Yay! It’s a new year!
But what does that mean, exactly?
The year, of course, is the time it takes for the Earth to
go around the Sun, right? Well, not exactly. It depends on what you mean
by “year” and how you measure it. This takes a wee bit of explaining,
so if you're done kicking 2016 to the curb and trying your best to hope
for 2017, sit back and let me tell you why we have a new year at all.
Round and Round She Goes
Let’s take a look at the Earth from a distance. From our
imaginary point in space, we look down and see the Earth and the Sun.
The Earth is moving, orbiting the Sun. Of course it is, you think to
yourself (unless you're a Geocentrist,
in which case this stuff still all works, just the other way around).
But how do you measure that? For something to be moving, it has to be
moving relative to something else. What can we use as a yardstick against which to measure the Earth’s motion?
Well, we might notice as we float in space that we are
surrounded by billions of pretty stars. We can use them! So we mark the
position of the Earth and Sun using the stars as benchmarks, and then
watch and wait. Some time later, the Earth has moved in a big circle
(OK, ellipse, but they're pretty close in this case) and is back to where it started in reference to those stars. That’s called a “sidereal year” (sidus is the Latin word for star). How long did that take?
Wikipedia user Tfr000
Let’s say we used a stopwatch to measure the elapsed time.
You'll find that it took the Earth 31,558,149 seconds (some people like
to approximate that as pi x 10 million = 31,415,926 seconds, which is an
easy way to be pretty dang close—better than a half a percent
accuracy). That's an inconvenient number of seconds, though. I think
we'd all prefer to use days instead. So how many days is that?
Well, that’s a second complication. A “day” is how long it
takes the Earth to rotate once, but we’re back to that measurement
problem again. But hey, we used the stars once, so let’s do it again!
You stand on the Earth and define a day as the time it takes for a star
to go from directly overhead to directly overhead again: a sidereal day.
That takes 23 hours 56 minutes 4 seconds = 86,164 seconds. But wait a
second (a sidereal second?)—shouldn’t that be exactly equal to 24 hours?
What happened to those 3 minutes and 56 seconds?
I was afraid you’d ask that—but this turns out to be important.
Illustration by Nick Strobel
It’s because the 24-hour day is based on the motion of the Sun in the sky, and not
the stars. During the course of that almost-but-not-quite 24 hours, the
Earth was busily orbiting the Sun, so it moved a little bit of the way
around its orbit (about a degree). If you measure the time it takes the
Sun to go around the sky once—a solar day—that takes 24 hours,
or 86,400 seconds. It’s longer than a sidereal day because the Earth has
moved a bit around the Sun during that day, and it takes a few extra
minutes for the Earth to spin a little bit more to “catch up” to the
Sun’s position in the sky.
A diagram from Nick Strobel’s fine site Astronomy Notes
(shown here; click to embiggen) helps explain this. See how the Earth
has to spin a little bit longer to get the Sun in the same part of the
sky? That extra 3 minutes and 56 seconds is the difference between a
solar and sidereal day.
OK, so we have a year of 31,558,149 seconds. If we divide that by 86,164 seconds/day we get 366.256 days per year.
Wait, that doesn’t sound right. You’ve always read it’s 365.25 days per year, right? But that first number, 366.256, is a year in sidereal days. In solar days, you divide the seconds in a year by 86,400 to get 365.256 days.
Phew! That number sounds right. But really, both
numbers are right. It just depends on what unit you use. It’s like
saying something is 1 inch long, and it’s also 2.54 centimeters long.
Both are correct.
Having said all that, I have to admit that the 365.25 number is not really correct. It’s a cheat. That’s really using a mean
or average solar day. The Sun is not a point source, it’s a disk, so
you have to measure a solar day using the center of the Sun, correcting
for the differences in Earth’s motion as it orbits the Sun (because it’s
not really a circle, it’s an ellipse) and and and. In the end, the
solar day is really just an average version of the day, because the actual length of the day changes every, um, day.
The Sun Rose by Any Other Name
Confused yet? Yeah, me too. It’s hard to keep all this
straight. But back to the year: That year we measured was a sidereal
year. It turns out that’s not the only way to measure a year.
You could, for example, measure it from the exact moment of the March equinox
(also northernhemispherictically sometimes called the vernal equinox)
—a specific time of the year when the Sun crosses directly over the
Earth’s equator in March— in one year to that same equinoctal moment in
the next. That’s called a tropical year (which is 31,556,941 seconds long). But why the heck would you want to use that? Ah, because of an interesting problem! Here’s a hint:
The Earth precesses! That means as it spins, it wobbles very
slightly, like a top does as it slows down. The Earth’s wobble means
the direction the Earth’s axis points in the sky changes over time. It
makes a big circle, taking over 20,000 years to complete one wobble.
Right now, the Earth’s axis points pretty close to the star Polaris, but in a few hundred years it’ll be noticeably off from Polaris.
Remember too, that our seasons depend on the Earth’s tilt.
Because of this slow wobble, the tropical year (from season to season)
does not precisely match the sidereal year (using stars). The tropical
year is a wee bit shorter, by 21 minutes or so. If we didn’t account for
this, then every year the seasons would come 21 minutes earlier.
Eventually we’ll have winter in August, and summer in December! That’s
fine if you’re in Australia, but in the Northern Hemisphere this would
cause panic, rioting, people leaving comments in all caps, and so on.
So how do you account for this difference and not let the
time of the seasons wander all over the calendar? Easy: You adopt the
tropical year as your standard year. Done! You have to pick some
way to measure a year, so why not the one that keeps the seasons more
or less where they are now? This means that the apparent times of the
rising and setting of stars changes over time, but really, astronomers
are the only ones who care about that, and, not to self-aggrandize too much, they’re a smart bunch. They know how to compensate.
OK, so where were we? Oh yeah—our standard year (also called a Gregorian year) is the tropical year, and it’s made up of 365.25 mean solar days (most of the time,
actually), each of which is 86,400 seconds long, pretty much just as
you’ve always been taught. And this way, the March equinox always
happens on or around March 21 every year.
Lend Me Your Year
But there are other “years,” too. The Earth orbits the Sun
in an ellipse, remember. When it’s closest to the Sun we call that
perihelion (the farthest point is called aphelion). If you measure the year from perihelion to perihelion (called an anomalistic year,
an old term used to describe the shape of an orbit) you get yet a
different number! That’s because the orientation of the Earth’s orbital
ellipse changes due to the tugs of gravity from the other planets,
taking about 100,000 years for the ellipse to rotate once relative to
the stars. Also, it’s not a smooth effect, since the positions of the
planets change, sometimes tugging on us harder, sometimes not as hard.
The average length of the anomalistic year is 31,558,432 seconds, or
365.26 days. What is that in sidereal days, you may ask? The answer is: I
don’t really care. Do the math yourself.
Let’s see, what else? Well, there’s a pile of years based on
the Moon, too, and the Sun’s position relative to it. There are ideal
years, using pure math with simplified inputs (like a massless planet
with no other planets in the solar system prodding it). There’s also the Julian year,
which is an ideally defined year of 365.25 days (those would be the
86,400 seconds-long solar days). Astronomers actually use this because
it makes it easier to calculate the times between two events separated
by many years. I used them in my Ph.D. research because I was watching
an object fade away over several years, and it made life a lot easier. Doctoral research is hard, shockingly, so you learn to take advantages where you can find them.
Where to Start?
One more thing. We have all these different years and
decided to adopt the tropical year for our calendars, which is all well
and good. But here’s an issue: Where do we start it?
After all, the Earth’s orbit is an ellipse with no start or finish. It just keeps on keeping on. But there are
some points in the orbit that are special, and we could use them. For
example, as I mentioned above, we could use perihelion, when the Earth
is closest to the Sun, or the vernal equinox. Those are actual physical
events that have a well-defined meaning and time.
The problem, though, is that the calendar year doesn’t line up with them well. The date of perihelion changes year to year due to several factors (including, of all things, the Moon, and the fact that we have to add a leap day roughly every four years). In 2013 perihelion was on Jan. 2, but in 2017 it’s on Jan. 4. Same thing with the equinox: It can range from March 20 to March 21. That makes using orbital markers a tough standard.
Various countries used different dates for the beginning of the year. Some had already used Jan. 1
by the time the Gregorian (tropical) calendar was first decreed in
1582, but it took time for others to move to that date. England didn’t
until 1752 when it passed the Calendar Act.
Not surprisingly, there was a lot of religious influence on when to
start the new year; for a long time a lot of countries used March 25 as
the start of the new year, calling it Lady Day,
based on the assumed date when the archangel Gabriel told Mary she
would be the mother of God. Given that a lot of ancient Christian
holidays are actually based on older, Pagan holiday dates, and the fact
that this was on March 25—very close to the equinox—makes this date at
the very least suspicious.
Still, in the end, the date to start the new year is an
arbitrary choice, and Jan. 1 is as good a day as any. And as a happy
side effect it does help establish the Knuckle Rule.
Resolving the New Year
So there you go. As usual, astronomers have taken a simple
concept like “years” and turned it into a horrifying nightmare of
nerdery and math. But really, it’s not like we made all this stuff up.
The fault literally lies in the stars and not ourselves.
Now if you’re still curious about all this even after
reading my lengthy oratory, and you want to know more about some of
these less well-known years, then check out Wikipedia. It has lots of
info, but curiously I found it rather incomplete. Every year (take your
pick which kind) I say to myself I'll submit an updated article to
Wikipedia listing all the different years and the number of seconds and
days of each kind in them.
Then every year I forget. But if you want to give it a shot,
feel free. It would come in handy when I update this article every
365.26 days or so.
Incidentally, after all this talk of durations and lengths,
you might be curious to know just when the Earth reaches perihelion, or
when the exact moment of the vernal equinox occurs. If you do, check out
the U.S. Naval Observatory website. It has tons of gory details about this stuff.
And, finally (for real this time) I have to add one more bit
of geekiness. While originally researching all this, I learned a new
word! It’s nychthemeron, which is the complete cycle of day and
night. You and I, in general, would call this a “day.” Personally, if
someone dropped that word into casual conversation, I’d challenge them
to a duel with orreries at dawn.
Hmmmm, is there anything else to say here? (Counting on fingers.)
Years, days, seconds, yeah, got those. (Mumbling.) Nychthemeron, yeah,
Gregorian, tropical, precession, anomalistic … oh wait! I know something
I forgot to say:
Happy New Year!
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