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Posts Tagged ‘Vernal Equinox’

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.

Addendum

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.

 

 

 

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03/20/2017 – Ephemeris – Spring starts today!

March 20, 2017 Comments off

Ephemeris for Monday, March 20th.  The Sun will rise at 7:45.  It’ll be up for 12 hours and 10 minutes, setting at 7:55.  The Moon, at last quarter today, will rise at 3:39 tomorrow morning.

This morning, at 6:29 (10:29 UT) the sun crosses overhead at the earth’s equator as it appears to head north, starting for us the season of spring.  It’s the vernal equinox.  As you can tell from my intro, we’re already above 12 hours of daylight, and we’ll add another 3 plus hours of daylight before summer begins in three months.  We are already adding about 3 minutes a day of daylight to that goal now, the maximum rate.  With the Sun out longer and its ascension higher in the sky each day, it is rapidly adding energy to the northern hemisphere.  We don’t feel that immediately.  While the land rapidly absorbs heat, the oceans and lakes, especially the Great Lakes are a big heat sink, taking a very long time to warm up.

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

Addendum

This March equinox also is the beginning of autumn for folks south of the equator.

Earth near equinox

Image from the DISCOVR satellite in halo orbit at the Earth-Sun L1 point, nearly a million miles (1.6 million km) sunward of the Earth. as of March 17, 2017. As usual Michigan is covered by a cloud.  Credit NOAA/NASA.

11/24/2016 – Ephemeris – The little constellation that used to start the seasonal year

November 24, 2016 Comments off

Ephemeris for Thanksgiving Day, Thursday, November 24th.  The Sun will rise at 7:52.  It’ll be up for 9 hours and 14 minutes, setting at 5:06.  The Moon, 3 days past last quarter, will rise at 3:54 tomorrow morning.

From antiquity, the first constellation of the Zodiac has been Aries the ram.  That’s the constellation the Sun entered on the first day of spring, or the vernal equinox.  Well that was a couple of thousand years ago.  Currently the vernal equinox point is in western Pisces.  This is due to the wobbling of the Earth’s axis called precession.  The spinning Earth like and top or gyroscope wobbles when force is applied to it.  In this case the Sun and Moon.  One wobble takes 26,000 years to complete.  Anyway, Aries is a small constellation of four stars in a bent line, below the triangular constellation of Triangulum, which is itself below Andromeda.  It’s a bit west or right of the Pleiades or Seven Sisters star cluster.

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

Addendum

Aries the ram

Aries the ram animated finder chart for 9 p.m. November 24, 2016. Created using Stellarium and GIMP.

The vernal equinox today

The vernal equinox today, where the blue line, the celestial equator and the orange line, the ecliptic or path of the Sun cross. The Sun is where these lines cross on the first day of spring (March 20th around here). Note that the vernal equinox is now in western Pisces. Created using Stellarium.

The vernal equinox in AD 100

The vernal equinox back in AD 100, where the blue line, the celestial equator and the orange line, the ecliptic or path of the Sun cross. The Sun is where these lines cross on the first day of spring. Note that the vernal equinox was at the east edge of Pisces. Created using Stellarium.

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.

Addendum

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.

Addendum

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.

03/18/2016 – Ephemeris – Spring comes this weekend!

March 18, 2016 Comments off

Ephemeris for Friday, March 18th.  The Sun will rise at 7:48.  It’ll be up for 12 hours and 4 minutes, setting at 7:53.   The Moon, 3 days past first quarter, will set at 5:48 tomorrow morning.

Sunday’s the day I’ve been waiting for.  Maybe you feel that way too.  Because at 12:31 a.m. EDT (4:31 a.m. UT) Sunday March 20th the season of spring will begin.  It’s not that we’ve had a hard winter.  As winters go this has been a mild one.  The Grand Traverse Bay never froze over.  My heating bill has been low.  Of course we have a chance for another snow storm or two before May gets here.  However at the top of the show notice we’re getting over 12 hours of sunlight even now.  The sun will reach its peak altitude of about 45 degrees at local noon.  Those at the Straits will have to wait only a few more days for he Sun to reach that altitude.  The Sun is rapidly moving northward, and the daylight hours are increasing by about 3 minutes a day.

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

Addendum

The Earth near the March Equinox

Getting close to the equinox. Earth image from NOAA DSCOVR satellite’s Epic camera in a halo orbit around the Earth-Sun Lagrangian point 1, a million miles Sunward of the Earth. Taken March 14, 2016.

Sun's path through the sky on the equinox

The Sun’s path through the sky from due east to due west on the equinox day from Traverse City, MI. Created using my LookingUp program.

Sunrise on the autumnal equinox

That’s not a pumpkin on the head of the motorcyclist. That’s the Sun rising as I’m traveling east on South Airport Road south of Traverse City Mi. on the autumnal equinox. This is the east-west section of the road. The Sun is rising over the hills some 6 miles to the east. Credit: Bob Moler.

Traverse City’s latitude is 1/3º south of 45º north latitude.  The Suns are plotted at 15 minute intervals.  Each day the Sun will rise higher and higher until the summer solstice when the Sun’s path in the sky looks like this:

The Sun's path on the summer solstice

The Sun’s path through the sky on the summer solstice day from Traverse City, MI. Created using my LookingUp program.

For those south of the equator, summer is ending and autumn is starting.

03/20/2015 – Ephemeris – Spring will spring forth at 6:44 p.m. EDT

March 20, 2015 Comments off

Ephemeris for Friday, March 20th.  The Sun will rise at 7:46.  It’ll be up for 12 hours and 8 minutes, setting at 7:55.  The Moon is new today, and won’t be visible.

The Arctic solar eclipse has just ended.  But there is one more event of note today.  At 6:44 p.m.  The Sun will cross the celestial equator heading northward, the projection of the Earth’s equator on the sky.  In doing that the season of spring will return to the northern hemisphere.  The Sun is already staying up for just over half the day.   That will increase to fifteen and a half hours by the summer solstice three months from now.  Not only will the Sun will be out longer, but it will rise higher in the sky, rising from 45 degrees altitude in the south at local noon to 69 degrees on June 21st.  If the sun stayed at this location it would get very uncomfortable with the heat.  As it is as the Sun is climbing down it will still get warmer.  Peak summer heat occurs about a month after the solstice.

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

Addendum

These are whole sky diagrams with the edge at the horizon.  The Sun’s motion is from left to right.  The Sun is plotted every 15 minutes.  The Sun’s motion is constant, however the projection causes squeezing of the positions near the zenith (center of the diagram) and stretching near the horizon.

Equinox

The sun’s daily path through the sky from horizon to horizon on an equinox the first day of spring or autumn. Credit My LookingUp program.

Summer Solstice

The sun’s daily path through the sky from horizon to horizon on the first day of summer, the summer solstice. Credit My LookingUp program.