I just read that the Gregorian calendar is off by 26 seconds a year from the solar calendar. That adds up to about 43 minutes ever 100 hundred years.
Does this mean that if it starts to get dark at 5:30 pm on the East coast on December 1st, that it got darker 43 minutes earlier or later 100 years ago and that it will be off by another 43 minutes 100 years from now?
That seems dubious to me. If the government goes so far as to add leap seconds to days occasionally, it would seem that we have a higher degree of control than 23 seconds a year.
I believe it’s for this reason that we don’t have leap years every 100 years, and do have leap years every 400 years, and don’t have leap years every 16,000 years, but I guess it could be possible for two days 100 years apart to be as far as one full day off.
Oh god I’ve got to correct some code stat!! 
First, the Gregorian calendar is not about length of day, but length of year. So it has nothing to do with time of sunset, which varies over the year, but is always the same (well nearly so) every year on a given day. The Gregorian calendar has the effect of omitting one leap year every 133 1/3 years (3 out of every 400). IIRC, a more accurate calendar would omit one leap year every 128 years. The difference will not add up to even one day for about 3200 years. I once read somewhere that they are supposed to omit the leap year in years divisible by 4000 (why not 3200?). If civilization should last so long, which I doubt.
What all this mainly effects is the date of the equinoxes. During the 20th century, the first day of spring in the easter time zone was always March 20 or 21. Later in this century it will drift to being March 19 and 20, and then, when there is no leap in 2100 will gradually revert.
The year actually varies by one or two seconds and in recent years there have been occasion to add a second at midnight on June 30 and Dec. 31 as necessary.
I think that this has something to do with the fact that there are 365.24 days in a year, so every 100 years, we skip the leap year because 100*.24=24, meaning we’d only need 24 leap years in a 100-year span. My only guess as to the other ones is that there’s more decimal places after 365.24 (wiki says .2425) that accounts to the extra needing of days occasionally.
I’m sure the NIST people have something in mind to prevent this happening. I do remember them shoving in a leap second every few years, usually at New Year’s when the last minute of the year would be 61 seconds long.
But we add back the leap day when the year is divisible by 400 (as in 2000), so the Gregorian year = 365.2425 days.
The mean tropical year (year of the seasons) is 365.2422 days and getting shorter over time. 0.0003 days * 100 = 43 minutes.
Ok, let’s merge the thought processes here so that the OP can understand what is really going on.
D_White, what you read is true, in a way. That is to say, as Freddy the Pig put it, over sufficient time, the Gregorian calendar does not match up with what the Earth is really doing. This is because the Earth, quite unfortunately for the quartz clock set, doesn’t spin in such a way that the rotation matches precisely with the period of revolution around the sun. That is to say, when we manage to get back to the same point in our orbit around the sun, we’ve completed 365 complete rotations, plus not quite a quarter addtional rotation. Thus, if we didn’t do anything about it, every four years we would be a day later in our calendar year in arriving at the same spot.
Because we are a bit anal about having our calendar match up to the seasons, we go through all sorts of gymnastics to try and keep the winter solstice, for example, on the same day every year. Every four years, we add a day to the year. But this doesn’t quite match the situation, so every 100 years, we don’t add that day when we otherwise should have. But that still isn’t QUITE enough, so every 400 years we DO add the day. That adds up to 146097 days in 400 years. Unfortunately, the Earth only has managed to complete 146096.88 rotations in that time frame. So, you can see, we are still not quite matched up.
Now, this has no effect upon our “day” or the time of things like sunrise. That’s because the time of events that occur on a daily basis are related not to our revolution around the sun, but instead to our rotation about our axis. We keep track of this by paying attention to when the sun sits in the same position in the sky; we’ve decided that a “day” of 24 “hours”, divided up into 60 “minutes”, divided up into 60 “seconds” manages to match up to the mean length of the day (the time it takes for the sun to return to exactly overhead varies during the year - see analemma). So, the sunrise on December 1 any given year will match up to the sunrise on December 1 any other year, pretty precisely. To the extent that the Earth is slowly slowing down its speed of rotation, we chuck in a second here and there to make this happen.
So what DOES the 43 minutes mean? It means that, in 2107, on December 18th, we will arrive at the same spot in our orbit around the sun 43 minutes earlier than did today. So if I post this at 10:10 am, and someone marked our position in our orbit around the sun, and we had that marked again in 2107, we would reach that position at around 9:27 am instead.
I had just gotten off work and didn’t feel like doing that math. ;p
