Vernal EQUINOX

North Pole

Equator

Summer SOLSTICE

Winter SOLSTICE

Our Western calendar is tied to the tropical year – the time between successive vernal equinoxes. At that moment, the sun’s position in the sky is exactly where the ecliptic (the plane of the

EARTH'S SEASONS

Autumnal EQUINOX

solar system and the path that the planets take as they move through the constellations) crosses the celestial equator (the projection of the Earth’s own equator onto the celestial sphere). Straddling the celestial equator, the sun splits its time exactly between the day side and the night side of the Earth. It returns to that place again in roughly 365.24219 days. Roughly. Now you can see where those alternating “divisible by 4, 100, and 400” leap year rules originate. At the end of 365 days, there are still 0.24219 days (just shy of six hours) to go before Earth gets back to the equinox line. After four years, however, this fractional 0.24219 of a day adds up to 0.96876, which is pretty close to one full day. If we were using only a 365-day calendar, the stars, and more importantly the months, corresponding to the seasons – crucial for agricultural societies – would slip behind. This was apparent to the Romans in the first century, as well as to the Olmecs and the Maya on the other side of the world. Thus decreed Julius Caesar in 46 B.C.: that every four years an extra day would be added to February. It was called the Julian calendar. MAKING UP THE DIFFERENCES

But adding one day every four years, in order to make up for that 0.96876 of a day in orbital spare change, is overcompensating. Caesar’s “every four” leap year prescription adds 0.03124 of a day too much. This makes the Julian calendar run fast by just over 600 seconds per year. Like with the spare coin jar in our house, small change like that takes a while to add up. It wasn’t until the age of Pope Gregory XIII, in 1582, that this mismatch was becoming a problem. After consultation, presumably with God, but particularly with his astronomer, Christopher Clavius, the pope adopted Clavius’ clever solution. The Julian calendar runs fast by 0.03124 of a day every four years; multiply both sides by 100, and see an excess of about three days after 400 years. Clavius’ solution was to make centuries exceptions – but that would lose too much, four days in 400 years, not three. So Clavius added one back, once every 400 years, starting in 1600. This Gregorian calendar, which we use today, has the following rules: • Every year divisible by 4: add February 29 • Every century (1800, 1900, 2000, 2100): do not add February 29 • Every century divisible by 400: add February 29

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February 2020

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