13. What the people of Zion picked up in Babylon

“Wailing Wall” painting by Gustav Bauernfeind (1848-1904).  The Wailing Wall, or Western Wall, in Jerusalem is what’s left of the wall enclosing the Temple Mount, the holiest site in Judaism.  Source: Sotheby’s, public domain {{PD-US}}.

My last two posts were on Mesopotamia and Egypt which came to prominence around 5000 years ago in the Early Bronze Age.  Over the next few 2500 years, empires rose and fell in Mesopotamia while Egypt, a safe distance away, remained one distinct civilization.  Then, the Hittite Empire, which had emerged in present-day Turkey, began to challenge Egyptian supremacy in the region directly East of the Mediterranean Sea.  This land was called Canaan then.  The tribes who occupied it were trapped between great powers.

But eventually those great powers crumbled while something that began with a few tribes of Canaan endured and spread to over half the world’s people.  This was the worship of one God in the tradition of a legendary disciple named Abraham.

It might have begun during the dark period from 1200 to 900 BCE between the Bronze Age and the Iron Age.  Nearly every major city in the Eastern Mediterranean was destroyed.  The Hittite empire disintegrated.  Egypt survived but entered a long period of decline.  The Neo-Assyrian Empire, which now controlled Mesopotamia, became the dominant force in the region.

In its shadow, a few tribes in southern Canaan consolidated to form the Kingdom of Israel.  According to the Hebrew Bible, this happened as early as the 11th century BCE.  To the south of Israel was the city of Jerusalem in a region called Judah.  Israel’s second king, David, who had gained fame in his youth for killing the giant Goliath, conquered Jerusalem and made it his capital.  His son and successor, Solomon, built the First Temple in Jerusalem.  Following Solomon’s death, Israel and Judah split into separate kingdoms.

On the left is Michelangelo’s “David” (1501-1504) at the Galleria dell’Academia in Florence.  Photograph by Jorg Bittner Unna via Wikimedia Commons.  The statue had special meaning for the Republic of Florence since it, like Israel, was surrounded on all sides by powerful rival states.  On the right is a painting, possibly by James Tissot (1896-1902), depicting the consecration of Jerusalem’s First Temple by King Solomon.  Source: Jewish Museum, New York, public domain {{PD-US}}.

There is little or no archaeological evidence for a Kingdom of Israel and Judah ruled by David or Solomon.  Most present-day historicans believe the Kingdom of Israel was founded in the 10th century BCE.  The Kingdom of Judah and the city of Jerusalem might have emerged independently only in the 8th century BCE.  Soon afterwards, the Neo-Assyrian Empire captured Israel but allowed Judah to continue existing as a vassal state.  Many Israelites fled to Judah.  Jerusalem continued to grow and prosper.

More and more people in Jerusalem, including some of the kings, began to see Yahweh, a god previously worshiped by a few scattered tribes, as the one and only God.  These people would come to be known as Yehudim or Jews.  Their religion would be called Judaism, after the Kingdom of Judah, which was itself named after a grandson of Abraham.

Life would always remain precarious for the Jews.  It was only a matter of time until the next invasion.

In the 7th century BCE, the Neo-Babylonians defeated the Neo-Assyrians to take over Mesopotamia.  Their second king, Nabu-kudurri-usur II (or Nebuchadnezzar II) seized Jerusalem.  He had become famous for building the Hanging Gardens of Babylon.  Now, he would become infamous for destroying Solomon’s Temple.  Most of the Jews were then exiled to Babylonia.  They would be freed nearly a century later when the Persians defeated the Neo-Babylonians but many would choose to stay.

“The Flight of the Prisoners” painting (c. 1896-1902) by James Tissot.  Source: Jewish Museum, New York, public domain {{PD-US}}.

What the Jews in Babylonia accomplished will be familiar to every successful immigrant today.  They retained their faith and identity while adopting elements of the local culture, including the language and, of course, the calendar.

The Babylonians had spent centuries perfecting the formula between lunar months and solar years.  In other words, they wanted integer values for x and y where x years would equal y months.  If they knew this, they could be proactive in adding an extra month to keep the year in line with the seasons.  By the 6th century BCE, they had figured out that eight tropical years was almost equal to 99 lunar months.  Since 12 x 8 = 96, you would add three months every eight years.  Such a calendar would only drift from the seasons by 1.6 days every eight years.  Later, under Persian rule, Babylonian astronomers came up with an even more precise formula – seven extra months every nineteen years.  That would make the calendar accurate to within one day in 210 years.

The Jews adopted this calendar and have periodically modified it.  An extra 30 day month is added to Years 3, 6, 8, 11, 14, 17, and 19.  The names of most of the months still retain their Babylonian origins.

Hebrew Months
Nisan (30 days)
Iyar (29 days)
Sivan (30 days)
Tamus (29 days)
Av (30 days)
Elul (29 days)
Tishrei (30 days)
Marcheshvan or Cheshvan (29/30 days)
Kislev (30/29 days)
Tevet (29 days)
Shevet (30 days)
Adar (29 days)

In leap years, Adar I (30 days) is added after Shevet and the regular Adar is referred to as Adar II.

The ecclesiastical new year begins in spring on the first day of the month of Nisan.  Passover begins on the 15th of Nisan.  The civil new year begins in autumn on the first day of the month of Tishrei and is observed as Rosh Hashanah.  Yom Kippur, the holiest day, is on the tenth of Tishrei.  Months alternate between 29 and 30 days except for the two months following Tishrei which can have either 29 or 30 days.

Since Jewish months always begin on a new moon, Jewish festivals always occur during the same moon phase.  The first of each month is a minor holiday known as Rosh Chodesh.  Passover, Purim, and the first day of Sukko always fall on a full moon.

Jewish monotheism is evident in how the days of the week are named.  Other than the Sabbath, the days are simply named “First Day,” “Second Day,” etc., following the creation story in the Book of Genesis.  Hebrew is not alone in this but certainly in the minority.  It is more common for the days of the week to be named after the Sun, Moon and five visible planets.  This goes back to the Babylonians or the Greeks, who worshiped heavenly bodies as gods, a practice which the Jews completely rejected.

Over the centuries, complicated rules were added to the Jewish calendar to ensure that certain dates not fall on certain days of the week.  For instance, Rosh Hashanah should never fall on a Sunday, Wednesday, or Friday.

The Jewish calendar is a living monument to ancient astronomy and mathematics.  Astronomers should love it because it accurately tracks lunar phases and seasons.  Mathematicians should love it because it is based on calculations instead of observations which means it is consistent, predictable, and objective.


12. Even a pharaoh can’t just fix the calendar

Figure of Ramesses II at the entrance to one of the temples at Abu Simbel.  Image by Nick Peretti via Wikimedia Commons.

The society I’ve discussed most extensively so far is Rome.  After all, that’s where the Gregorian calendar, which we all use, comes from.

Rome was heavily influenced by Greece, the birthplace of Western civilization.  The Greeks, in turn, were well aware that there was a land far more ancient than their own, with more magnificent works of architecture.

That land was Egypt.

Egypt was under Greek rule from the time Alexander the Great invaded in 332 BCE until the Romans took over in 30 BCE.  The Greeks in Egypt marveled at the towering monuments all along the Nile.  The temple at Karnak was the largest in the world.  But the top attractions were, and still are, the pyramids and sphinx in Giza.  When the Parthenon was built in Athens nearly 2500 years ago, the Giza pyramids were already 2000 years old.

Image of the Karnak temple by Luck-one via Wikimedia Commons.  One of the twin obelisks at the entrance, the tallest ever built, is still standing.
Great sphinx and pyramid of Menkaure in Giza.  Image by Mstyslav Chernov via Wikimedia Commons.

In 2500 BCE, the pharaohs of the Old Kingdom could get 10,000 people to toil for 30 years to build a pyramid.  What they couldn’t do was command the people to switch to a new calendar.  Matters like that had to be handled delicately.

Until then, the Egyptians, like the Mesopotamians, followed a lunar calendar.  The months were based on observed lunar phases which meant they could have either 29 or 30 days.  A thirteenth month was added to the religious calendar every few years to bring it in line with the seasons.  

While the Mesopotamians used the shadows of a gnomon to measure the length of the year, the Egyptians appear to have used observations of Sirius, the brightest star in the sky after the Sun.  Sirius is visible in the Egyptian sky for nearly 300 days of the year.  The year began when Sirius reappeared after going missing for a couple of months.  

And just like in Mesopotamia, Egypt appears to have originally also had a separate 360 day calendar with twelve 30-day months.  

Here is where the two stories completely diverge.  In Mesopotamia, the 360 day calendar was only used by the astronomer-priests to make their astrological calculations easier.  The observation-based lunar calendar was far more important.  Major religious festivals took place during a new moon or full moon.  It was not that big a deal that twelve lunar months was less than one tropical year.  When the new year had drifted too far from the spring equinox, the king would add an extra month to bring it back in sync.  

In Egypt, on the other hand, the annual flooding of the Nile became even more important than lunar phases as agriculture depended on it.  Having the length of the year vary became unacceptable.  Having it be 360 days long was also unacceptable since observations of Sirius, which predicted the annual flooding with reasonable accuracy, showed that it was closer to 365 days.  Therefore a 365 day calendar had to somehow be sold to the people.

This appears to have been accomplished through an ingenious myth which goes back at least to the Fifth Dynasty (25th-24th century BCE).  Here is Hernst Zinner’s retelling of it, taken from Saha & Lahiri (1955):

“The Earth god Seb and the sky goddess Nut had once illicit union.  The supreme god Ra, the Sun, thereupon cursed the sky goddess Nut that the children of the union would be born neither in any year not in any month.  Nut turned to the god of wisdom, Thoth, for counsel.  Thoth played a game of dice with the Moon-goddess, and won from her 1/72th part of her light out of which he made five extra days.  To appease Ra the Sun-god, these five days were given to him, and his year gained by five days while the Moon-goddess’s year lost five days.  The extra five days in the solar year were not attached to any month, which continued to have 30 days as before; but these days came at the end of the year, and were celebrated as the birthdays of the gods born of the union of Seb and Nut, viz., Osiris, Isis, Nephthys, Set and Anubis, five chief gods of the Egyptian pantheon.”

Detail of Geb (or Seb), Nut, and Shu from the Book of the Dead of Nesitanebtashru.  The Earth god, Geb, is separated from the sky goddess, Nut, by the wind god, Shu.  Photographed by the British Museum; original artist unknown [Public Domain].
Note that the real loser in this myth was the Moon, who had nothing to do with the forbidden union between the Earth and the sky.  The myth appears to have accomplished the extraordinary task of completely removing lunar phases from religious life.  The important feasts that used to take place during specific lunar phases were transferred to specific dates on this new civil calendar.  The people stopped using the Moon as a timekeeper.

As the Moon lost its privileged position, so did astronomers.  The beginning of the month no longer had to be announced by the astronomer-priest.  No complicated calculations had to be performed to bring the month in line with the year.  Anyone can remember that there are twelve months with 30 days each and five extra days at the end of the year.  

If astronomers had continued to have a voice, they might have pointed out that the year is actually slightly more than 365 days long.  Within a few centuries, it was apparent that the new year kept drifting relative to the seasons.  Adding six extra days, instead of five, every four years would have made the calendar nearly perfect.  The Greeks who ruled Egypt in the 3rd century BCE did just that that but the people wouldn’t accept the change.  

The Greek pharaohs failed to understand something the pharaohs of the Old Kingdom had known all too well.  No mortal, not even a pharaoh, could fix the Egyptian calendar by decree.  When you mess with the calendar, you mess with religion.  The calendar had to adhere to the will of the gods.

Two hundred years later, the Egyptians finally warmed up to the addition of the leap day.  Even with this revision, their calendar was the simplest in the world.

And here’s the great irony.  While the simplicity of their calendar had rendered Egyptian astronomers redundant in the 3rd millenium BCE, that same simplicity made it the preferred choice of later astronomers.  The most influential Greek astronomer in Egypt, Claudius Ptolemy, would use it as would his most famous challenger, Nicolaus Copernicus, 1500 years later.

Egyptian farmers continue to use their ancient calendar.  So does the Coptic Orthodox Church, with the additional leap day.  The Egyptian calendar also inspired the Ethiopian Calendar and the French Republican Calendar.

11. Calendars in the cradle of civilization

The ziggurat of Ur, built by the Neo-Sumerian king Ur-Nammu and his son and successor Shulgi in the 21st century BCE.  Image by Kaufingdude via Wikimedia Commons.

Today it’s called Iraq.  Its residents were the earliest known practitioners not only of astronomy but also writing and mathematics.  They might have even invented the wheel.

The southern region of Sumer came to prominence first.  Cities emerged along the Idigna and Buranuna rivers.  The Greeks would later refer to these rivers as the Tigris and Euphrates and the land as Mesopotamia which means “between rivers.” 

Sumerian cuneiform dates back to the 4th millennium BCE.  The third millennium BCE saw the rise of Akkad, a region to the North of Sumer inhabited by Semitic people.  As Sumerian and Akkadian kings competed for dominance, their languages merged.  Art, architecture, music, religion, philosophy, mathematics, astronomy, and medicine thrived.  Sumer collapsed around 2000 BCE due to ecological factors by which time there were two separate Akkadian nations, Assyria and Babylonia.  All of Mesopotamia came under the rule of the Babylonian king Hammurabi in the 18th century BCE and the city of Babylon became a major religious and cultural center.  

This 18 century BCE relief shows Hammurabi (standing) receiving his royal insignia from a Babylonian god.  Below the relief are Hammurabi’s code of laws.  Excavated by Jacques de Morgan in 1901-1902.  Louvre Museum, Mesopotamie, Room 3, 24656.  Image by Luestling via Wikimedia Commons.

Babylonian kings felt the need to appease the gods.  This is much easier to do if you know what the gods want.  Animals would be sacrificed and markings on their livers would be interpreted by priests as messages from the gods to the kings.

It occurred to someone at some point that patterns in the heavens could be a more sophisticated way for the gods to communicate with the king.

Astrology was born.  Astronomy became central to Babylonian religion.  Astronomer, astrologer, and priest were now one and the same.  As the one person who could interpret the will of the gods, he, or perhaps occasionally she, enjoyed a privileged position in the king’s court.  

Thousands of astrological omens are listed in a collection of cuneiform tablets on Anu and Enlil, the gods of the sky and the wind.  Tablet 63 in the series lists the rising and setting times of Venus over a period of 21 years during the reign of Ammisaduqa, the fourth Babylonian king after Hammurabi.  The more recent MUL.APIN is much more comprehensive, describing observations of the Sun, Moon, planets, stars, and constellations and associated astrological omens.  

Venus tablet of Ammisaduqa.  This tablet was made in the 7th century BCE but the text is believed to date back to the 17th century BCE. British Museum, Room 55, K.160.  Image by Fae via Wikimedia Commons.

The Babylonians, and to a large extent the Sumerians before them, had mastered the basics of observational astronomy.  Using a gnomon, they figured out the cardinal directions and the dates of the solstices and equinoxes.  They kept track of seasonal daylight variations.  They developed an early version of the zodiac after noticing that the Moon and planets only wander through these constellations.  And they noticed that the different celestial cycles do not fit together neatly.  

An astronomer-priest would announce the beginning of the month when he or she could see the waxing crescent moon around sunset.  Consequently, months would have either 29 or 30 days.  A year was twelve months or around 354 days.  Every few years, the king would announce the addition of a thirteenth month, at the advice of the astronomer-priests, to bring the year in line with the seasons.  Religious festivals were based both on the lunar cycle and the agricultural cycle which depended on seasons.  The king’s legitimacy rested, in part, on bringing these cycles into harmony.

Then something happened.  Someone conceived of an ideal world which is different from the natural world.  Months that vary between 29 and 30 days are not ideal.  Of the two, 30 seems preferable.  It is half of 60, a number so ideal the entire Babylonian numeral system was based on it.  Twelve ideal months would add up to 360 days.  Dividing the hour into 60 minutes and the circle into 360 degrees could have its roots in Babylonian idealism.

If it’s not clear to you how big a deal the new calendar was, let me illustrate with an example.  The following two observations are mentioned in the Venus tablet of Ammizaduqa:

“In Month XI 18th Day, Venus in the East became visible.”

“In Month VIII 11th Day, Venus disappeared in the East.”

How many days elapsed between the two observations?  

To answer to this question, you would have to know which calendar was used by the authors or translators.

If the dates had been converted to Gregorian dates, Month XI 18th Day would refer to November 18th and Month VIII 11th day would refer to August 11th.  If you assume the observations were made on consecutive years, you could look at last year’s and this year’s calendar and count the days from November 18th to August 11th.  If you don’t know which year the second observation was made in, your answer could be off by one day since February could have had either 28 or 29 days.

On the “ideal” Babylonian calendar, the calculation is much simpler since each month has exactly 30 days.

Now imagine doing the calculation if the length of each month was not predetermined but was instead either 29 or 30 days, depending on when the astronomer-priest saw the waxing crescent moon.  To calculate the elapsed time, we would have to look up how many days each month had in each of those years, assuming those records are even available.

The Babylonians did not abandon an observation-based lunar calendar once the 360 day calendar had been developed.  Both systems existed in parallel.  

This was a major precursor to the invention of science.  The ancient Babylonians did not practice science.  They were engaged in pseudoscience.  They thought they saw patterns between celestial events and worldly events and got carried away.  They did not yet possess the tools required to answer big questions regarding the nature of the universe.  But their practice of maintaining two separate calendars, one of which was a record of natural processes in their true complexity and the other an artificial creation that was easier to work with, bears a striking resemblance to modern astronomy.

Today there are two types of astronomers.  An observational astronomer examines the universe as it appears to be.  A theoretical astronomer, on the other hand, constructs models of the universe.  Each model is not designed to be a perfect replica of the real thing, just similar enough to serve a specific purpose.

A scientific model is a bit like a mannequin.  Imagine you have a month to design a dress for a celebrity.  You have no direct access to her and so you build a mannequin on which you’ll try out your creations.  Initially, you just want to see how different types of dresses will fit and so the mannequin just needs to have the same figure as the celebrity.  It doesn’t need eyelashes or even eyes.  Or maybe even a face.  But that will not do for your final product. So you look at as many pictures and videos of the celebrity that you can get your hands on.  You will use these to refine your mannequin.  You give it the same skin tone, hair color, and eye color as the celebrity.  But it still might not need toes.  And it certainly doesn’t need a nervous system.

To astronomers, the elusive celebrity is the universe itself.  Observers catch glimpses of it with their telescopes while theorists build models of it.  The first models are always simple.  You may even call them primitive.  But a theorist would call them ideal.

Where I went to college, there was a sign in the Society of Physics Students room that read: “You Might Be a Physics Major If…”  One of the items on the list was that you assume a horse is a sphere to make the math easier.

An ancient Babylonian astronomer would’ve got the joke.

10. He came. He saw. He concocted a calendar.

Caesar and Cleopatra by Pietro da Cortona (1596-1669) at the Musée de beaux-arts de Leon.  After spending some time in Egypt, Julius Caesar decided to reform the Roman calendar.

Who was born in England on September 3rd, 1752?  No one.  How about on September 4th of that year?  Again, no one.  The 5th, 6th or 7th?  Then too.  How about in New York and Boston?  There too.  No one died either.  

In fact, nothing happened.  Those dates did not even exist.

If you went to sleep on the night of the September 2nd, 1752 anywhere in the British empire, when you woke up, it was September 14th.  September 3rd through September 13th never existed.

How could this have happened?  

In 1752, Britain officially switched from the Julian calendar to the Gregorian calendar.  

The Julian calendar is named after Julius Caesar.  So our story begins in ancient Rome.  

It’s impossible to separate fact from myth when it comes to the original Roman calendar.  After all, it was named after Rome’s founder, Romulus, who was said to have been fathered by the god Mars and suckled by a wolf.  The calendar might have looked like this:

Calendar of Romulus
Martius (31 days)
Aprilis (30 days)
Maius (31 days)
Iunius (30 days)
Quintilis (31 days)
Sextilis (30 days)
September (30 days)
October (31 days)
November (30 days)
December (30 days)

We can see that the ancient Romans had abandoned the Moon as a timekeeper.  Months in lunar calendars are usually either 29 or 30 days long since one cycle of lunar phases takes 29.5 days.  A year consisting of six 29-day months and six 30-day months would be 354 days long, which is shorter than a tropical year by over 11 days. 

It appears that the early Romans wanted the spring equinox to occur during the first month which was then Martius (March).  This explains the choice of 30 and 31 day months.  Seven 30 day months and five 31 day months would produce a 365 day year.  

But notice that the year didn’t have 12 months.  It only had 10.  There were only 304 days in a year.  The days of winter, between December and Martius, were not assigned to any month.

By simply adding another 30 day month and another 31 day month, the ancient Romans could have prduced a 365 day calendar.  They could have done even better by adding a leap day every few years.  It was well known, at least to their neighbors in Greece and Egypt, that a tropical year was a little less than 365.25 days long.

But no.  Things got complicated.

Two more months, Ianuarius and Februarius, were indeed added.  But Februarius would have only 28 days.  Each of the 30 day months would lose a day because even numbers were considered unlucky.  It was okay for Februarius to have an even number of days because it was the month of purification.  The year now had 355 days.  An extra month would be added periodically to bring the year back in line with the seasons.

At some point, the New Year was shifted from the beginning of Martius to the beginning of Ianuarius.  This meant there was no longer any connection between the new year and the spring equinox.  It also meant that the months from Quintilis to December would no longer be the fifth to tenth months, as their names indicate, but the seventh to twelfth months.

This calendar was attributed to Numa Pompilius, Rome’s second king, at least according to legend.

Calendar of Numa
Ianuarius (29 days)
Februarius (28 days)
Martius (31 days)
Aprilis (29 days)
Maius (31 days)
Iunius (29 days)
Quintilis (31 days)
Sextilis (29 days)
September (29 days)
October (31 days)
November (29 days)
December (29 days)

It became clear to Julius Caesar that this calendar had to go.  Not because the month had nothing to do with the Moon.  Or because the names of the last six months did not make sense.  Or because the year did not begin on an equinox or a solstice.  The real problem was that extra months were added not according to how much the year had drifted relative to the seasons but when politicians found it advantageous to do so.  Like the Greeks who had been ruling Egypt, Caesar preferred a 365 day year with a leap day every four years.

This is essentially the calendar we still use today.  It was introduced by Julius Caesar in 46 BCE.  Following his assassination, Quintilis was renamed Iulius in his honor and subsequently Sextilis was renamed Augustus after his successor.

There’s just one little thing.  The tropical year is not exactly 365.25 days long.  The discrepancy is around three days every 400 hundred years.

That was fine for the ancient Romans but not the Christians in charge later.  The problem was Easter.  It was supposed to fall on the Sunday after the full moon following the spring equinox.  This was determined not by observation but by computation.  March 21st was taken to be the date of the spring equinox although the actual spring equinox gradually drifted to earlier and earlier dates.  The ancient Babylonian calculation relating lunar months to tropical years also needed to be revised.  Astronomy again became integral to religion.

During the 16th century, the Council of Trent had astronomers work on the problem for a couple of decades.  The new calendar was instituted in 1582 by Pope Gregory XIII.  The Gregorian calendar would have three fewer leap days every 400 years than the Julian calendar.  Years that are multiples of 100 would not be leap years unless they were also multiples of 400.  So 1600 would still be a leap year but 1700 would not.  

Since the Julian calendar had already drifted relative to the seasons by ten days, a one-time fix was needed to realign the calendar.  In most of the Catholic countries in Europe, October 4th, 1582 was followed by October 15th.

Protestant Europe did not switch to the Gregorian calendar until the middle of the 18th century.  Since they had treated 1700 as a leap year, they now had to drop eleven days from their calendar when they switched.  This was why September 2nd was followed by September 14th in 1752 throughout the British Empire.

The date of the northern summer solstice on the Gregorian calendar.  By BasZoetekouw via Wikimedia Commons.

The Julian calendar has not completely disappeared.  It’s still used by most of the churches in Eastern Christianity to compute the date of Easter.  The heads of major Christian denominations continue to discuss the possibility of a common date for Easter.

When will the Gregorian calendar need to be reformed again?  Not for thousands of years.

A tropical year is 365.2422 solar days while a Gregorian year is 365.2425 solar days.  That would imply an error of one day per 3,300 years but to calculate the actual error, we’d have to take into account all kinds of non-variability in the Earth’s rotation, orbit, and precession.  If we’re still using the Gregorian Calendar thousands of years from now and find out that it’s off by a day, we can simply take out a leap day to bring it back in sync.

This calendar we inherited from the Romans just might endure for another 2000 years or longer.  Even a man as ambitious as Julius Caesar couldn’t have imagined that.


9. Does Earth orbit the Sun once a year?

Astronomical clock installed at Hampton Court Palace in Greater London, England around the year 1540.  Besides the day, month, and lunar phase, it’s supposed to show where the Sun is in the zodiac.  What it actually shows is where the Sun was in the zodiac 2500 years ago.  Image by Mike Cattell via Wikimedia Commons.

One of the themes of this blog has been that our units of time are based on the way things appear, not the way they really are.  A day is based on when the Sun appears highest in the sky, not how long the Earth actually takes to rotate once.  The month is based on when the Moon appears to complete a cycle of phases, not how long it actually takes to orbit the Earth.  The last couple of posts have been on the year, which I defined as one cycle of the seasons.

I never mentioned anything about the Earth orbiting the Sun once a year.  Does it?



Just like there’s a sidereal day and a sidereal month, there’s a sidereal year which is one orbit of the Earth around the Sun.  In theory, you could measuring how long that is by seeing which star the Sun is lined up with at some time and waiting for that to happen again.  In practice, that’s not possible because we can’t see the stars that are up during the day, let alone those that are directly behind the Sun.  What you can do is see which stars rise just before dawn.  One sidereal year later, the Sun will return to the same position relative to those stars.  Unfortunately, this will actually happen during the day (because a sidereal year is around 365.24 days) and so you won’t get to see it.  You might have to track the position of the Sun relative to the stars for several years before you can accurately measure the length of the sidereal year.

The point is that it’s not surprising ancient peoples didn’t use the sidereal year.  Defining a year as one cycle of the seasons makes much more sense.  That is called a tropical year.

But do we actually need two different definitions of the year.  Aren’t they exactly the same length?  The time it takes the Earth to orbit the Sun should be the same as one cycle of the seasons, right?

The animation below (which was also in the last post) certainly makes it look that way.  When the Earth is on the right side, the Northern Hemisphere is tilted towards the Sun and the Southern Hemisphere is tilted away from it.  So it’s the summer solstice in the Northern Hemisphere and the winter solstice in the Southern Hemisphere.   After one orbit, we get back to the same alignment.

Animation showing the Earth orbiting the Sun.  By tfr000 via Wikimedia Commons.

There’s just one problem.  The animation’s wrong.  Or you could say what it depicts is a convenient lie.

The direction of Earth’s tilt changes.  This is called precession.  It’s the least obvious motion of the Earth because it happens so slowly.  It takes around 26,000 years to complete one precession cycle.

If the animation had been accurate, the direction of the tilt will slowly rotate away from you.  Initially, you wouldn’t have noticed.  Within one orbit or even a hundred orbits, the tilt won’t change much.  But if you read this entire post and then scroll back up, you should see that the tilt is pointed in a different direction.  You should but you won’t.  Because it’s wrong.  If you find an animation that shows the Earth orbiting the Sun and also precessing, let me know.

A sidereal year is around 20 minutes longer than a tropical year.

Focus on the Earth when it’s on the right side in the animation.  Now imagine that the tilt rotates away from you slightly.  This means the Earth wouldn’t quite have to complete one full orbit before the Northern Hemisphere is tilted towards the Sun again.  In other words, we don’t have to wait until the Earth is all the way to the right.  Just before then, when it’s slightly on the near side, the Northern Hemisphere will be tilted towards the Sun.  One tropical year has been completed.  When the Earth makes it all the way to the right side (after one sidereal year), the tilt is not pointing directly towards the left but mostly towards the left and ever so slightly away from you.

Thirteen thousand years from now, the tilt will point towards the right in the animation.  At that point, it will be summer in the Northern Hemisphere when the Earth is on the left side.  The summer solstice will still take place in late June but the constellations we see then will be the ones on the left side, not those on the right side (because the left side of the Earth is the nighttime side).

Even if you observe the heavens carefully all your life, you won’t notice precession happening.  It doesn’t produce any changes that are visible to the naked eye within a human lifetime.

However, the changes add up over time.  Currently, there is a bright star, aptly named Polaris, that is almost perfectly aligned with the North Pole.  But this has only been true for a few centuries.  In fact, it was only named Polaris during the European Renaissance.  When Stonehenge and the Pyramids of Giza were being built, a star called Thuban was our North Star.  In the coming millennia, other bright stars will serve as our North Star at certain times and there will long periods without a North Star.  Polaris will once again be our North Star 26,000 years from now.

One precession cycle of the Earth.  By tfr000 via Wikimedia Commons.

The figures below show the stars that are aligned with the North and South Poles at different times.  The numbers shown are calendar years (+2000 is 2000 CE, -2000 is 2000 BCE, etc.).  Since the entire cycle takes 26,000 years, -2000 is the same as +24000.

Polaris is at the end of the Little Dipper’s handle, just to the left of +2000 on the figure at the left.  Currently there is no bright star that is aligned with the South Pole (+2000 on the figure at the right).

The path of the North (left) and South (right) Celestial Poles among the stars due to precession.  By Tao’olunga via Wikimedia Commons.

Imagine how perplexing precession would have been for an ancient astronomer.  You find records from a thousand years ago indicating that a constellation is visible just before dawn on the spring equinox but it isn’t.  Or the most famous monument in the land was built to line up with certain stars on certain nights but it doesn’t.

It took an extraordinary astronomer who also had access to centuries of astronomical records to realize that the seasons are indeed drifting relative to the stars.  That person is believed to have been the Greek astronomer Hipparchus, a  who lived in the 2nd century BCE.

Over the next two millennia, precession was alternately accepted and rejected by astronomers in different parts of the world.  Many who accepted it argued incorrectly that it doesn’t go in one direction but back and forth every few hundred or few thousand years.  This went on until the 17th century when Isaac Newton provided a physical explanation for precession.  Even Newton didn’t have the last word on the matter because his equations didn’t work and had to be refined by later scientists.

A great barrier to accepting precession was the deep attachment many astronomers had to zodiac astrology.  This is the idea that there is an enduring connection between you and the constellation the Sun was in when you were born.

During the course of the year, the Sun wanders through a dozen constellations.  Some are larger than others and so the Sun takes longer to cross them.  But for convenience, the path of the Sun was divided into twelve equal parts with one constellation in each.

The Babylonians first did this around 2500 years ago.  Since then, the zodiac has drifted backwards by one full constellation due to precession.  So if your zodiac sign is Cancer, the Sun was actually in Gemini when you were born and so on.

The constellations are not where they used to be.  The Sun is in your astrological sign not on your birthday but around one month earlier.  By Trex via Wikimedia Commons.

In ancient times, studying the stars was often not an end in itself but a means to explain and predict life events.  The idea that the stars which are supposed to guide our lives are themselves not fixed must have made an ancient astronomer extremely agitated.

Even more than you were when you found out the Earth doesn’t go around the Sun once a year.


8. Why do we have seasons?

In my last post, I described how an astronomer living 5000 years ago could have measured the length of the year by tracking the path of the Sun through one cycle of the seasons.  The story wasn’t set at any specific location because we don’t know who first did this.  It’s likely that people from different parts of the world figured it out independently.

By around 5000 years ago, seasons had become enormously significant to many societies.  The year became as important as the month, if not more so.  Every new moon was observed.  But a new moon that occurred close to a solstices or equinox was celebrated.  Monuments were aligned with the cardinal directions or with the Sun on a solstice.

Many Egyptian monuments, including the Great Pyramid in Giza, are aligned almost perfectly with the cardinal directions.  Image by Nina via Wikimedia Commons.

This does not mean people figured out, 5000 years ago, why we have seasons.  In fact, most people were wrong about this even 500 years ago.

To figure out why we have seasons, we had to observe how the seasons change not just from month to month but also from place to place.  Our perspective had to go from local to global.

Over the centuries, different parts of the world came in contact with each other through trade and conquest.  If you lived in a major city, you could meet people from distant lands.  They could tell you that some places have long days and short nights followed by short days and long nights while other places have equally long days and nights throughout the year.  And that the Sun is directly overhead on certain days in some places but that this never happens in other places.

You could incorporate all this information into a model of the Earth and the Sun and use it to explain seasons.  Chances are, your Earth would have been flat.  The mythologies of ancient Mesopotamia, Egypt, India, China, and Greece all depict a flat Earth.

Your Sun would orbit your flat Earth once a day.  And it would also slowly drift north or south.  It would be furthest to the north or the south on the solstices and halfway between these points on the equinoxes.

In fact, evidence that the Earth was round, not flat, was all around us.  As Aristotle noted:

Our observation of the stars make[s] it evident, not only that the Earth is circular, but also that it is a circle of no great size.  For quite a small change of position on our part to south or north causes a manifest alteration of the horizon.  There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward.  Indeed there are some stars seen in Egypt and in the neighborhood of Cyprus that are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set.

Aristotle, On the Heavens, Book II, Chapter 14, 297b 26-298a 5 (Oxford trans., pp. 488-489)

In Greece, the transition from flat Earth to round Earth happened around 2500 years ago.  According to Steven Weinberg, earlier philosophers could not accept a spherical Earth because they thought travelers would fall off.

The real challenge is often not what you have to learn but what you have to unlearn.  If you’re sure the Earth is flat, no amount of data indicating that it is round will be enough to change your mind.

While Aristotle was right about the approximate shape of the Earth, he and most of the other ancient Greeks were still wrong about why we have seasons.  They still believed the Sun orbits the Earth.

In the geocentric (Earth-centered) model, the Sun slowly drifts towards the north for half the year and towards the south for the other half of the year.  The furthest north it gets is 23.4 degrees North of the celestial equator (the Tropic of Cancer).  This takes place on June 20th or 21st and is called the summer solstice in the Northern Hemisphere.  Then the Sun moves south until it is on the celestial equator.  This is on the autumnal equinox in the Northern Hemisphere which takes place on September 22nd or 23rd.  The Sun continues moving south until it is 23.4 degrees south of the celestial equator (the Tropic of Capricorn).  This is the winter solstice in the Northern Hemisphere and takes place on December 21st or 22nd.  Then the Sun heads northward.  It will cross the celestial equator again around March 20th, which is the vernal (spring) equinox in the Northern Hemisphere, on the way to the next summer solstice.

Seasons in the Southern Hemisphere are the opposite of those in the Northern Hemisphere.  Northern summer solstice is southern winter solstice and northern autumnal equinox is southern vernal equinox.

Here is a video of my wife demonstrating the apparent motion of the Sun.

Arguably, the greatest revolution in the history of science was the shift from the geocentric model to the heliocentric (Sun-centered) model of the solar system around 400 years ago.

It is the Earth that moves around the Sun, not the other way around.

Today, we explain seasons by giving the Earth a tilt.  The Earth’s axis of rotation is tilted by 23.4 degrees relative to the plane in which it orbits the Sun.  When your hemisphere (Northern or Southern) is tilted directly towards the Sun, the Sun appears higher in the sky than when it’s tilted away from the Sun.  This is shown in the animation below.  If it makes you dizzy, don’t stare at it.  You can focus on the figure below it which shows snapshots of the Earth on the two solstices.

Animation showing the reason for seasons.  When the Earth is on the right, the northern hemisphere is tilted towards the Sun and the southern hemisphere is tilted away from the Sun.  So it is then summer in the northern hemisphere and winter in the southern hemisphere.  The opposite is true when the Earth is on the left.  The equinoxes take place when the Earth is in the front or the back.  By tfr000 via Wikimedia Commons.
The Earth on the two solstices.  During the June solstice, the Northern Hemisphere is tilted towards the Sun.  The direct rays of sunlight fall on the Tropic of Cancer.  This is the summer solstice in the Northern Hemisphere.  During the December solstice, the Northern Hemisphere is tilted away from the Sun and so it is the winter solstice in the North.  The direct rays of sunlight fall on the Tropic of Capricorn that day.  On these figures the tilt is shown in the opposite direction in the animation above, as it would be if you were looking at the Earth from the opposite side of the Sun.  By cmglee, NASA via Wikimedia Commons.

Now that we have telescopes and satellites, the idea of a motionless Earth at the center of the universe might seem absurd.  But the geocentric model explained almost everything you can see with the naked eye just as well as the heliocentric model did.

If you were an ancient astronomer, would there have been any way for you tell which model is right?

7. What is a year?

The Sun on the equinox (Sep. 23, 2011) at the equatorial line in Ecuador.  The Sun rises due East and sets due West twice a year, on the equinox days.  At the equator, the Sun, Moon, and stars rise and set vertically.  So on the equinox days, the Sun will stay on the East-West line the whole day and be directly overhead at noon.  Image by Cristocobo via Wikimedia Commons.

“How old are you?”



“I’m 13,662 days old.”


We’re used to years.  It’s probably because we prefer small numbers.  When the number gets large, we switch units.  Parents generally state the age of a child in days for the first couple of weeks, in weeks for the first couple of months, and in months for the first couple of years.  After that, it’s years.

Whether we’re talking about the age of a person or of the universe itself, we prefer years.  If we ever use other units, like centuries or millennia, they’re still just multiples of years.

As a child, one of my favorite movies was The Jungle Book.  In the transition from the first scene to the second scene, the narrator, who is Bageera the panther, says “Ten times the rains had come and gone.”  I found this fascinating – the idea that you can use the monsoons to keep track of time.  Panthers probably don’t but people could have, a long time ago.  

For people in other parts of the world, the key annual event could have been the first snowfall, the sprouting or falling of the leaves, the sighting of certain animals or birds, or the flooding of a river.  Keeping track of years, using the seasons, must go back a very long time, even longer than astronomy.  But astronomy helped us do it more precisely.

Let’s play ancient astronomer again.  You live somewhere north of the tropics, 5000 years ago.  Using just a stick, you have figured out how to measure the length of a day.  Now you’re about to extend this to the year.

For generations, your people have been aware that there are warm seasons and cool seasons.  During the warm season, the Sun is higher in the sky and up for more hours than during the cool season.  And a year, which is one cycle of the seasons, is a little over 12 months long.  

But the month is based on the Moon.  Using lunar cycles to keep track of seasons is unreliable and clumsy.  It’s time to measure the length of the year directly, using the Sun.  

It’s another morning.  The Sun rose slightly to the left of a tree.  A few days ago, it rose directly behind that tree.  You turn around to look at the spot where you think it’s going to set.  You point to the Sun, without looking at it directly, and then trace out with your finger the path you think it will take today.  You do this a couple more times.  You can sense you’re on to something.

You look down at the meridian line you drew some days back.  Every day at noon, the shadow of your stick falls on this line.  

Your meridian line defines North and South.  The shadow of your stick points North at noon because the Sun is in the South at noon.  Until now, you haven’t bothered to exactly define East and West because the Sun rises and sets in a slightly different direction every day.

You draw a line perpendicular to the meridian.  This is your East-West line.  You face East.  Today’s sunrise point is not straight ahead but to your left.  The Sun rose North of East today.

Later that evening you see that the Sun set North of West.  These days, the Sun rises in the Northeast, arcs to the South at noon, and arcs back to set in the Northwest.  Every day, the Sun rises and sets slightly further to the North and is slightly higher in the sky at noon.  You wonder if the Sun will ever be directly overhead.  If it does, the noon shadow, which has been slightly shorter every day, will disappear altogether.

That day never comes.  You notice one day that the noon shadow is longer than it was a couple of days earlier.  You had suspected that this would happen because this morning, the Sun rose slightly to the right (South) of where it had risen yesterday instead of continuing to rise further and further to the left.  You’re disappointed.  You missed a key day – the day the Sun rises and sets furthest to the North and is highest in the sky at noon.  It will come to be known as the summer solstice.

You’re going to count the days from one summer solstice to the next.  Today is Day 3.  Or maybe Day 2.  You settle on Day 3.  You’ll have to keep counting the days as the noon shadow gets longer and longer and then shorter and shorter until the day comes when it is again shortest.  At that point, exactly one year would have gone by.

You draw three small lines on the wall.  Every day, as soon as you wake up, you will need to add another line.  This will be a long, tedious project.  But there are some things you can do to make it easier and more interesting.

You already have a lunar calendar.  It’s just that the new crescent moon sometimes appears after 29 days and sometimes after 30 days.  Until now, it hasn’t mattered whether a month was 29 or 30 days long.  From now on, it does.  On your day count, you will note down when the new moon and full moon occurred.  That way, if your project gets interrupted for some reason, you can get back on track using lunar phases and your count will only be off by a day or two.

After a couple of months, your wall looks like this:


One month later, the Sun rises directly in the East and sets directly in the West.  The day this occurs will later be referred to as the autumnal equinox.

A couple more months go by.  The days are short and the Sun stays low in the sky all day.  The shortest day of the year is almost here.  On that day, the Sun will rise and set furthest to the South and be lowest in the sky at noon.  You’re determined not to miss it.  For the last few days, you’ve been marking the exact length of the noon shadow.  You’ve also been paying close attention to exactly where the Sun rises and sets.  Hopefully the sky will stay clear.

The day you’ve been eagerly awaiting is finally here.  The noon shadow is as long as it will ever be.  The Sun has stopped rising further and further to the right (South).  From tomorrow, it will rise a little bit further to the left every day.  Your descendants will refer to this day of the year as the winter solstice.

It was around 183 days summer solstice to winter solstice.  The year must be around twice this or roughly 366 days.

Images of the Sun taken on the summer solstice (top), autumnal equinox (middle), and winter solstice (bottom) from Bursa, Turkey.  North is up, East is to the left, South is down, and West is to the right, as in a star chart.  Photo credit: Tunc Tezel and The World At Night (TWAN).

Your lines showing the days are now close to the floor.  This wall represents the days from summer to winter.  You erase the line you drew this morning and start a new count on a different wall.  This will be the winter to summer wall.

Your project is only half over.  But it has gone as planned.  You know what you’re doing.  When you’re finished, you will be the first person to figure out how many days there are in a year.