# why didnt the sunrise come at noon the year after leap year?

It’s fairly common knowledge that year is 365 days 5 hours 48 minutes and 46 seconds and we lag behind every year until we’d be off by nearly a day every four years if we didn’t add a day every fourth February. (Whew!) It gets more complex figuring in that we don’t count a leap year every 100 years excepting every 400 years, etc. ala Straight Dope http://www.straightdope.com/mailbag/mleapyr.html

So my question is: If we fall behind nearly six hours every year, why does the sun rise and set at virtually the same time every year? Why not 5hrs and 48min later until we reset it on Feb 29th?

I’m a pretty resourceful guy and I come up with zilch, is the answer right in front of me?

Because a day is 23 hours, 56 minutes, 4 seconds long - which added up over a year almost cancels out those 5-and-a-bit hours.

I don’t know that this will completely answer your question, but we also have leap seconds

i dont get it, if a year is almost 6 hours too long and our year is almost 6 hours short, how do we fall behind?

how can they tell? : “Well, the sun rose at the same time it did the year before…we must have lost 6 hours!”

i understand we may be looking into the heavens and falling behind, but how does that affect earth time? are we adjusting for the earth via the sun or the earth via some far away star?

should i think of a day as a 365th of an ellipse around the sun and not 365 revolutions of the earth, ie: the earth does spin 365 times a year, but at that time we’re only 364.25 days around the sun?

OK, I think I’ve figured this out…

The Earth spins once on its axis 236 seconds faster than a 24-hour day. Therefore, the sun should be at its highest four minutes earlier each day.

However, at the same time, we move 1/365th of the way around the sun each (23hr 56 min… ) day. Which means that the sun is overhead 235.91 seconds later each day.

Obviously, these very nearly cancel each other out. The sun’s overhead point only changes away from noon by 0.089 secs each day.

The purpose of leap years is nothing to do with keeping the sun overhead at noon. It’s about keeping the longest day at 21st June.

(The 0.089 secs/day adds up to 22.7 hours after 400 years. That’s why years divisible by 400 are not leap years, to compensate for this very gradual creep. Eventually we’ll need another compensation for the 1.3 hr gap still present in this, but not for a couple of millennia)

One year is the time it takes for the earth to go around the sun one full circle. One day is the average length of the day, i.e. the average length of time from noon one day to noon the next day. If the year was an integer multiple of a day (e.g. exactly 365 days), you don’t need a leap year. But in reality, one year is something like 365.25 days.

Today is August 21st. Lets’s say it’s noon right now. and at my location the sun is at the highest point. In exactly 365 days, (August 21, 2005) it will be noon again, and the sun will once again be at the highest point. However during that time, the earth hasn’t moved one complete circle - it takes 0.25 more days. So it actually comes back to the same point in the orbit at 6pm August 21, 2005. It comes back again at midnight on August 21, 2006. And again at 6AM August 22, 2007, then noon August 22, 2008. Aha! The earth comes back to the same spot at noon this time! But now the calendar is one day ahead. No problem - we’ll modify the calendar and call it August 21. You can do that by removing any one day from the calendar every 4 years.

Does that make sense? Sorry if that doesn’t help - this type of question is hard to answer, because I’m not sure which part of the whole picture you are confused about.

The short answer is that if leap days were not added to the calendar every so often, eventually dates on the calendar would slide around the physical year, and January 1 would come in the summer.

It is theoretically possible to adjust for the odd length of the year by shifting clock times by 5 hours, 48 minutes, and 48 seconds every year, but to do so would obviously be ridiculously complicated and inconvenient.

The solution has been to add leap days: whole days, not portions thereof. Since the year is not quite six hours longer, one leap day every four years doesn’t quite fix the problem, and various exceptions have to be made.

As for the details:

A day is the amount of time it takes the earth to rotate on its axis once, and is by definition, exactly* 24 hours. (GorillaMan’s period of 23 hours, 56 minutes, 4 seconds is a sidereal day, with which we need not be concerned at this moment.)

A year is defined as the time it takes the earth to revolve around the sun once. Its period is not, as the OP pointed out, an even multiple of the length of the day, and there is no particular reason why it should be. Indeed, it would be a nearly unbelievable coincidence if it were.

What does this mean? At exactly midnight tonight, reach out a couple hundred miles above the earth and make a mark in space. Now next August 22, keep your eyes open for that mark and you’ll notice that it shows up at about 5:48 am instead of midinght. So in 2008 it will show up almost a whole day late.

So some adjustments become necessary to the calendar. Leap days.

(I see on preview that scr4 has beaten me to part of my explanation. Well done, scr4.)

• Okay, the second is defined independently of the day, and leap seconds are added rather than adjusting the length of a second to the changing rate of the earth’s rotation, but we don’t need to be concerned about this now, either.

A year is 1 revolution around the sun. A little bit less than 365 day. We add leap a leap day so we don’t mess around when the seasons happen on our calender.

A day is 1 rotation around the earth’s axis. A little bit less than 24 hours. I can’t remember how we account for this but we do.

Basically our position in the orbit around the sun does not effect the surise. (The direction our axis is tilting does.) So the extra day had nothing to do with when the sun would rise.
etgaw1

Argh commasense 2 min earlier and much better reply. I hate it when that happens. Oh well thank you for enlightening us.

etgaw1

But if we define 24 hours as one axial rotation, then 6 months later noon will be dark and midnight light? Are you not wanting to define 24 hours as one complete rotation with respect to the sun?

A few definitions might help here:
Sidereal day
Solar day
Sidereal year (and solar year)

OK, fair enough, a solar day is 24 hours

As to the OP’s original question, I think I’ve got a simple answer now…

…because we artificially start each consecutive year 5hr 48min earlier, and every fourth year add an extra day to balance it out. In other words, the second year begins 5 hours before the earth has made a complete rotation of the sun.