11 June 2009

The Exact Middle of the Year - A Numerical Debate

So on my way to work yesterday and today, I was curious to know exactly when the middle of the year was. Of course, figuring out the day is pretty easy: 365 days/2 = 182.5 ~ 182 ==> July 2nd. However, I decided to push this a little further: what was the exact hour of the day that is the center? Well, seeing as how the number we got was actually rounded down by 0.5 (or half a day), then the exact middle of the day by hour is July 2nd at 12pm. However, a problem presents itself: this is all based on a 365-day calendar year, but what about with leap years?
According to the Julian calendar, the exact year is 365.25 days, which means that every 4th year we have an extra day, hence the reason February 29th exists only on years divisible by 4. This made me think a little, and so I came up with this: ((365.25*24)/2), which produces a result that puts the time on July 2nd at 3pm. Now, this seems to fit a little, since after 4 years we produce exactly midnight on the year after the leap year, but is this really correct? Even though computationally it seems correct, it just feels a little incorrect since there is a 3-hour difference. Oh well, I guess the exact middle hour of a Julian-calendar year is July 2nd at 3pm.
However, according to Wikipedia, a closer time may be calculated with resolution down to the second depending by what definition we use for the exact year. For example, using the value of a year based on the sidereal year, we can calculate the middle as ((365.256363051*24*60*60)/2 which is gives July 2nd at 3:04:34PM (it is rounded down since there is a small remainder).
I think that I like that result, so being the geek that I am I've set an alarm to go off on July 2nd at 3:04:34PM to remind me that I've hit the middle of the year to the second.

6 comments:

AJ said...

So what will you do to commemorate the middle of the year?

Anonymous said...
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Anonymous said...

Who knows. Maybe asked to be beamed back up??!! ha ha

Maxo said...

Is that really correct though? In practical terms, an individual year isn't 365.25 days, but either 365 or 366 days. You're calculations are correct, but according to that logic, the mid point of the Julian year should change 3 more times before repeating itself, and wouldn't stay constant every year, since we don't have some sort of 6 hour limbo period every new year. The most practical and constant midpoint we can come up with is based on each individual year, and while the midpoint you calculated is correct, it can't be adapted to fit any kind of date/time system we use, since we don't average out our years (that would completely set off our day/night schedule by 6 hours every year). The most practical midpoint would be (assuming you're on daylight savings time) July 2nd, 1:00PM on non-leap years and July 2nd, 1:00AM on leap years

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