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Question:** My new day-planner says 2012 will be a leap year. What’s up with that? — JR, Vatican City

**Answer:** Leap years can be confusing. Normally, any year divisible by 4 will be a leap year, so 2012 obviously qualifies. But first, let’s talk about what that whole leap year concept is based on. Nobody likes math, but if you want to understand leap years, you’ll need to do some arithmetic.

When you watch the video above, you’ll see that as Earth orbits around the Sun, it’s also rotating. One rotation equals one *day*. One orbit equals one *year*. The animation shows Earth as seen from above the North Pole, so its rotation and orbit are both counter-clockwise. The animation is not to scale, either in distance or size.

We show only 30 rotations of Earth … 365 would make you dizzy. But the point is, the number of rotations in a year does not equal 365. When Earth gets back to the starting point in its orbit, it’s actually rotated (approximately) 365.24220 times. So the year ends before the day ends, and this really complicates matters when you’re in the calendar business.

The Julian calendar, established in 45 BC, assumed exactly 365.25 days/year. This required an extra day to be added every 4 years. It’s what we now do every 4 years in February, when we extend that month to the 29th.

If we choose to ignore the difference between 0.25 and 0.24220 days, as Julius Caesar did, and decree a year = 365.25 days exactly, then over time things will get out of sync. The calendar will be saying it’s Summer, but Earth will be saying it’s still Winter. This is just what happened in 1582, when Pope Gregory XIII (at the advice of his Jesuit astronomers) decreed that 10 calendar days would be dropped to re-synchronize with Nature.

Further, in the new Gregorian calendar, not every fourth year would be a leap year. Centuries divisible by 400 would be skipped. Thus, 1900 was a leap year, and 2100 will be a leap year, but 2000 was not. That correction brings the long-term average days per year to 365.2425. If you do the arithmetic, that means that we’re good for some 3000 years. At that point, we’ll need to correct by one day to make up for the difference between 365.24220 and 265.2425.

Are we splitting hairs here? Perhaps. But when you look at your calendar, and see that it’s June, you expect to go outside and not see snow. Without calendar corrections, this wouldn’t happen.

Well Done! Nice animation too.

Thank you sir. I finally figured out how to embed SWF files into WordPress. It’s vector based animation, so even at 700×500 pixels w/ 15 fps, the file is small and it loads quickly. Expect to see more of these in future posts. Opens up a whole new realm of topics!