Posts Tagged ‘Easter’

04/14/2014 – Ephemeris – Why does Easter occur on a different Sunday every year?

April 14, 2017 Comments off

The answer is astronomical!

Ephemeris for Good Friday, Friday, April 14th.  The Sun will rise at 6:59.  It’ll be up for 13 hours and 26 minutes, setting at 8:26.  The Moon, 3 days past full, will rise at 11:48 this evening.

Easter will be celebrated by western and eastern christian churches this Sunday.  Easter is a movable feast in that it falls on a different date each year following the first full moon of spring.  It’s an attempt to follow the Jewish Passover, which starts on the 15th of the month of Nisan.  Being a lunar calendar the 15th the generally the night of the full moon.  And since the Last Supper was a Seder, the Christian church wanted to follow Passover as closely as possible using the Roman solar based calendar where the year was 365.25 days long.  Passover started at sunset this past Monday night.  The western churches eventually adopted the Gregorian calendar to keep in sync with the seasons.  The Eastern churches did not, however Easter is late enough this year so they both fall on the same date.

The times given are for the Traverse City/Interlochen area of Michigan. They may be different for your location.


The seasonal, or officially the Tropical Year, from vernal equinox to vernal equinox is approximately 365.24220 days long, about 11 1/2 minutes shorter than the Julian (after Julius Caesar) Calendar year.  The Julian Calendar kept up with the year by having three 365 ordinary years and one leap year of 366 days.  It over corrects.  To make the calculation for Easter easier in the various dioceses of the far-flung church, the vernal equinox, the day the Sun crosses the celestial equator, heading northward was defined as March 21st.  The actual vernal equinox was falling behind the Julian Calendar by 0.8 days every century.

By 1582 the Roman Catholic Church under Pope Gregory XIII decided to correct the problem.  By then the real vernal equinox occurred on March 11th.  Easter is supposed to be a spring feast, and using March 21st as the vernal equinox would eventually push Easter into summer.  The Pope instituted a commission to look into the problem.  This commission headed by Christophorus Clavius* came up with what we know as the Gregorian Calendar.  First, eliminate 10 days from the calendar.  This was done in October 1582 between October 4th and 15th.  Then to keep the calendar in sync with the actual year it was decreed that leap years would continued for years divisible by 4; except that century years, those divisible by 100 be ordinary years, except those by also divisible by 400.  Thus the year 1900 was an ordinary year, but the year 2000 was a leap year, and the year 2100 will be an ordinary year.  Adoption of this as a civil calendar took 400 years to be universal.

The Greek Orthodox and other eastern churches kept the Julian Calendar, so on occasion their Easter is sometimes celebrated in May.  The Jewish Calendar is, as I alluded to in the program transcript, a lunar calendar.  It has a relationship to the Julian Calendar in that 19 Julian Years equals 235 lunar months almost exactly. This is called the Metonic Cycle.  Those 235 months equal 12 lunar years of 12 and 13 months.  So without correction Passover too will slowly head into summer in millennia to come.

* Clavius was honored by having a large, rather spectacular crater on the Moon named for him.  Search these posts for Clavius to find it.




03/25/2016 – Ephemeris – Easter, the reason for our calendar

March 25, 2016 Comments off

Ephemeris for Good Friday, Friday, March 25th.  The Sun will rise at 7:35.  It’ll be up for 12 hours and 26 minutes, setting at 8:02.   The Moon, 2 days past full, will rise at 10:17 this evening.

The so-called movable feasts of the church calendar are based on the date Easter falls on.  They span from Ash Wednesday to Pentecost.  And Easter is determined by astronomical events.  In 1582 the fact that the actual vernal equinox had fallen 10 days behind the Julian calendar then in use which was decreed by Julius Caesar in 45 BC.  Pope Gregory XIII in the 1580’s resolved to fix the situation and commissioned some astronomers to work on the problem.  The solution was to fix the 10 day problem by eliminating the days October 5th through 14th of the October 1582 calendar and modifying the leap year rule to keep February 29th in calendars whose years were evenly divisible by 4, except those century years not also divisible by 400.  Thus the year 2000 was a leap year, but 1900 and 2100 was and will not be.

Times are for the Traverse City/Interlochen area of Michigan. They may be different for your location.


The Gregorian Calendar in essence decoupled Easter from Passover by keeping the formula first Sunday after the first full moon after March 21st, as a marker for the vernal equinox, and keeping March 21st on or near the vernal equinox.  Passover this year starts sunset on April 22nd,  while Orthodox Easter will occur on May 1st.  The reason is the relationship between the Jewish lunar calendar and the Julian Calendar I mentioned in yesterday’s post. The difference between the Julian and Gregorian Calendars is now 13 days.

The error in the Gregorian calendar is at most 1 day in 3,300 years, in relation to the seasonal year.  But the Gregorian Calendar makes calculating the date of Easter more complicated.  It introduces something called Epact to the list of chronological cycles in an almanac.  The quantity called Epact is the age of the moon on January 1st, and still has a relationship with the Metonic Cycle and the Golden Number which I discussed yesterday.  This year the value is 21.

As I’ve admitted before, the first paragraph of these posts are generated by a computer program.  Part of that program is a list of holidays, and those designated as movable feasts use the date of Easter as a starting point.  I use the 10 step method from Astronomical Algorithms by Jean Meeus.  Easter for the Julian Calendar is a simpler 6 step method.


03/24/2016 – Ephemeris – Why is this Sunday Easter?

March 24, 2016 Comments off

Ephemeris for Thursday, March 24th.  The Sun will rise at 7:37.  It’ll be up for 12 hours and 23 minutes, setting at 8:01.   The Moon, 1 day past full, will rise at 9:19 this evening.

This Sunday is Easter, only 5 days later than the earliest Easter can ever be.  Yesterday’s full moon or the tabular date for it is called the Paschal Full Moon, an attempt for the Christian Church to match the solar Roman calendar to the Jewish lunar calendar in regards to the date of Passover.  It doesn’t always work, especially when Easter turns out to be early as it is this year.  The simple formula for western churches is the first Sunday after the first full moon after the vernal equinox which is defined as March 21st, no matter the date spring actually started, which was the 20th, this year.  All this started to be counted using the Julian Calendar, which is 11 minutes longer than the seasonal or tropical year.  We’ll see how that was corrected for tomorrow.

Times are for the Traverse City/Interlochen area of Michigan. They may be different for your location.


The Jewish calendar does not have a relationship with the Gregorian Calendar, so Passover will drift later and later into spring over the years.  The Jewish calendar does have a relation to the Julian Calendar in that 19 years equals 235 lunar months.  This was probably discovered by the Babylonians but was popularized by the Athenian Menton in the 5th century BCE.  It’s a way to relate the lunar calendar to the solar or seasonal calendar.  We call it the Metonic cycle.

In  a lunar calendar the months alternate between 29 and 30 days because the lunar month is 29.53 days.  Also a 365.25 day year is 12.37 lunar months.  The solution for all this is quite complex, with 12 common or 12 month years and 7 13 month great years to fit the 19 year cycle.   It also means that the phases of the moon repeat on or near the same date at 19 year intervals.  If you see a quantity called the Golden Number in almanacs, which happens to be 3 this year, that’s where we are (1-19) in the Metonic cycle.  The Gregorian Calendar breaks this relationship.  We’ll see how tomorrow.

02/28/2016 – Ephemeris Extra – The years of our lives

February 28, 2016 1 comment

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.


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

03/29/2013 – Ephemeris – How we know this Sunday is Easter

March 29, 2013 Comments off

Ephemeris for Good Friday, Friday, March 29th.  The sun will rise at 7:28.  It’ll be up for 12 hours and 38 minutes, setting at 8:06.   The moon, 2 days past full, will rise at 11:14 this evening.

Wednesday was the day of the Paschal full moon, the full moon after the first day of spring, which is defined by Christian churches as March 21st.  For the date of Easter the actual full moon isn’t used, but a rather complicated formula is used to find the new moon.  There’s a complicated correction to then find the date of the full moon, which 2 days ago.  This year that formula works out correctly.  It can be a day off either way.  The next Sunday then is Easter.  Orthodox churches use the Julian calendar and a different formula but they’ll celebrate Easter on May 5th.  The formula was set up to approximate the Jewish lunar calendar.  It works out close this year because Passover started at sunset last Sunday night.

Times are for the Traverse City/Interlochen area of Michigan.  They may be different for your location.

02/12/2013 – Ephemeris – Astronomical basis for Lent and Easter

February 12, 2013 Comments off

Ephemeris for Fat Tuesday, Tuesday, February 12th.  The sun will rise at 7:46.  It’ll be up for 10 hours and 20 minutes, setting at 6:07.   The moon, 2 days past new, will set at 9:17 this evening.

The western ecclesiastical season of Lent starts tomorrow.  It lasts 40 days excluding Sundays ending with the celebration of Easter on March 31st this year.  It is a movable feast in that it’s on a different date each year following the first full moon of spring.  It’s an attempt to follow the Jewish Passover, which starts on the 15th of the month of Nisan.  Being a lunar calendar the 15th the generally the night of the full moon.  And since the Last Supper was a Seder, the Christian church wanted to follow Passover as closely as possible using the Roman Solar based calendar.  The western churches eventually adopted the Gregorian calendar to keep in sync with the seasons.  The Eastern churches did not.  Their Easter this year is on May 5th.

Times are for the Traverse City/Interlochen area of Michigan.  They may be different for your location.


The first day of spring is set by the churches as March 21st.  In Michigan’s time zone spring now it always starts on March 20th, and will occasionally start on the 19th until 2103 after the Gregorian correction takes place in 2100.  The Julian Calendar, instituted by Julius Caesar, was the official calendar for all the Christian world until 1582.  The problem with the Julian Calendar is that the leap year every 4 years overcompensated for the seasonal or tropical year.  The average year of 365 1/4 days turned out to be 11 minutes 14 seconds too long.  By 1582 the actual vernal equinox or first day of spring had slipped back to March 10th.

Astronomers under Pope Gregory XIII proposed a change that was adopted by the Roman Catholic world.  First remove 10 days from the calendar between October 4 and 15 1582.  Then modify the leap year formula to keep the leap year on years divided by 4,  except century years.  Century years were ordinary 365 day years unless divisible by 400.  This 1900 was an ordinary year, but 2000 was a leap year.   The western protestant countries came around eventually.  However the eastern churches still use the Julian calendar to set their feasts, thus Eastern Orthodox rarely coincides with western churches.

Note that the dating for Excel spreadsheets, starts the day count on January 1, 1900, except they thought that 1900 was a leap year.

03/30/2012 – Ephemeris – April Preview

March 30, 2012 Comments off

Ephemeris for Friday, March 30th.  The sun will rise at 7:26.  It’ll be up for 12 hours and 41 minutes, setting at 8:08.   The moon, at first quarter today, will set at 3:36 tomorrow morning.

The 4th month of the year begins Sunday with Palm Sunday.  Daylight hours in the Interlochen/Traverse City area and will increase from 12 hours and 48 minutes Sunday to 14 hours 13 minutes on April 30th.  The altitude, or angle, of the sun above the southern horizon at local noon will be 50 degrees Sunday and will ascend to 60 degrees on April 30th.  The altitude of the sun in the Straits area will be a degree lower.  The actual time of local apparent noon this month for the Interlochen/Traverse City area, when the sun passes due south, will be about 1:43 p.m.  The full moon next Friday is the Pascal full moon meaning the western churches will celebrate Easter the following Sunday.  Passover starts that Friday night, while Orthodox Easter is the 15th.

* Times are for the Traverse City/Interlochen area of Michigan.  They may be different for your location.