Bob Moler's Ephemeris Blog

The continuing story of a small planet revolving around its star

Updated from the originally published in the January 1997 Stellar Sentinel, the monthly newsletter of the Grand Traverse Astronomical Society and republished in the February 2016 edition.

This year, 2016, is a leap year.  In leap years we have the US presidential elections, the Summer Olympic Games, and February has 29 days.  So what exactly is a leap year, and why am I writing about this earthly phenomenon in an astronomical society newsletter?  Well it’s astronomical of course. And if you think a year is a year is a year, well think again.
The calendar we use today is based on the Sun.  In ancient times the calendars of the Babylonians, Jews and many other ancient civilizations were based on the Moon, using the lunation, the period of about 29.5 days between new moons, as the basis for the calendar.  Lunar calendars tended to have months alternating 29 and 30 days, and years of 12 or 13 months to keep the whole scheme roughly in sync with the seasonal year.  There are vestiges of this system today in the various folklore of planting by the Moon.

The ancient Egyptians actually used two calendars.  The first was one based close to the sun and had 365 days.  It had 12 months of 30 days, each containing three 10 day decans.  There were 5 days at the end of the year that were holidays, and belonged to no month.  This civil calendar was used for state and accounting purposes.  The agricultural calendar was based on the Moon.  These two calendars were reconciled every 25 civil years which equaled 209 lunations, divided into 16 ordinary 12 month years, and 9 ‘great’ years of 13 months.  Still, since the Egyptian civil year is nearly a quarter of a day a year short, the civil calendar shifted slowly in relation to the seasons.  The Egyptian agricultural year started with the flooding of the Nile, which in those days was coincident with the heliacal rising of the brightest night time star Sirius, which they called Sothis.  A heliacal rising is when a star or planet is first visible in the morning twilight.  This heliacal rising occurs at a mean interval of 365.2507 days.  Thus the Egyptian civil calendar would be in sync with the agricultural year every 1460 years, a period called the Sothic Cycle.

The ancient Greek calendars were lunar ones.  Early on, each locality had their own calendar.  Starting in the 6th century BC the calendar situation got better when a cycle synchronizing lunar calendars with the sun was discovered.  It is the Metonic Cycle, probably discovered in Babylon.  Here 19 years of 365.25 days equal almost exactly 235 lunations.  That’s 12 ordinary 12 month years and 7 ‘great’ years of 13 months.  We find remnants of the Metonic Cycle with the Golden Number for the year given in almanacs, a number ranging from 1 to 19.  This year’s Golden Number is 3.  The year 1 BC was 1.  Under the old Julian calendar it was use to help determine the date of Easter.

The Julian Calendar is named for Julius Caesar who instituted it as a part of calendar reform he instituted in 46 BC.  The old Roman calendar was a lunar one, but in the earlier years of Julius Caesar’s reign the adjustments, called intercalations, such as 13th months in some years to keep the calendar roughly attuned to the sun, were neglected.  To straighten all this our, the year 46 BC was made 445 days long.  Starting in 45 BC the new calendar was instituted using the year of length 365.25 days.  Each 4 years an intercalary day was added.  This was February 29th, giving a 366 day year.  This we call a leap year.  Year 45 BC was a leap year, but due to some misunderstanding about the calendar reform, the one leap year in every four, was not kept.  In fact too many leap years were added, so in Caesar Augustus’ reign leap years from 8 BC to AD 8 were omitted to get back on track.

The western world ended up adopting the Julian calendar, and it was humming along just fine with leap years every 4 years.  However the Catholic Church and Pope Gregory XIII became alarmed that Easter was in danger of no longer being a spring feast.  The early church, adopted the Julian calendar rather than the Jewish lunar calendar.  But the most important feasts, the Crucifixion and Easter were tied to the Jewish feast of Passover, a spring feast starting in the middle of the month at full moon time.  Part of the problem was that the Vernal Equinox for ecclesiastical purposes was assumed to fall on March 21st, whether it actually did or not.  The first Sunday after the first full moon was Easter.

The problem is that the seasonal or tropical year is 11 minutes and 14 seconds shorter than the Julian year of 365.25 days.  In 400 years this amounts to about 3 days error.  So the easy correction is to eliminate 3 leap years out of 400 years.  The formula is simple.  All years divisible by 4 are leap years except century years which are not also divisible by 400.  Thus the year 1900 was not a leap year, but 2000 was, and 2100 will not be.

The other part of the reform was harder to swallow.  It was the elimination of 10 days because the real Vernal Equinox was by the 16th century falling on March 11th.  The Church was able to have this adopted in Catholic countries right away, so in the calendar of 1582 ten days were omitted between October 4th and 15th.  Protestant countries generally followed suit later.  England and the American Colonies converted to this new Gregorian Calendar in 1752 when by then 11 days were omitted between September 2nd and 14th.  The last to convert to the Gregorian Calendar was Greece and Orthodox Christianity who also made further improvements for the future.

I had once investigated how Microsoft Excel spreadsheets store dates.  It’s stored as a consecutive date starting with date 1 on January 1, 1900.  I had to convert dates downloaded from an IBM AS400 computer into a format compatible with Excel.  The dates came one day off.  It turns out that Microsoft or whoever devised the Excel dating scheme forgot that the year 1900 was not a leap year in the Gregorian calendar.  For my astronomical research I use dates both far in the past I use dating algorithms that use the Julian and Gregorian calendars where appropriate and takes into account the Gregorian discontinuity of 1582 into account.  These algorithms convert calendar dates to another type of consecutive day scheme called Julian Day Numbers of Julian dates for short, and back again.  In astronomy we see cycles of planetary orbits, variable star periods, etc.  They don’t fit into our hodgepodge of different month and year lengths.  We just want to know how many days between event A and event B.  Julian dates work for us.  The Julian dates start on January 1, 4713 of the Julian calendar, which predates any known historical date.  Oh by the way:  Julian dates start at noon Universal Time (UT) or Greenwich Mean Time (GMT), and fractional days are decimal.
I didn’t even touch when the year begins.  In Great Britain when the 1752 reforms took place they also changed the start of the year from March 25th to January 1st.

Bibliography

• The Exact Sciences in Antiquity by O.  Neugbauer. Dover Publications
• Explanatory Supplement to the Ephemeris H.M. Nautical Almanac Office