I don’t usually repost blog entries, but it’s the end of the year, and my post at this time last year took me forever to research and write, and I like it so much I’m gonna just plop it down here to end 2007. Enjoy.
Yay! Tonight at midnight it’s New Year!
But what does that mean, exactly?
The year, of course, is the time it takes for the Earth to orbit 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 put down the champagne, take the lampshade off your head, and hang on.
First, I will ignore a few things. For example, time zones. These were invented by a sadistic watchmaker, who only wanted to keep people in thrall of his devious plans. So for now, let’s just ignore them, and assume that for these purposes you spend a whole year (whatever length of time that turns out to be) planted in one spot (though I’ll note that as I write this, it’s already 2007 in Australia and other points west of the international date line).
However, I will not ignore the rotation of the Earth. That turns (haha) out to be important.
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. 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 zillions 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 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?
Let’s say we used a stopwatch to measure the elapsed time. We’ll see 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 close). But 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, 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?) — why isn’t that exactly equal to 24 hours?
I was afraid you’d ask that — but this turns out to be important.
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.
Here is a diagram from Nick Strobel’s fine site Astronomy Notes that will help 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 4 minutes (really 3 m 56 s) 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 this 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.
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 vernal equinox in one year to the next. That’s called a tropical year. 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, 21 minutes or so. If we don’t account for this, then every year the seasons 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, bloggers blaming each other, etc.
So how do you account for it? 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 they’re a smart bunch. They know how to compensate.
Okay, so where were we? Oh yeah– our standard year (also called a Gregorian year) is the tropical year, and it’s made up of 365.24 mean solar days, each of which is 86,400 seconds long, pretty much just as you’ve always been taught. And this way, the vernal equinox always happens on or around March 21 every 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. If you measure the year from perihelion to perihelion (an anomalistic year) 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. It takes 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 346.6 solar days, or 29,947,974 seconds 365.26 days, or 31,558,432 seconds. 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 a 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 PhD research because I was watching an object fade away over several years, and it made life a lot easier.
So there you go. As usual, astronomers have taken a simple concept like "years" and turned it into a horrifying nightmare of nerdy details. 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. They have lots of info, but curiously I found it rather incomplete. I may submit something to them as an update (like how many seconds are in each kind of year; they only list how many days, which is useful but could be better).
I have to add one more bit of geekiness. While researching this entry, 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 beat them with my orrery and astrolabe.
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. They have tons of gory details about this stuff.
Hmmmm, anything else? (counting on fingers) Years, days, seconds, yeah, got those. Nychthemeron, yeah, Gregorian, tropical, anomalistic… oh wait! I know something I forgot to say!
Happy New Year.
December 31st, 2007 at 4:39 pm
Sorry to correct you but time zones were invented by Sanford Fleming. But I am just glad this is nearly over.
http://en.wikipedia.org/wiki/Sandford_Fleming
December 31st, 2007 at 6:07 pm
oops should of said I am glad this year is nearly over. And happy new year.
December 31st, 2007 at 6:11 pm
Will the people who overindulge for the New Year also be considered to be ‘precessing’?
hic
J/P=?
December 31st, 2007 at 6:23 pm
Happy New Year to Bad Astronomy from the Great Orange Satan!
December 31st, 2007 at 6:28 pm
BA, don’t the stars also move, thus making measurements like you describe inaccurate?
Bahhhh! I’m going back to my booze and lampshade after reading this! I’ll just buy a calendar.
Happy New Year!
December 31st, 2007 at 7:27 pm
Just wanted to point out that up here in the nordic countries we have a common, every day word, for a complete cycle of day and night, dygn in Swedish, døgn in Danish and Norwegian, and I seem to recall that there is one in Icelandic and Finnish as well.
This might be cultural bias, but i think that dygn flows a bit better then nychthemeron =)
December 31st, 2007 at 7:40 pm
Happy New
YearArbitrary Orbital Marker, Phil and all you BABers! I really liked the article (both times), but I truly appreciate last year’s article title and am compelled to repeat it here. - g^2December 31st, 2007 at 7:42 pm
Okay for the year and day…so why are there 60 seconds in a minute, 60 minutes in an hour and 24 hours in a nominal day? There’s not a firm astronomical foundation for those divisions. I guess it’s because we have 24 fingers and toes
Let me know if you find historical documentation on those.
December 31st, 2007 at 7:47 pm
Also, check out the 180 degree star swirl that was at Spaceweather.com on 12/30.
Apparently, Polaris is no longer a pole star. It has an arc.
December 31st, 2007 at 8:09 pm
For something a bit tangential… who knows the significance of November 17, 1858? Budding time nerds might find it interesting. The older time nerds already know.
December 31st, 2007 at 8:13 pm
Dave, was that the day Time Zones were invented?
December 31st, 2007 at 8:21 pm
Errrr……. Phil, don’t you mean already 2008 in Australia? We’ve had 2007 already and I’d really prefer to leave it behind and not experience it again.
December 31st, 2007 at 8:24 pm
That was fabulous, BA. Thanks for the time and effort put into that post. Happy New Year! #Should algorithms be forgot, and days be redefined? Should algorithms be forgot? B.A. blew my mind! He blew my mind, oh dear! He blew my little mind! I’ll drink to stellar objects when the B.A. blows my mind!# Tweeeeeeee!
December 31st, 2007 at 8:32 pm
Bill Nettles, its because earlier civilisations used a duodecimal (base 12) and a sexagesimal (base 60) system.
http://www.sciam.com/history-of-science/article/id/experts-time-division-days-hours-minutes/topic_id/11
Happy New Year one and all from the UK and a big thanks Phil for an excellent site.
December 31st, 2007 at 8:35 pm
Hi Michael, alas, it’s a more tangential than that. It is a curious date chosen by the Smithsonian Astrophysical Observatory back in the ’50s to track satellites. I started using it back in my VAX/VMS days and have always enjoyed it as an obscure bit of time trivia.
http://vms.tuwien.ac.at/info/humour/vms-base-time-origin.txt
December 31st, 2007 at 8:56 pm
I should have known that the evil inventor of timezones would be Canadian! What with it being the whore of Babylon and all…
December 31st, 2007 at 9:24 pm
Hey what about dog years? Aren’t they about 4.5 mega-seconds?
The 60 seconds, 60 minutes stuff is generally credited to the Babylonians, but is probably older. 60 has lots of factors and fractions were cutting edge math back then, so anything that made computing a bit easier was worth it.
December 31st, 2007 at 9:30 pm
Yes, it isn’t often that we have a convenient word that english lack but that is one.
Btw, I wonder if it is in any way connected to our habit of using 24 hour clocks, a shorter and less error prone format, instead of the 12 hour AM/PM contrivance that english speaking nations often use? Any speculations on our long summer days and/or the lesser stamina of anglosaxon populations are welcome.
December 31st, 2007 at 11:53 pm
What is your short answer when someone asks you, “Why don’t we have lunch at the same time tomorrow?”
Happy New Year, Phil!
January 1st, 2008 at 12:04 am
Phil, I’d like an answer to GaryK’s question
It’s still just under an hour away for me, but I’ll be AFK, so here it is one last time (maybe):
Happy New Arbitrary Orbital Marker Everyone!!!1One!
g^2, who’s been burning his brain reading about geoids and Draconic months and Metonic cycles - OH MY!!!
January 1st, 2008 at 12:11 am
To all who drop into this site, I wish a very pleasant rotational period of your choosing. I am now enjoying a twelve-year-old Macallan scotch (regardless of how the years were measured, it is one of the better things to begin a new rotational period of indeterminate duration drinking).
To quote my favorite Broadway musical (no, I’m actually quite straight, I have a wife, I just happen to be fond of a certain type of [non-Webber] musical):
“To Life,
To Life,
L’chai’im”
Much love to all,
Autumn
January 1st, 2008 at 12:42 am
Happy New Year!
By the way, ABC aired a “Cloverfield” trailer during their New Year’s show! It was nice seeing it full-sized and unpixelated at last!
January 1st, 2008 at 2:06 am
[…] år egentligen är, vore passande så här på det nya året. Phil på badastronomy har skrivit en artikel om detta, han försöker förklara vad ett år är både fysiskt och […]
January 1st, 2008 at 4:33 am
Happy new Year!!
January 1st, 2008 at 5:48 am
>Just wanted to point out that up here in the nordic countries we have a
>common, every day word, for a complete cycle of day and night, dygn in >Swedish, døgn in Danish and Norwegian, and I seem to recall that there >is one in Icelandic and Finnish as well.
Slavic languages (Russian, Ukrainian, Polish and probably a lot of others) have such a word too. It’s pronounced something like: “sutki”.
January 1st, 2008 at 5:50 am
Oh yes, forgot to add: “sutki” is in Russian, Ukrainian word is “dob” as is the Polish word.
January 1st, 2008 at 7:29 am
Good gosh Gertie, what a post. Happy New Year.
January 1st, 2008 at 7:37 am
That was very interesting. Please explain why we have two high tides every (approx) 24 hours. Very many moons ago Isaac Asamov wrote an article about this. After 40 years, I cannot remember his explanation, though, at the time, it made perfect sense. Anyone out there, please contact me at rob1941@westnet.com.au Cheerio Robbie White
January 1st, 2008 at 8:01 am
Robbie, I think Phil has already explained that: http://www.badastronomy.com/bad/misc/tides.html
January 1st, 2008 at 8:47 am
Happy New Year, BA!
January 1st, 2008 at 9:01 am
[…] New Year 2008! By TonyF Happy New Year! What exactly is a year, anyway? Bad Astronomy has the […]
January 1st, 2008 at 9:15 am
Happy New Year!
Can someone help me untangle my hair from this lampshade please?
January 1st, 2008 at 9:26 am
Also looking for an explanation of how the earliest sunset is about 10 days before winter solstice. I’ve long thought it was due to difference between mean sun and actual sun, but have also heard it’s due to earth’s tilt.
January 1st, 2008 at 9:30 am
Bummer! I blew the joke: “a lesser stamina” of course, to be supported by any speculations.
That’s what posting under the influence of the new years spirit(s) get you. Oh, btw, Happy New Year!
January 1st, 2008 at 10:11 am
So I think I get the year thing.
But what gravitational effect does the collapsing star Dick Clark have on the timing and velocity of that big shiny ball in Times Square?
January 1st, 2008 at 10:11 am
Happy New Year, Phil and all..!
Here’s to your health and BA in ‘08..!
January 1st, 2008 at 11:19 am
All of us must be bleary-eyed. You wrote “as I write this, it’s already 2007 in Australia”
You mean 2008.
Happy New year!
January 1st, 2008 at 12:11 pm
Tressa, I’ll be right over…
January 1st, 2008 at 1:23 pm
For those of you commenting on the “2007″ reference… this is a repost. Just like it says in the title, and in the opening sentence.
Put down the champagne and back slowly away from the computer. You shouldn’t be surfing teh intertubes right now.
January 1st, 2008 at 1:23 pm
Bruce: go to www.analemma.com. That’ll learn ya.
January 1st, 2008 at 2:15 pm
A wonderful, informative post! With your permission I plan to use it in my Physics and Earth Science classes!
Happy New Arbitrary Orbital Marker!
Jim
January 1st, 2008 at 5:20 pm
Congratulations. You made my brain hurt.
January 1st, 2008 at 7:41 pm
Indeed. For the still bleary-eyed, at the top of the entry, Phil also said
So it was truly 2007 in Australia when he wrote it, a year ago.
A happy, healthy, and productive New Year to all!
MJ, who is still recovering the use of her legs after First Night
January 1st, 2008 at 7:42 pm
Drat, that’s what I get for taking a nap, and the replying without refreshing the page for updates.
And I didn’t even get any champagne!
MJ
January 1st, 2008 at 11:07 pm
[…] Read the article. I hope that you enjoy his blog, I know that I […]
January 2nd, 2008 at 1:48 am
[…] It rotates more than 360 degrees for each of our days. So what is then a year? Phil Plait explains it with pictures. […]
January 2nd, 2008 at 8:33 am
Robbie White writes:
[[Please explain why we have two high tides every (approx) 24 hours. Very many moons ago Isaac Asamov wrote an article about this. After 40 years, I cannot remember his explanation, though, at the time, it made perfect sense. ]]
Gravity works by an inverse square law. The ocean just under the moon is pulled a little more strongly than the Earth under the ocean, and the Earth is pulled a little more strongly than the ocean on the side opposite the Moon, so you get two tidal bulges rather than one. And, if I remember correctly, it’s every 25 hours rather than every 24, isn’ it? Dr. Plait, am I remembering that wrong?
January 2nd, 2008 at 1:27 pm
Dear Phil:
Your assertion, “The Earth orbits the Sun in an ellipse, remember.”,
is NOT strictly correct, for, the trajectory is much more complex than
that of an ellipse, I believe!
January 2nd, 2008 at 2:35 pm
Barton Paul Levenson wrote:
And, if I remember correctly, it’s every 25 hours rather than every 24, isn’ it?
Assume you remember it correctly. Since the earth rotates in the same direction as the Moon orbits the Earth, this would mean that the Moon advances on its orbit equivalent to one hour in one day, as seen from the Earth. Consequently, the Moon would orbit the Earth in 24 days, which would be the time interval between, say, two full moons. This estimate is already pretty close to the observed time interval of about 27 days.
We can make a further refinement by taking into account the orbital motion of the Earth around the Sun, which affects the full moons, because during the full moon the Sun, the Earth and the Moon are aligned along a straight line. We can multiply our estimate by (1+1/12) and end up with 26 days, which is closer still.
This calculation is rather crude (there are more than 12 full moons a year), but seems to support the idea that the tides should occur twice in about 25 hours rather than twice in 24 hours.
Regards
Eric
January 5th, 2008 at 12:01 pm
[…] What is a year, anyway? […]
January 17th, 2008 at 11:38 pm
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