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 Credit: Cristocobo via Wikimedia Commons.

“How old are you?”

“13,662”

“Huh?”

“I’m 13,662 days old.”

“Weirdo.”

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.

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.