This month has an extra day, the 29th, an intercalary or leap day, added every fourth year except century years, unless divisible by 400. Without it, the seasons would drift from what we expect by about 6 hours per year, or 24 days a century. Pope Gregory’s tweak to Emperor Julius Caesar’s calendar will keep the dates of the solstices and equinoxes nearly fixed for many thousands of years. And since 2000 did properly have a leap day, the simple, every four years rule works fine for all practical purposes—until 2100.

Predictability of the heavens is what we use to define our day, month, and year, but few other astronomical periodicities are as easy to remember. The Moon’s phases change rapidly, yet it is not simple to extrapolate more than a week or so ahead. There are 29.530588853 days (that’s 29 days, 12 hours, 44 minutes and 3 seconds) on average between like phases, but calendar months vary from 28 (29 this year) to 31 days in length so moon phases advance by about a day each month, again on average. Not exactly rocket science, but if you’re like me, you need a calendar or web page to know when the next dark skies observing night or star party will be scheduled.

Nevertheless, there are two simple periodicities of the moon phases. Full moons (all phases in fact) fall close to 11 days earlier in successive years. After 19 years, moon phases repeat on the same dates or very nearly so. For example, moon phase calendars for this year, 2027, and even 2046 are virtually identical. The new moon on the February 7th this year repeats on the 6th in 2027, and the 5th in 2046 and 2065, the 6th in 2084. Nineteen solar years equal 235 lunar months to a close approximation: this is the Metonic cycle first investigated by an Athenian astronomer around 432 BC.

Eclipses also exhibit patterns: they always come in pairs (a solar and a lunar), sometimes triplets, usually four per year, sometimes six (as in 2009). The alignment of the Sun, the Earth, the Moon and one of the two nodes of the moon’s orbit repeats every 18 years, 11 days and 8 hours. This Saros cycle was known to the ancient Babylonian Chaldean astronomers. Compare the eclipses for this year, with those predicted for 2026: the total lunar eclipse on the 21st this year repeats on March 3rd, 2026. For many more comparisons, browse the NASA eclipse pages (lunar or solar): eclipses for thousands of years are available. Can you find the half-Saros, where solar and lunar eclipses alternate? How about the Inex of 358 lunations, or 29 years less 20 days? Just for fun, can you find an eclipse on your birthday sometime in this century? (Unfortunately, I have to wait until 2059.)

There are simple planetary cycles as well. Mercury’s visibility repeats in alternating cycles of  6 and 7 years, and even more precisely for the combined 13 year period. Venus has an 8-year cycle, and a much longer 243-year one associated with transits. Mars comes to opposition roughly every other year, but well-placed or particularly close oppositions occur at 15-year intervals. There are cycles of 32, 47, 79 and 284 years as well.

Ancient cultures were far more attuned to such cycles than western cultures nowadays, and you’d be very fortunate to enjoy astronomy as a hobby over more than two full Metonic or Saros cycles. Yet these patterns do provide some satisfying regularity and predictability to the heavens when viewed in the longer term. As part of the International Year of Astronomy 2009, professionals and star gazers alike will celebrate Galileo’s first use of the telescope for astronomy and publication of Kepler’s laws of planetary motion. If we’ve learned anything about the Universe in those 400 years, it’s that aren’t we at the center, and it is much bigger and far older than imagined. The immense and ancient are integral to astronomy.