orbit of the earth, such that the earth essentially progresses roughly 4 min further along its orbit relative to the sun everyday. And if we take the sun out of the picture the stars will be rising 12 hours off after 180 days.

Is this at all correct? Am I explaining it with any success?

Your guess is right. A solar day is around for minutes and change longer than a sidereal day, because the rotation of the earth has to “catch up” with the sun which has moved relative to the earth’s rotation.

To put it another way, clocks don’t lose 4 minutes per day relative to the sun. They lose 4 minutes per day relative to the stars, which adds up to exactly 1 extra revolution per year. Since we care more about the position of the sun in the sky than we do about the position of Betelguese or Rigel, we calibrate our clocks to display solar time rather than sidereal time.

But there are clocks which are calibrated according to the stars, instead of the Sun. They’re used, unsurprisingly, by astronomers.

This was a plot device in Jules Verne’s Around the World in Eighty Days

The protagonist, Phileas Fogg, traveled east … thus he gained an hour for every 15º longitude he covered … the surprise ending is he took 81 days to travel around the world, but the Reform Club had only experienced 80 days … so Phileas Fogg won the bet after all …

Not quite the same thing, since he was going around the Earth, while this thread relates to the Earth going around the Sun. But it’s a similar effect.

A lot of modern clocks are synced to National Time Services, like the WWV signal from the US National Institute of Standards. That is adjusted periodically for leap-years (and even leap-seconds, now). So even if the day was short a few seconds or minutes, many clocks would be automatically reset to the agreed-upon national time standard.

That is an interesting issue, because the current standard only allows for at most one leap second per month, or 12 seconds per year. With the Earth’s rotation slowing down, this will “soon” become a problem for the (solar) day.

Am I missing something here? 23.97 hours is only 108 seconds short of 24 hours, not 4 minutes.

Must be a typo. The current revolution rate is once per 24 hours minus 236 seconds, or approximately 23.93 h.

Pietro Martire d’Anghiera, historian and chaplain to the King of Spain, commented on this in his De Orbe Novo:

246060/(365.24+1) = 235.9 seconds. Coincidence?

Or to rephrase the OP’s question: A star that sets shortly after sunset will 180+ days later be rising shortly after sunset.*

*Assuming you are at the equator, or the days in question are equinoxes, or some other hand wave to ignore issues about when the sun sets.

When Karl Jansky invented radio telescopy, he noticed a loud source he couldn’t quite track down - but he noticed that the loudest part of the noisy area was setting 4 minutes earlier every day, which led him to realize (eventually) that he was picking up the signal from the center of the Milky Way.

His first discovery was that the source rose and set at all, thus proving that it was astronomical in origin. But as it happens, those first observations were in late December, when the Sun is very close to that point in the sky, so he initially assumed that the Sun itself was the source (a reasonable hypothesis, really). If it hadn’t been for that coincidence, he wouldn’t have needed the fact that it set according to sidereal time.