Leap years: proof that Earth is always running late

Unless you’ve been living under a rock, you’re probably aware 2016 is a leap year. February will have 29 days as part of a four-year mathematical cycle that has been observed in the Gregorian calendar since 1582. The reason we do this? To make up for a slight discrepancy in the Earth’s orbit around the sun.


As humans, we like to count things and measure our lives by predictable cycles, so Western cultures designed a calendar counting 365 days in a year. However, Earth’s true orbit is actually 365 days, five hours, 49 minutes and 16 seconds. That’s right; every New Year’s Eve, Earth is little under six hours late to the party. Talk about procrastination!

To make up for Earth’s tardiness, we add those six hours together every four years to make a full day. This keeps the calendar from drifting through the seasons over time. It might take a while, but if we didn’t add leap days, in 31 leap years (or 124 years), Jan. 1 would occur the first day in February. That means the Spring Equinox would happen Feb. 20 instead of in March!

But that’s not the end of the problem. In adding a day every four years, we overcompensate by 10 minutes and 44 seconds. (Remember Earth doesn’t really take another full six hours to complete its trip around the sun.) However, the Gregorian calendar accounts for this, as well.

epa04383191 A handout picture made available by NASA on 04 September 2014 shows a view of Earth taken by NASA astronaut Gregory Reid Wiseman of the US from the International Space Station (ISS) on space, 02 September 2014. The Expedition 40 crew has been busy on the ISS performing health checks and humanoid robot upgrades. A trio of orbital residents is packing up gear as they prepare to return home in less than two weeks. Commander Steve Swanson powered down and stowed Robonaut 2 after wrapping up its mobility upgrades this week. He installed new legs on the humanoid robot including external and internal gear as well as cables. This sets the stage for more upgrades in the fall before Robonaut takes its first steps as an assistant crew member. Robonaut was designed to enhance crew productivity and safety while also aiding people on Earth with physical disabilities.  EPA/NASA/REID WISEMAN  HANDOUT EDITORIAL USE ONLY

A view of Earth by NASA.

Over a period of 400 years, the true length of the leap cycle, this overcompensation amounts to a total of three days. So in every century that isn’t divisible by 400, we don’t add a leap day. The last one was back in 1900. The year 2000, divided by 400, equals five, so we did observe leap year the February after Y2K. But you’ll have to live until 2100 to notice the next time we skip it. Your kids and grandkids will probably still be around, though, likely talking about lazy Earth and the crazy math behind leap years!

When the renovated Burke Baker Planetarium opens March 11, you can see leap years in action with a full map of Earth’s orbit, as well as the rest of the planets in the Solar System. Speed up time to compare rates and see how Earth measures up. Travel to the edge of our neighborhood and meet up with Pluto and other dwarf planets, and see how astronomers found evidence of a new Planet Nine! (I wonder how long that calendar is…)

Happy New (Chinese) Year!

On Sunday, Feb. 14, while we were observing Valentine’s Day, a much bigger celebration got underway in the Far East.  That was the  Chinese New Year, the day when the Year of the Ox ended and the Year of the Tiger began.  And the celebration is still ongoing, as it lasts until the Lantern Festival on the 15th day of the month (this year, Feb. 28).

Creative Commons License photo credit: ken2754@Yokohama

Like most Americans, I learned the sky as imagined by westerners around the Mediterranean basin, with images from Babylon, ancient Egypt, ancient Greece and Rome, and star names preserved during the Middle Ages by Arabs. So I find it fascinating to think of an entirely different culture and how they imagined the night sky. The Chinese New Year celebration is a perfectly appropriate time to do this, especially since objects in the sky, in particular the moon and Jupiter, serve as the basis of the ancient Chinese calendar.

The date of Chinese New Year varies; it can occur as early as Jan. 21 or as late as Feb. 19. However, anyone familiar with the lunar cycle can easily predict the date for a given year. That’s because China’s New Year always begins with the second new moon after the winter solstice.

Our Gregorian calendar is a solar calendar, based on the apparent position of the sun (and thus, on the Earth’s orbit around the sun).  However, the apparent position of the sun compared to the stars is difficult to observe.  Much more readily observable are the phases of the moon.  Thus the Chinese, like many ancient cultures, adopted a lunar calendar, measuring months from new moon to new moon.  Unlike the Islamic or ancient Roman calendars, the Chinese calendar begins months with the dark of the moon–the day the moon is invisible, not the first slender crescent seen at dusk.

Full Moon
Creative Commons License photo credit: Andréia

It would be convenient if one year equaled an even number of phase cycles. In fact, however, the moon takes about 29.5 days to go through one phase cycle, so 12 such cycles is 354 days.  This is significantly less than the solar year of 365.25 days, so a purely lunar calendar quickly becomes disconnected from the seasons and useless as a guide for when to plant or harvest.   To keep their lunar months connected with the seasons, the Chinese added a rule: the second-to-last lunar month must contain the winter solstice.  If the old crescent moon of the eleventh lunar month is waning towards new and the winter solstice has not yet happened, that month is repeated.  Similar rules exist for the second lunar month (which must contain the spring equinox), the fifth lunar month (which must contain the summer solstice), and the eighth lunar month (which must contain the fall equinox).  Accordingly, the first new moon after the winter solstice always begins the last month in the Chinese year, and the second new moon after the solstice begins the next year.

Chinese astronomers noticed that every twelve years, Jupiter reappears next to the same stars.   (This is because Jupiter takes 11.86 years to orbit the Sun.)  There were twelve months in a typical Chinese year (although occasionally one was doubled, as explained above).  Also, the Chinese divided the day into twelve double-hours.  They used a system of twelve ‘Earthly Branches’ to designate the months of the year and the double-hours in a day.  Jupiter’s motion in the sky established a cycle of years analogous to the cycles of months and double-hours.  Thus Jupiter became the ‘Year Star’ (Suixing) and years, too, were designated with the Earthly Branches.

Lion Dance
Creative Commons License photo credit: geoftheref

Later, as a mnemonic device, the Chinese began to associate the Earthly branches with animals.  (Sources disagree as to exactly when.)  Legends tell that Buddha (or the Jade Emperor) summoned all of the animals to him; each of the first twelve to appear became associated with an Earthly Branch.  The twelve animals are:

1) Rat  2) Ox  3) Tiger  4) Rabbit  5)Dragon  6)Snake  7)Horse  8)Sheep  9)Monkey  10)Rooster  11)Dog  12)Pig

The signs of the Chinese zodiac, then, unlike those of the western zodiac, are not constellations in the sky.  The most well known of the Chinese constellations are the 28 ‘lunar mansions.’  These are small groups of stars very roughly arrayed along the ecliptic, which is the apparent path of the sun, moon and planets across the sky.  As you’ll see in the links below, the Chinese used some stars, such as those in Orion, that are too far from the ecliptic for the moon to pass through them.  The 28 mansions were subdivided into four groups of seven; each group of seven represented one of four Chinese animals associated with the directions and the seasons:

1) The Blue/Green Dragon (Qing Long) of the East, associated with spring.  Note that the ancient Chinese color word qing was quite broad in meaning.  Blue and green were considered different shades of this broadly defined color.

2) The Red Bird (Zhu Que) of the South, associated with summer.   This mythical bird, with red and orange plumage, is distinct from the feng huang, also called the Chinese phoenix.

3) The White Tiger (Bai Hu) of the West, associated with autumn.

4) The Black Tortoise (literally Dark Warrior, Xuan Wu) of the North, associated with winter.  Xuan Wu was always shown as a tortoise with a snake wrapped around it, reflecting the folkloric belief that all tortoises were female and needed to copulate with snakes to reproduce.

Of the stars in tonight’s evening sky, those in Orion and Taurus form part of the White Tiger, while Gemini and the dimmer stars south and east of it belong to the Red Bird.

Along with the four large animals, Chinese astronomers defined three large constellations known as the three enclosures.  The largest of these is the ‘Purple Forbidden Enclosure‘ (Zi Wei Yuan) which includes all those stars near the North Pole of the sky which never set as seen from mid-northern latitudes.  The enclosure is ‘forbidden’ because it includes the North Star, which was the Emperor of Heaven because it always remains in one spot while other stars seem to go in circles around it, as if paying court.

The ‘Supreme Palace Enclosure‘ (Tai Wei Yuan) actually rises in the late evening in February.  Look east about 9 tonight for a set of stars in the shape of a backwards question mark.  We see this as the head of Leo, the Lion.  Rising under the backwards question mark is a right triangle of similar brightness.  For us, this is Leo’s hindquarters, but in China, it’s the northwest corner of the Supreme Palace enclosure.  The other side of this enclosure is a semi-circle of stars westerners recognize as part of Virgo, the Virgin.

The final enclosure, the ‘Heavenly Market Enclosure‘ (Tian Shi Yuan), won’t rise until very early in the morning in February, and isn’t in the evening sky until late May.  It centers on our constellations Ophiuchus and Serpens (Caput and Cauda), just north of the bright summer constellations Scorpius and Sagittarius.

So, I wish everyone a happy Year of the Tiger.  I’ll celebrate it by looking at the stars in a way I ‘m not accustomed to seeing them.