Happy New Year Arbitrary Orbital Marker!

By Phil Plait | December 31, 2006 11:53 am

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.

CATEGORIZED UNDER: Astronomy, Cool stuff, Humor, Science, Time Sink

Comments (61)

  1. I’m going to spend the next few hours processing all that, and then I’m going to go out and destroy every brain cell still in operation. It’ll be interesting to see what I recall tomorrow.

    Happy New Year, Sugarbaby!

  2. Max Fagin

    I am sick and tired of all this insistence that humans conform to the time intervals the universe sets for us!

    To correct this problem, I am announcing the formation of a new kind of year. All citizens of the Earth must adopt this standard or be executed at once.

    It’s called the Broadway year:

    Five hundred twenty-five thousand six hundred minutes. THAT is how we measure a year! :)

    Happy New Year everyone!

  3. This new year thing sounds vaguely pagan to me. :P But happy new year!

  4. J. D. Mack

    OK, Phil. Now tell us why this is year 2007 ; ).

    J. D.

  5. james

    Hi BA, on a better day I would have already edited your entry out of recognition ( to placate the gods of plagarism ) and have updated wikipedia to conform to your praiseworty high standards. However I have to be back at work in 62 minutes . do you mind tracts of your blog being lifted verbatim? Cos if not, then someone else might have that sorted by the next time I log on. Anyway, back to the salt mines, 4 hours to go here in Greenwitch mean ( or Real Time as we citizens of the empire like to call it ), Glasgow’s town centre celebrations have been shut down by some of the worst storms since LAST new year, gusting 70mph, and I’m going to cycle back to work in a kilt! Slainte Mhath, and happy Hogmanay!

  6. So, just like with astrology, I can blame the stars for any bad year I have? I can’t wait to throw that in my tarot cards face. Boo-yah! (Coincidentally, iTunes is playing “Don’t Ask My Why” by Billy Joel and the line “Now your calendar’s complete” was just sung. The stars again?)

    I’m kidding, of course — about astrology not about Billy Joel. That actually happened.

    This is a most excellent post and will be including a link to it in my New Year’s Post. It’s amazing that people forget that space, like water, is 3 dimensional (another simplification) and adds all sorts of weirdness to measurements, so basically we’d need to be merpeople to understand what you’ve just said.

    To Max: What happens when the year flops? We close it down after three weeks and have a new year? That’s cool with me. More days off!

    Happy New Year, Phil.

  7. Geoff

    That was very well done. You must have done a great job because I understood most of that so much my head is spinning.

    Happy New Year Phil!

    Thanks for a great blog. It makes my day.

  8. frogmarch

    so there are 364 sidereal days in a solar year?
    1 less because of the 1 orbit?

  9. frogmarch

    no! I got that wrong, there must be 1 more ie 366?

  10. Hey! Snap! I blogged about this (in a far less mathematical, and far shorter more rantier way). And now I can throw in a link to you to explain it all! :)

    http://jamasenright.blogspot.com/2007/01/12-months-later.html

  11. Time Sink – NO KIDDING! However, this was an excellent way to spend a little time regardless of the hour, day, or year of any kind. One question, though: isn’t rounding a siderial year to PI*10^7 a little rough? That’s more than 1.5 nychthemerons off! Gotta run, now – Phil’s comin’ with the astrolabe. . . – g^2

  12. That is absolutely fascinating. I’ve always taken the concept of the year as immutable, even given all those extra seconds we keep getting given.

    Which just goes to show how gullible I really am.

  13. Gary Ansorge

    Wow! You have an orrery? Is it old(’cause I’m beginning to get used to
    old,hee,hee,,,)

    Happy new year, Phil. May you knock the socks off the anti-science crowd in 2007.

    Wow I had no idea there were so many ways to measure our year. Wonder how that messes with the astrologers???

    Hey, I’m a physics oriented guy, in which mass is in gm/kg, sec are X number of cesium good vibes and 1.88 meters is about how tall I am,,,like, constants, man,,,

    Peace,

    GAry 7

  14. Cindy

    So, Phil, are you ever going to blog about the arbitrary setting of the Julian date?

    Happy New Year!

  15. MKR

    Conveying intensely technical things in an easy to read manner is quite rough, and you’ve done a commendable job. I was able to understand all of that. :P

  16. Brett

    I can picture a prog rock band using the name ‘Nychthemeron’.

  17. British Julian/Gregorian Calendar for 1752 AD

    11 days omitted in September – page/scroll down for more details.

    January February March
    S M T W T F S S M T W T F S S M T W T F S
    1 2 3 4 1 1 2 3 4 5 6 7
    5 6 7 8 9 10 11 2 3 4 5 6 7 8 8 9 10 11 12 13 14
    12 13 14 15 16 17 18 9 10 11 12 13 14 15 15 16 17 18 19 20 21
    19 20 21 22 23 24 25 16 17 18 19 20 21 22 22 23 24 25 26 27 28
    26 27 28 29 30 31 23 24 25 26 27 28 29 29 30 31

    April May June
    S M T W T F S S M T W T F S S M T W T F S
    1 2 3 4 1 2 1 2 3 4 5 6
    5 6 7 8 9 10 11 3 4 5 6 7 8 9 7 8 9 10 11 12 13
    12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20
    19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27
    26 27 28 29 30 24 25 26 27 28 29 30 28 29 30
    31

    July August September
    S M T W T F S S M T W T F S S M T W T F S
    1 2 3 4 1 1 2 14 15 16
    5 6 7 8 9 10 11 2 3 4 5 6 7 8 17 18 19 20 21 22 23
    12 13 14 15 16 17 18 9 10 11 12 13 14 15 24 25 26 27 28 29 30
    19 20 21 22 23 24 25 16 17 18 19 20 21 22
    26 27 28 29 30 31 23 24 25 26 27 28 29
    30 31

    October November December
    S M T W T F S S M T W T F S S M T W T F S
    1 2 3 4 5 6 7 1 2 3 4 1 2
    8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9
    15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16
    22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23
    29 30 31 26 27 28 29 30 24 25 26 27 28 29 30
    31

    In 1752,Great Britain and its colonies moved to the Gregorian calendar
    with the omission of 11 days in the month of September, as shown in
    the calendar above. 1752 was also the first year in Great Britain
    in which the year began on January 1 rather than on March 25, as in
    previous years. As a result, 1751 in Great Britain was even shorter
    than 1752, since it ran from March 25 to December 31.

    Phil——this readjustment in time must always be a part of the calandar equation

  18. I do believe you have the anomalistic and eclipse years confused (too much early celebrating i presume). The anomalistic years is 365.259 days, and is why perihelion seems always to occur on the first few days of January. The eclipse year, the time between successive passages of the ascending node of the moon’s orbit, is why eclipses slide slowly backwards from year to year.

    It’s a great blog. Happy New Year.

  19. Grand Lunar

    I heard of the differences between sidereal time and solar time.
    I didn’t know of the differences with the rest of the stuff mention, Phil! Thanks for the lesson.

    Well, time waits for no one (unless you’re a Time Lord), so I shall enjoy the rest of 2006 any way I can. Well, almost any way.

    Have a happy new year, everyone!

  20. Glad to learn of the word ‘nychthemeron’ – I had long thought it strange that English lacked a word for a full 24-hour period, when the other languages I speak all have a (commonplace) word for that.

    Of course, I should’ve known better – it’d be hard to beat English for breadth of vocabulary. You’re exactly right, though, that this particular word is unlikely to see much use, verbally at least :-)

  21. slang

    I’m way too drunk to grok all that now.. but i got the important part! HAPPY NEW YEAR!

  22. MrEphemeris, you’re right– I cut and pasted the wrong number. I fixed it, thanks!

  23. spacewriter

    Whew!

    what an intricate way to say “Happy New Year!”

    ;)

  24. Happy New Arbitrary Orbital Marker, Phil! I was going to blog about this very topic, but you did such a good job, I figured I’d do something else about the New Year.

  25. This is the first time I’ve properly understood the tropical year–thanks!

  26. chemdude

    All that being said, a new year by any other term is just as sweet (to parapharse an old dead guy).

    Happy New Year everyone!!!

  27. Squatch

    I should have read this way earlier in the evening. I’ll have to read it again tomorrow afternoon.
    Thanks for doing all of this thinking for us Phil.

    And, Happy New Year!

  28. Well, having read all that (at least what my poor brain had courage to let me read after the new year party), happy new year anyway!

  29. so put down the champagne, take the lampshade off your head, and hang on.

    But if I take the lampshade off my head, I’ll be naked! We wouldn’t want that now, would we?

    oh.

    iguesswewouldwouldn’twe?

    OK, sans lampshade now!

    I think I’m guilty of T.U.I. (typing under the influence) but just a little. (so far)
    (hey, what’s the legal limit on that?)

    Anyways, I’d just like to thank you all for throwing such a nice big party for my birthday.

    THANK YOU WORLD! It’s aweful sweet for all of you to mark your calandars from Kate’s birthday to Kate’s birthday.

    :)

  30. Great posting. Great job this year. Squid Cats aside, this is my favorite blog on the web.

    Keep up the good job and thanks for all the great stuff I’ve learned this year.

    Happy New Year

  31. Dan

    The grgorian year is not quit the same as the tropical.

    The topical year is 365.242191 days.
    The Gregorian (ie calendar) year averages 365.2424 days.

    (ps I’ve been getting a bunch of SQL errors here….)

  32. Happy New year 2007 :)

    mark_smith

  33. Paul Clapham

    Perihelion? What is it that actually makes its closest point to the Sun at that moment? Is it the centre of the Earth, or is it the centroid of the Earth-Moon system which is actually doing the revolving around the Sun?

  34. Me

    “time zones. These were invented by a sadistic watchmaker, who only wanted to keep people in thrall of his devious plans” – Sir Sandford Fleming, a rail road engineer actually.

  35. You may be interested in the puzzle I posted on my page:

    Short version: which day of the week is New Years most likely to fall on?

  36. ABR

    Sorry for the cross-comment, but the Comments appear to be closed next door in Rats! This bioBABloggee will suggest that you may have a tarsometatarsus (kind of an expanded metatarsal or lower, lower leg) from a bird, rather than a leg bone from a rat.

  37. Randall

    Wasn’t the Gregorian year exactly 365.2425 days long, on average? Was 365.24 just rounding down?

  38. ABR, I screwed up and had commenting turned off (but then how could you comment here? WordPress freaks me out sometimes). Anyway, a bird does seem likely; we have plenty in the area.

  39. Every so often, I come across a Biblical apologist who has calculated that Jesus will return Real Soon Now because it’s almost X thousand years/days/weeks since some event (e.g., 2000 years since the crucifixion of Jesu). The unstated assumption is usually that the “thousands” part is significant because God has a fondness for round numbers in base 10.

    Presumably that’s why there are exactly 10 planets in the solar system, exactly 100 naturally-occurring elements, 10 lunar revolutions in a year, 300 days (sidereal, solar, or whichever you like) in a year, and so forth.

  40. Dr. Plait, just curious: in your “Rats!” post, you invited the opinions of your readers, but have closed the post to comments-is this because of the server problems or something else?

  41. shoeshine boy

    Forget all the fancy calculations, the new year starts when the ball at One Times Square slides down the flagpole. After all, New York City is the center of the universe. (Just ask any New Yorker.)

    http://www.timessquarenyc.org/nye/nye_ball.html

  42. Steve

    Happy New Year, whenever it was or will be.

  43. Gary Ansorge wrote: Wow I had no idea there were so many ways to measure our year. Wonder how that messes with the astrologers???

    Most western astrologers use the Tropical zodiac. Since this was first defined in approximately 220 BC, the astrological signs are now about a month off. (For example, I was born on 2 October which would make me a Libra, but at that date the Sun was actually in Virgo.) They should really use the Sidereal zodiac.

    Not that it makes any difference, of course – they’d just be replacing one arbitrarily set of made-up rules with another arbitrarily set of made-up rules. Astrology is crap either way. It’s amusing to see how they try to justify it though.

  44. Irishman

    Hey, what is all this astronomy in my political/humor/rant blog? No fair! ;-)

    J. D. Mack said:
    > OK, Phil. Now tell us why this is year 2007 ; ).

    Because someone (Bishop Usher?) assigned year 1 to some arbitrary point in time and we’ve been adding consecutively since.

    Happy Birthday, Kate! I’d get naked with you, but text somehow doesn’t convey the same amusement factor.

  45. DennyMo

    As was pointed out, the time zones were invented by/for the railroads, not sadistic watchmakers. ;) But I have a grammar question: is it pronounced “side-real” or “cy-deer-ee-uhl” or something else?

  46. Nychthemeron! Excellent. Russian has “day” “night” and “24-hour-cycle” (den, noch, and sutki), and I felt that English had a lack. Now I can tell my students to translate “sutki” as “nychthemeron” … Well, possibly not. ;-)

    While pronunciation isn’t, strictly speaking, grammar, it’s sy-DEER-ee-ul, except the syllable break is between the de- and the -ree.

  47. DennyMo

    Thanks for the clarification, and the correction on my “diction”… ;)

  48. sirjonsnow

    I remember you clarifying a sidereal day to me in email a few years ago! I was bored at work or something when it popped into my head that if a day was exactly 24 hours, then half a year later midnight/noon would be mixed up – so I emailed you. To this day I still have no idea why my mind wandered to that.

    But anyway, still love the blog!

  49. suturself

    ok, now I know there is an explanation, and can almost understand.

    “A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.” – George Bernard Shaw. What happens when you do nothing but make mistakes?

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