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Should there be a mention that on other planets the year is different? --Daniel C. Boyer

It does seem to now: perhaps editted since your undated comment? As it looks out of date, lets agree if you do not repeat it within a month of this query I'll do a clean-up (talk)--BozMo 22:25, 9 May 2004 (UTC)

the same is here: :P

Can some physics guru out there calculate the shorting of the year due to the mass loss of the sun over time. Because the rate is so gradual I do not expect there to be non equillibrium effects. Assuming a circular orbit, the radial orbit change(accelleration) should be able to be calculated from a force balance of the centripetal and gravitational forces. This radial change will give a new period since the kenetic and potential energy is related in orbital mechanics. I'm currious about the change in the period over time, since it has implications on the age of the earth, and the rate of energy output of the sun.

This also has an impact on the alinement of planets the ancients saw when the looked up at the sky. Does anyone know if celestia takes this into account when calculating historical star chart data?

Block Request for Admins[edit] was trolling this page (length of a year changed in all instances to aprox 100 days) and when I checked his edit log, all edits were vandalism, as such I request that this user is blocked by an Admin —Preceding unsigned comment added by (talk) 21:47, 10 January 2009 (UTC)

Seasonal Year edit[edit]

I removed "the hottest day of the year" as an example starting point for a seasonal year because it is not a definite/conclusive starting point in that there could always be a unexpected hotter day later on. All the other given examples have definite starting points, for instance when flowers start to bloom, you know that's the start of that flowers "season". I also added "the first scheduled game of a certain sport" to throw in a man-made seasonal year example into the mix. Comments?

The "hottest day of the year" would be a great idea--but only if it were done in a talk page which shows the date and exact time. The only problem then would be that you would not know "where" this "hottest day of the year" was located. Too bad that in the talk pages it doesn't show the "exact location" of where it was "reported" from as well as the time. —Preceding unsigned comment added by (talk) 20:21, 16 November 2010 (UTC)

Astronomical Year section reformatting[edit]

I added bullets to the listings of the astronomical years because I think it looks better in general and breaks up the different types for easier reading. I don't know if doing this is within Wiki-policy, anyone care to comment or take a vote on it?

Calendar repetition[edit]

I think it would be nice to have information regarding calendar repetition, that is, is there a way to tell when is this year's calendar going to be repeated? For example, 2005 is a Common year starting on Saturday. When in the future will the 2005 calendar be repeated, like August 12 will be friday and all other days will be the same week day as in 2005? When in the past was it repeated like that?

I've never heard of any such calculations, just wondering if anybody has.

For a common year, step forward a year at a time, counting one for each common year passed and two for each leap year, until you reach a common year at a count which is a multiple of 7. That will be 6 or 11 or 12 years ahead.
For a leap year, step forward four years at a time, counting one for each common year passed and two for each leap year, until you reach a count which is a multiple of 7 at a leap year. That will be 12 or 28 or 40 years ahead. Note that a leap year with its following three common years counts as -1, and four consecutive common years (xx00-xx03) count as 4.
If and only if no missing leap year would be passed, a leap year repeats after 28 years.
Check those. Page section demonstrates the repeat intervals. (talk) 18:48, 9 May 2011 (UTC)
You cite a wikipage that already lists the years that have identical calendars, so I gather you don't just want to know what years are identical, but how to determine them by calculation. Unfortunately, I don't know of any such calculation. I can only mention that whatever the repetitions are, they must repeat on a 400-year cycle. — Joe Kress 18:54, August 12, 2005 (UTC)
All solar calendars with a leap year every four year and a 7-day-week repeat in principle every 28 years (=4x7). But a additional leap year interrupts this so-called solar cycle. Thus Gregorian calendar years 1801, 1829, 1857, 1885 began with a Thursday, like 1901, 1929, 1957, 1985 with a Tuesday. There are exactly 20871 weeks in a Gregorian 400 years cycle, so it well repeats after each full cycle. All in all, there exist only 14 calendars. 7 for common years, 7 for leap years.
--Peter 2005 12:51, 14 August 2005 (UTC)
To find out when the next Gregorian calendar year occurs that is identical to the current one, you need to know the number of the current year (e.g., 2008). Calculate three quantities: the remainder after dividing by 4 (call it Q), the remainder after dividing by 100 (call it C), and the remainder after dividing by 400 (call it M).
For all the years from 1901 to 2071, all you need to know is Q.
  • If Q equals 0, the next identical calendar is in 28 years.
  • If Q equals 1, the next is in 6 years.
  • If Q equals 2 or 3, the next is in 11 years.
The above also holds for all years where M is greater than 300 or equal to zero. It holds for most other years as well, the only exceptions being:
  • If C is greater than 71 and Q equals zero, then the next is in 40 years.
  • If C is equal to 90, 91, 97, or 98, the next is in 12 years.
  • If C is equal to 94, 95, 99, or zero, the next is in 6 years.
Rwflammang (talk) 18:41, 28 October 2008 (UTC)

The Gregorian calendar includes lunar as well as solar aspects (although the lunar aspects are usually only used for religious purposes). I doubt Rwflammang's technique finds the next year that is identical in both the solar and lunar sense. --Gerry Ashton (talk) 18:56, 28 October 2008 (UTC)

It certainly does not. It simply finds the next time one of the 14 calendars mentioned by Peter 2005 is repeated, which is all that was asked for. Rwflammang (talk) 14:43, 29 October 2008 (UTC)

Oriental great year[edit]

The following statement was added to the article by I have moved it here because I have never heard of it even with my fairly extensive knowledge of Chinese astronomy and Creation myths, and no citation is given. It is doubtful that it is the source of the Western 24-hour day because the Chinese used a clock with twelve double hours, not one with 24 hours. The standard explanation for the Western 24-hour clock is that the Egyptians used 24 seasonal hours (12 daylignt and 12 nighttime).

Oriental astronomy puts the length of one Great Year at 24,000 years comprised of one ascending cycle of 12,000 years and one descending cycle of 12,000 years. Some scholars believe this may be the original basis for the current system of daily time; a 24 hour day with 12 hours of increasing light (AM) and 12 hours of increasing darkness (PM).

A citation is needed before it can be added to the article. Don't use the weasal words "some scholars". Cite which scholar or scholars.

Joe Kress 01:00, 22 November 2006 (UTC)


Why is gigayear redirected here if theres nothing about it? —The preceding unsigned comment was added by (talk) 11:19, 12 January 2007 (UTC).

Likely because a gigayear is just 10E9 years and is no more special than 2 years, 3 years or even one year. —Preceding unsigned comment added by (talk) 14:50, 30 October 2009 (UTC)
A year consists in 365.25 days of 86400 seconds = 31,557,600 seconds, which equals 10E^7.499104 seconds. So a gigayear sounds like a long time, but when you convert it you get 10E^16.499104 seconds or say 10E^16.5 seconds, which doesn't sound near as bad.WFPM (talk) 23:05, 5 March 2012 (UTC)

Re Gaussian Year[edit]

The present Wiki section on "Gaussian Year" is not adequate (the length is a result; it is not the definition).

I think it needs a "1 A.U." or equivalent, and a reference to the Sidereal Year.

The definition in should be reliable. 12:08, 29 January 2007 (UTC)

TP: I don't see anything factually wrong in that section; you are correct that the year length is a derived value, but this page does not imply otherwise. What exactly do you object against? —The preceding unsigned comment was added by Tom Peters (talkcontribs) 21:33, 29 January 2007 (UTC).

OK, I now see that, while the (Newtonian) gravitational constant G is a constant of the universe, the Gaussian constant is parochial and is governed by the orbit that the Earth happens to have - it could be called the Earth's Gaussian Gravitational Constant.

I still prefer the Kaye&Laby statement as a description of the Gaussian Year, but it is less direct as a definition.

I think that more people will be familiar with SI units than with Astronomers' units.

In "Calendar year", the day is the (mean) solar day, defined by light-and-dark, of 86400-plus-a-bit SI seconds (the bit represents leap seconds). The Julian Year apparently uses the same unit. The Sidereal Year is given explicitly in SI seconds.

The Gaussian Year, however, being dependent solely on the Gaussian constant which is a fixed value not dependent on SI, seems at first to be in astronomers' units; but Kaye & Laby says that astronomers' seconds are SI seconds.

So : in the Year page, I now think that, for the avoidance of doubt, it would be well :-

  1. to mark every expressed duration as "mean solar days" or "SI days" or whatever it happens to be;
  2. to mark all exact values with "exactly" or similar, and all approximate values with a numerical uncertainty or with "approximately" or similar (the Gaussian year could be put as "exactly 2π/k"). 13:19, 30 January 2007 (UTC)

Draconic years instead of 365 day year[edit]

Much better solution would be adopting septenary 343-day year derived from draconic year defined here: because it has nothing to do with satanic 6*6*10, and is defined as God's 7 days *7 weeks *7 seasons. God purposedly instituted draconic year in Solar System to give chance of avoiding satanic multiples in time measurements. 10:24, 15 March 2007 (UTC)

A "solution" implies a problem or purpose. If the purpose is to appease the religious nutjobs, I guess 343 has its uses (until someone comes along who says 343 is satanic); if the purpose is to keep track of the seasons, better to stick with the tropical year God gave us. If God wanted us to use 343-day years, why establish a 346-day cycle and make it so far from obvious? —Tamfang 05:35, 3 April 2007 (UTC)
A comprehensive proof of evilness of these unholy numbers such as 6,60,90,180,270,360,666,3600,6666, which refuses to be completed up to multiples of holy seven is placed here: [1] Thus better use purely septenary system. Both draconitic and tropical year are not ideal 360 and 343 days, but their approximations such as 365.24218967 and 346.620075883 days. That proves that God provided us possibility of choosing between blessing and curse (Deuteronomy 30:19), namely between God's 343-day septenary year and between devil's 360-day sexagesimal year. 346 excess above 343 by 3 days, and 365 excess above 360 by 5 days, making draconic year closer to God's 7*7*7=343, than tropical year to devil's 6*6*10=360. More about full septimalization of all units here: [2] Only pharisee can apply satanic etiquette to God's 7*7*7=343. 08:21, 10 April 2007 (UTC)
Are honeybees satanic too, with their hexagonal cells? —Tamfang 21:51, 3 May 2007 (UTC)
I see that some prefer 7, so I'll chime in with a fact that might be found a little more appealing as regards the current system (and previous Julian): (365+1/4)^4=17797577732+7^2/2^8. This has a simpler relative you may like less (but there is a seventh power): (365+1/4)^2=3^7*61+9/16.Julzes (talk) 06:45, 26 May 2009 (UTC)
Honeybees are domestified wasps, and all dangerous animals came after original sin. Before original sin they yet didn't existed. 07:52, 23 May 2007 (UTC)
Doesn't God essentially run a Dictatorship? T'was apparently the deveil who gave humans freedom of thought.... Anyway 666 isn't really the Devil's number. Pwnd. -- (talk) 11:36, 23 June 2010 (UTC)


The article states that the Julian calender has 365.25 days per year but something is not right. How can there be 52 weeks in a year times seven days a week which equals 364 days? Is it safe to conclude that there are really weeks in a year, but we just round down to make it an even number ? —Preceding unsigned comment added by (talk) 06:47, 18 February 2008 (UTC)

Anyone who states that there are 52 weeks in a year is not being precise. The Julian year has either 365 or 366 days thus 52 weeks and either one or two extra days beyond that number of whole weeks. But these two values mean that a single value for the number of weeks in a year ( is possible only as an average value. — Joe Kress (talk) 08:33, 19 February 2008 (UTC)

orbital chaos[edit]

The Earth orbit varies by a chaotic way, but in a interval quite more reduiced than the orbits of the nearest planets.

What does this mean? —Tamfang (talk) 06:26, 20 May 2008 (UTC)

Can you please tell us where in the article that text is? Karl (talk) 10:24, 20 May 2008 (UTC)
Search the article for the word 'chaotic': it's in Year#Variation_in_the_length_of_the_year_and_the_day. —Tamfang (talk) 22:51, 23 May 2008 (UTC)

Merge from Annum[edit]

It seems to me that Annum is just a scientific synonym of "year", and therefore Annum should just redirect here, with any of its salvageable content moved here. The current article reads to me like original research, or at least an original synthesis, and the listed references don't really support the main body of the article.--Aervanath lives in the Orphanage 04:31, 11 July 2008 (UTC)

The listed refs went through a revision process, so the links were broken when ISO 31-1:1992 was replaced by ISO 80000-3:2006 recently. I haven't yet had a chance to review the new issues. Likewise the implementing NIST pub was revised in 2008. The merge may be a good idea, we'll have to give it some consideration. But simply replacing the page with a redirect didn't cut it. LeadSongDog (talk) 05:53, 11 July 2008 (UTC)
Fair enough. The BOLD, revert, discuss cycle is working well in this case. But you haven't yet addressed my concerns about OR and SYN.--Aervanath lives in the Orphanage 22:25, 11 July 2008 (UTC)
The existing Year is completely unreferenced. The existing Annum is a little better, though admittedly not much. I'm fairly confident the bulk of either can be supported in available refs. Were there specific statements that you see as OR or as SYN? If so, don't hesitate to tag the cases that trouble you most.LeadSongDog (talk) 06:11, 14 July 2008 (UTC)

I subscibe the proposed merge of this page with the page for the Year. SAE1962 (talk) 11:39, 12 December 2008 (UTC)

It is 2010 and the tag is still in place. I'm lifting it for lack of sufficient interest to pursue combined with a view that there is scientific usage for annum in geology and other fields. Cheers - Williamborg (Bill) 03:44, 6 January 2010 (UTC)

Too technical too quickly[edit]

I read this article with a hope to better understand what's happening astronomically that causes what we experience as seasonal variation. I soon got bogged down in too many similar-sounding definitions of a year and links to other articles (like the one on precession) which also failed to make things any clearer.

It seems to me that the historically first and lay definition of the year involves this cyclic change of climate. It would seem natural to lead into the article with a discussion of this definition of a year, so that readers are grounded in something they find familiar. I'm sure there's an astronomical correlate of this "year of the seasons" I'm talking about, although from the article I can't tell what it is (probably the tropical or sidereal year). This should be the first concept to be introduced and other definitions of a year should follow from there.

I think that would make the article far more useful, particularly to people with no background in astronomy. I hope this suggestion helps.

Ben Arnold (talk) 10:28, 17 May 2009 (UTC)

Yes, the cycle of seasons is the tropical year. —Tamfang (talk) 02:15, 18 May 2009 (UTC)

Question on being Reverted[edit]

I tried adding "The experienced average approximate year is 365.25 days." before the fact that 400 Gregorian years make an integral number of weeks near the end of the article. It was as a remark that we all happen to live near the year 2000 intended with humor in the way I assume all of the overly specific counting is. Should I undo?Julzes (talk) 06:03, 26 May 2009 (UTC)

I don't think the goal here should be humor, especially of the kind that isn't humorous. Ilkali (talk) 08:55, 26 May 2009 (UTC)
Are you saying "in the experience of people living between 1900 Mar 1 and 2100 Feb 28, the average year-length is 365.25"? With a bit of effort I can see some humor in that, but not enough to justify going out of one's way to mention it in the article. —Tamfang (talk) 23:45, 27 May 2009 (UTC)
That was a part of it.Julzes (talk) 06:17, 29 May 2009 (UTC)

365.242199 days in a year[edit]

I'm surprised there is no mention on the page, the universally accepted estimate of the number of days in a year. The article should at least mention it somewhere, does anyone else second that? --Thelazyleo (talk) 22:18, 2 August 2009 (UTC)

There are many kinds of years. What kind of year is 365.242199 days and what reliable source says this estimate is universally accepted? --Jc3s5h (talk) 22:23, 2 August 2009 (UTC)
The mean tropical year according to Simon Newcomb was 365.24219879 days at J1900.0. Needless to say, the approximation 365.242199 days is quite old. The J2000.0 value of the mean tropical year is already in the article alongside values for the sidereal, anomalistic, and draconic years. — Joe Kress (talk) 05:37, 3 August 2009 (UTC)

365.44 days[edit]

I was recently informed that some authorities assert that one year is 365.44 day, instead of 365.25. I did a quick Google search on the two terms but was unable to find any intelligible information corroborating or even elaborating on this assertion. If anyone knows something about this, please provide information. __meco (talk) 12:42, 14 August 2009 (UTC)

Sounds like bogus to me. The only lengths of a tropical year I have heard of are the refinements of the original Julian year length -- i.e. close to (and never larger than) 365.25 days (whatever a day is). —Preceding unsigned comment added by (talk) 14:58, 30 October 2009 (UTC)

Rough calculations[edit] recently added a section on rough calculations, with the justification that the calculations could be done mentally. However, the calculations involved raising a number to the 7.5 power. Very few people can do that mentally. Therefore I removed the new section. --Jc3s5h (talk) 15:10, 18 January 2010 (UTC)

Platonic year[edit]

I have removed the term "Platonic year" because no source was cited for it and the sources I can find do not agree with each other. The most plausible source I found so far is but that does not have the feel of a truly authoritative source in my mind. Jc3s5h (talk) 13:08, 9 April 2011 (UTC)

Start of year[edit]

I suggest a mention of the starting dates for Gregorian and Julian year numbers. In England before 1752, the numbering changed in March. (talk) 13:13, 8 May 2011 (UTC)

This article covers too many years, including many that do not even have dates, to warrant such a minor historical detail for a specific calendar. See Julian calendar#New Year's Day and Gregorian calendar#Beginning of the year for dates other than 1 January and 25 March on which the Julian calendar began. — Joe Kress (talk) 22:54, 8 May 2011 (UTC)

Duration of sidereal year[edit]

I just made a check using JPL planetary ephemeris:

  • The Earth was at its pericenter MJD 2.22129411, i.e. 2000/01/03 05:18:39 ephemeris time
  • The Earth was back to the same angle relative ICRS at MJD 367.47518921 ephemeris time

This "sidereal year" was therefore precisely 365.2538951 SI days or 365 days 6 hours 5 minutes 36.5 seconds

In the text it is said that the average value for a "sidereal year" is 365 days 6 hours 9 minutes 9.7676 seconds

Quite a deviation! Anyway, very misleading to give the seconds with 4 decimals!

Stamcose (talk) 16:12, 11 June 2011 (UTC)

I repeated exactly the same computations for the sidereal year 10 years later, i.e for 2010. This sidereal year was 365 days 6 hours 8 minutes 28 seconds.

They do vary, seconds or even fraction of seconds make no sense!

Stamcose (talk) 16:33, 11 June 2011 (UTC)

I have edited the article to limit the precision to hundredths of a second, which matches the source that was used in the main article for that section, Sidereal year. Your calculation does not agree because it is for a specific year, not a mean sidereal year, and because the sidereal year is relative to the mean northern vernal equinox of J2000 while the ICRS is relative to an origin based on long baseline interferometry of distant galaxies. Jc3s5h (talk) 17:39, 11 June 2011 (UTC)

I made a more complete analysis using the JPL ephemeris covering 15 years:

The mean tropical year is 365.242 UTC days, the yearly variations in the order of +- 20 minutes The mean sidereal year is 365.255 UTC days, the yearly variations again (obviously same as above!) +- 20 minutes

The article clearly states that the sidereal year is counted relative the celestial sphere (distant stars/galaxis, i.e. ICRS as used for the JPL ephemeris!) while the tropical year is with respect to the vernal equinox. For this I used the standard precession model to find the momentary position of the vernal equinox in the ecliptic plane which is different for different years (relative ICRS)!

What is the source for your article? I would like to (critically!) examine its contents!

Stamcose (talk) 18:52, 11 June 2011 (UTC)

Here are the results of my computations:

This is the part of the JPL ephemeris I have handy! (1999 - 2026)

Times are in ephemeris time deviating from UTC with about a minute (depending on leap seconds!)

Stamcose (talk) 19:21, 11 June 2011 (UTC)

I don't understand what your are getting at, or where your comments are leading.
As for your question "What is the source for your article?", are you addressing this to Wikipedia editors in general? The sources are documented in the article, to some degree. Any other sources not documented in the article are unknown. If the question is addressed to me, I never wrote an article about the year; I just made a few small changes to this article.
By the way, the results of your computations are not suitable for inclusion in the Wikipedia article (see WP:NOR, but asking questions on this talk page is just fine. Jc3s5h (talk) 20:22, 11 June 2011 (UTC)
The sidereal and tropical years were calculated via an analytical solution of Newton's universal theory of gravitation applied simultaneously to all planets performed by the Observatory of Paris called VSOP. The result is the position of all those planets in the form of a mean position polynomial plus thousands of sinusoidal terms yielding an accuracy of about a milliarcsecond. Considering only Earth, if we ignore all sinusoidal terms and take the derivative of its mean longitude poynomial we obtain both the sidereal year (relative to the fixed equinox J2000.0, equivalent to a fixed star) and the tropical year (relative to the equinox of date, that is, the precessing equinox). The mean positions were revised by Simon et al. in 1994 which is referenced by the IERS Useful Constants. On page 675 of Simon is the mean longitude of Earth λ refered to the mean dynamical ecliptic and equinox J2000, where t is the number of Julian millennia each containing 365250 days. The coefficient of t is 1295977422.83429"/Julian millennia. Calculating
(1296000" × 365250 days/Julian millennia) / (1295977422.83429"/Julian millennia)
gives the IERS value for the mean sidereal year, 365.256363004 days. Similarly on page 678 calculating
(1296000" × 365250 days/Julian millennia) / (1296027711.03429"/Julian millennia)
gives the IERS value for the mean tropical year, 365.242190402 days. — Joe Kress (talk) 07:09, 12 June 2011 (UTC)

Using the JPL planetary ephemerisis I computed the averages from mid-winter 1998/1999 to mid-winter 2037/2038

Mid-winter is defined as the epoch when the Earth passes the projection of the Earth axis (computed using standard precession matrix) on the osculating orbital (ecliptic) plane. 39 mid-winter to mid-winter years took in total 14244.4553 SI days => average tropical year 365.2424 SI days. In the article the value given is 365.24219 days.

The sidereal day was computed by "freezing" the earth axis of mid-winter 1997/1998 and using the projection of this "frozen" earth axis on the osculating orbital (ecliptic) plane. 39 such "years" added up to 14244.9904 SI days => average sidereal year 365.2562 SI days. In the article the value given is 365.256363004.

Both values agree but in the article much too many decimals are given considering that a typical variation of individual years is +- 20 minutes.

I do not doubt that evaluating the approximate analytical formulas used one gets the values presently in the article but the real significant accuracy is at most 3 to 4 decimals when expressed in days. These analytical formulas are only approximations! The numerical methods with JPL ephemeris I use give the highest accuracy that can be achieved! My individual tropical/sidereal years are practically error-free! But my averages are just averages of 39 consecutive years!

Stamcose (talk) 09:39, 12 June 2011 (UTC)

Don't denigrate VSOP. It is NOT an approximation. It is directly comparable to the JPL ephemeris DE200. Indeed, the integration constants of VSOP were explicitly fitted to DE200, causing their mean years to be identical. Both were used to calculate their respective almanacs from 1984 until at least 2000, DE200 for the Astronomical Almanac and VSOP for its French counterpart, Connaissance de Temps, the oldest national astronomical almanac in the world, a century older than the British version and two centuries older than the American version. During 1900–2100, the position of Earth calculated by VSOP did not deviate from that calculated by DE200 by more than 0.005", which corresponds to a tenth of a second (six fractional decimal digits of a day). There is no detectable gradually increasing deviation between VSOP and DE200 positions for Earth over a century, as expected since their mean years are the same. See VSOP82 (French article with English summary) and VSOP87 (English). VSOP82 and VSOP87 have comparable accuracy—the VSOP87 solution was presented in a greater variety of coordinates, including Cartesian and spherical coordinates relative to both the fixed J2000 equinox and the equinox of date. JPL confirms that VSOP was fitted to DE200 in The observational basis for JPL's DE200. JPL stated that the mean sidereal year of DE200 was 365.25636300 days on page 300 of Orientation of the JPL ephemerides, DE 200/LE 200, to the dynamical equinox of J 2000, virtually identical to 365.256363004 days in VSOP. — Joe Kress (talk) 05:50, 13 June 2011 (UTC)


"The sidereal and tropical years were calculated via an analytical solution of Newton's universal theory of gravitation applied simultaneously to all planets performed by the Observatory of Paris called VSOP. The result is the position of all those planets in the form of a mean position polynomial plus thousands of sinusoidal terms yielding an accuracy of about a milliarcsecond."

If I understand this correctly this is an analytical approach to find the mean over a period when the whole Solar System has recycled, i.e. a period of time for which all (or at least all large) planets has made an integer number of orbital revolutions. But if this corresponds to a period of thousands of year this is a limited interest for us living here and now. We are left with the fact that duration of the different years varies with about +- 25 minutes.

Stamcose (talk) 18:13, 13 June 2011 (UTC)

My wording was poor. All national ephemerides from about 1750 to 1983 were based on analytical (or semi-analytical) solutions of Newton's universal theory of gravitation specified as a mean position polynomial (its derivative is the mean year) plus a series of sinusoidal terms, including Simon Newcomb's solution used by the Astronomical Almanac until 1983. These solutions involved a transformation of coordinates or variables from Cartesian or spherical to the six osculating elements of an elliptical orbit. The result includes the masses of the planets to various powers or orders. Before 1984, hand calculation limited the order of the masses to one or two, but the advent of electronic computers allowed VSOP to increase the order to three (six for the gas giants). I do not know how the position, hence year, polynomials were determined, although least squares regression was probably used to fit scattered points to a polynomial curve. — Joe Kress (talk) 20:03, 21 June 2011 (UTC)
By "the order of the masses" do you mean significant figures, or what? —Tamfang (talk) 11:38, 22 June 2011 (UTC)
Mass squared, mass cubed, etc. See [3] and subsequent pages, including the next chapter. Analytical keeps the masses of the planets as variables, whereas semi-analytical replaces them with their numerical ratios relative to the mass of the Sun before solving the system of equations. This assumes that the masses are virtually constant over the period that the equations are valid, a few thousand years around the present. — Joe Kress (talk) 06:01, 26 June 2011 (UTC)

Proposed rewrite of section "Sidereal, tropical, and anomalistic years"[edit]

Following the recent discussion "Duration of a sidereal day" I would propose the following rewrite of section "Sidereal, tropical, and anomalistic years". If no one objects here I will do the change on Wednesday. Here follows the proposed rewrite:


Each of these three years can be loosely called an 'astronomical year'.

The sidereal year is the time taken for the Earth to complete one revolution of its orbit, as measured against a fixed frame of reference (such as the fixed stars, Latin sidera, singular sidus).

The tropical year is "the period of time for the ecliptic longitude of the Sun to increase by 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of the seasons. The tropical year is usually defined as the time from two successive "mid-winters" (the point of the Earth orbit when the direction to the Sun takes its south-most value. Because of the precession of the polar axis of the Earth this year is about 20 minutes shorter then the sidereal day.

The anomalistic year is the time taken for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (January 3 in 2011), and the aphelion, where the Earth is farthest from the Sun (July 4 in 2011). The anomalistic year is usually defined as the time between two successive perihelion passages.

If the Earth had been in a perfect Kepler orbit around the Sun successive years would have had exactly the same duration and the durations of a sidereal year and an anomalistic year would have been the same. But due to the gravitational forces from the other planets the Earth follows slightly different trajectories in different years and the duration of the years (defined as "sidereal" as well as "tropical") will because of this vary with about +- 25 minutes.

The duration of a sidereal year is 365 days 6 hours 9 minutes +- 25 minutes
The duration of a tropical year is 365 days 5 hours 49 minutes +- 25 minutes

These variations +- 25 minutes due to the small differences between the trajectories of the Earth in different years caused by the varying constellations of the other planets affect both types of year in the same way, the sidereal year is therefore every year about 20 minutes longer then the tropical year.

The rule for the insertion of leap days is based on the fact that the average tropical year is slightly shorter then 365.25 days.

Stamcose (talk) 16:50, 12 June 2011 (UTC)

Today is Tuesday. Do you still intend to make the change on Wednesday? :P —Tamfang (talk) 19:52, 14 June 2011 (UTC)

In for example Japan "16:50, 12 June 2011 (UTC)" corresponds to Wednesday! Otherwise I have no objection to your improvements of the language as far as the meaning is not changed. English is possibly your mother tongue! A table (possibly reduced) similar to what I put in into Tropical year would possibly illustrate these "+- 25 minutes" variations better!

Stamcose (talk) 08:14, 15 June 2011 (UTC)

The section "Variation in the length of the year and the day"[edit]

Here it is said:

The precession of the equinoxes changes the position of astronomical events with respect to the apsides of Earth's orbit. An event moving toward perihelion recurs with a decreasing period from year to year; an event moving toward aphelion recurs with an increasing period from year to year (though this effect does not change the average value of the length of the year).


Each planet's movement is perturbed by the gravity of every other planet.

Not very logical!

The (secular) rotation of the apsidal line is a consequence of the "perturbation by the gravity of every other planet". Technically one distinguishes between "(short) periodic" and "secular" orbital perturbations but this is not the place to analyse these perturbation in detail! This is for example done in Orbital perturbation analysis (spacecraft) and Perturbation (astronomy)

The other 4 reasons mentioned are practically not detectable or at least of a completely other order of magnitude! If they should be metioned at all this should be pointed out!


The variations of the duration of a year depends on the gravitational effect of the planets (secular and periodic orbital perturbations!)!

Stamcose (talk) 12:49, 16 June 2011 (UTC)

You seem to be saying that the two quoted assertions cannot both be true. I don't see why not. —Tamfang (talk) 19:14, 16 June 2011 (UTC)

A list as follows is given as if there were 6 different reasons for this phenomenon:

The exact length of an astronomical year changes over time. The main sources of this change are:
  • The precession of the equinoxes changes the position of astronomical events with respect to the apsides of Earth's orbit. An event moving toward perihelion recurs with a decreasing period from year to year; an event moving toward aphelion recurs with an increasing period from year to year (though this effect does not change the average value of the length of the year).
  • Each planet's movement is perturbed by the gravity of every other planet.
  • Tidal drag between the Earth and the Moon and Sun increases the length of the day and of the month (by transferring angular momentum from the rotation of the Earth to the revolution of the Moon); since the apparent mean solar day is the unit with which we measure the length of the year in civil life, the length of the year appears to change. Tidal drag in turn depends on factors such as post-glacial rebound and sea level rise.
  • Changes in the effective mass of the Sun, caused by solar wind and radiation of energy generated by nuclear fusion and radiated by its surface, will affect the Earth's orbital period over a long time (approximately an extra 1.25 microsecond per year.Cite error: A <ref> tag is missing the closing </ref> (see the help page).

However, what is given as "reason 1" is just one of the effects (manifestations!) of "reason 2" what in reality is the only (significant!) reason for these variations (changes)!

Stamcose (talk) 21:18, 16 June 2011 (UTC)

According to Axial precession (astronomy), "The precession of the equinoxes is caused by the gravitational forces of the Sun and the Moon, and to a lesser extent other bodies, on the Earth." That says to me that perturbation by other planets is not "the only (significant!) reason" for the precession. —Tamfang (talk) 06:24, 17 June 2011 (UTC)

"The precession of the equinoxes" is the cause for the tropical year to be 20 minutes shorter than the sidereal year. But it has nothing to do with the fluctuations of the durations of the different (subsequent) years. Nutation on the other hand causes some fluctuations of the durations of the different tropical years (obviously not the sidereal years!). This could be mentioned although these fluctuations are much smaller then those caused by the gravitation of the other planets!

Stamcose (talk) 07:32, 17 June 2011 (UTC)

The length of the tropical year is the sum of three parts. (1) The mean length of the tropical year in the form of a polynomial. Newcomb's version had a constant term and a linear term. The VSOP version has a constant term and several higher degree terms. (2) The length of four seasonal years: the vernal equinox year, summer solstice year, autumnal equinox year, and winter solstice year, depending on what solar longitude the year begins. They differ by about two minutes from each other as Earth's perihelion or aphelion approaches or recedes from the specified equinox or solstice. This is your reason 1. It is due to the period of Earth's elliptical orbit (its mean anomalistic year or the derivative of its equation of the center) differing from the period of its mean tropical year. This in turn is due to the secular actions of the other planets on Earth's perihelion or aphelion. (3) The periodic perturbations by the other planets and the Moon on Earth's orbit amounting to many minutes (your estimate of ±25 minutes may or may not be correct). This is your reason 2 (periodic), which is distinct from reason 1 (secular). I view the movement of the perihelion/aphelion relative to the equinoxes and solstices as a secular change because they move relative to either the mean tropical year or the Gregorian year in only one direction. However, the resulting seasonal years are periodic over millennia when given in SI days. But these seasonal years oscillate around a linearly decreasing length when Earth's year is specified in lengthing mean solar days (1.75 ms/cy) (cause 3). See [4]. — Joe Kress (talk) 08:42, 20 June 2011 (UTC)

Variation in the length of the year and the day[edit]

I think this section should be completely removed!


The gravitational attraction of the Earth to the other planets causes the year to vary with the comparatievly hugh amount of up to +-25 minutes. But these variations are indeed periodic. For example Jupiter having the orbital period of 11.86 years causes periodic variations with a period of this magnitude. On top of these periodic variations one could possibly discuss theoretical non-periodic orbital period changes of extremely small size, for example the loss of Solar mass due to radiation etc.


"Tidal drag" makes no sense, the duration of the year is measured with SI time, otherwise these small changes are completely neglectable/non-observable. Which they are even with atomic time!

The shortening of the year due to the decreasing Sun mass is a theoretical construction beyond any possible observability! "nano-seconds"/ "atto-seconds", forget about this when the year varies with +-25 minutes!

This article is about "year" not about "day". That the rotation of the Earth around the polar axis must decrease due to tidal friction is clear from basic physical principles. But when editors of WIKIPEDIA state that this is the reason why leap seconds must be inserted to avoid that SI times runs ahead of the Earth rotation I think they are ahead of science ("relayable references", please). To my knowledge this decrease of rotation rate is also with atomic time and observations of distant quasars not observable and that the bias of SI time (a too short SI second to fit Newcomb's formula) for the Earth rotation) has been there from the start of atomic time!

Stamcose (talk) 18:32, 18 June 2011 (UTC)

The increasing length of the mean period of earth's rotation on its axis, as measured in SI seconds, is clearly observable. See Delta T. Also, "the duration of the year is measured with SI time" is not true, with the possible exception of some narrow scientific audience. The length of the year has been based on the seasonal cycle since prehistoric times. The dominant calendar in international commerce and affairs is the Gregorian calendar, which implicitly counts actual solar days, since at the time it was created in the 14th century, there was no clock that could approach the accuracy of solar timekeeping. I am not aware that the Roman Catholic Church has announced a change from a count of observed solar days to a count of days of 86,000 86,400 SI seconds, and I am not aware of any other institution having claimed to do so either. Jc3s5h (talk) 19:33, 18 June 2011 (UTC) revised 19 June 16:34 UT.

I looked at the article Delta T.

I says that:

"over many centuries tidal friction inexorably slows Earth's rate of rotation by about 2.3 ms/day/cy"

But no reference for this figure is given nor is it said if this a theoretical or an observed value. But that it is a theoretical value should be clear from the rest of the article where it is said that other rather unpredictable effects changing/decreasing the moment of inertia of the Earth (melting of ice etc) counteracts this spin rate caused by torque from the Moon/Sun gravitation on the tidal bulb.


This is a highly speculative figure of some scientist that is not really verified by actual observations. Note that in Newcomb's formula there is no trace of a spin rate decrease! The insertion of UTC leap seconds is irregular with absolutely no detectable tendency of a systematic spin rate decrease.

Stamcose (talk) 09:02, 19 June 2011 (UTC)

I have added a citation to the Delta T article. Of course Newcomb's formula has no trace of a spin rate decrease; the formula was intended to be used over a period of a century or so, and the clocks available near the end of the 19th century, when the formula was created, were not accurate enough to detect the decrease. Jc3s5h (talk) 16:32, 19 June 2011 (UTC)

Why does the year "start" at the position in Earth's orbit that it does?[edit]

It's a good article, but I went looking for an answer to that question and couldn't find it, though maybe I missed it. What is the reason or origin of attributing the "start" of the year to the (arbitrary?) position the earth is at in its orbit on what we can "January 1st?" --Ds13 (talk) 18:18, 31 December 2011 (UTC)

I believe that comes from Roman pre-history. Jc3s5h (talk) 19:39, 31 December 2011 (UTC)
Likely it was once at the winter solstice and drifted because of imperfect observations, sloppy record-keeping, who-knows-what. —Tamfang (talk) 04:52, 28 May 2012 (UTC)
Before the Julian calendar was implemented in 45 BC, March in the Roman quasi-lunar calendar was usually a spring month, but the vernal equinox could occur on any day of the month. Julius Caesar also made March a spring month in his Julian calendar. Because that calendar was a solar calendar, the vernal equinox occurred on March 22–25. By the 3rd century, the vernal equinox had moved to about March 21. For the next 13 centuries, the vernal equinox continued to move, reaching March 10 near the end of the 16th century. The Gregorian calendar moved the vernal equinox back to near March 21 and drastically reduced its drift away from that date after many centuries. The position of January 1 relative to the winter solstice is an accidental by-product — it has no significance. — Joe Kress (talk) 06:14, 28 May 2012 (UTC)
As Joe Kress's discussion implies, and as those who study historical chronology must be aware, the year has been taken to begin at various times of the year. A common tradition was to take the beginning of Spring as the beginning of the year, that is when the Sun was at the vernal equinox (entering the sign of Aries) and its celestial longitude (λ) was 0.0°. Perhaps some discussion of these historical matters belongs in the article. SteveMcCluskey (talk) 20:11, 28 September 2012 (UTC)

The year increase due to solar mass loss is incorrect[edit]

The proper way to do this is to assume that the orbital angular momentum is constant so that when the Suns mass decreases, both the radius of the orbit and the period of the orbit increase at the same time. The cited note only takes into account a period increase. I would just edit the number directly (it should be 6.3 microseconds instead of 1.25 microseconds) but that would screw up the note citation and I am not sure how that should be handled. I wrote an answer on Quora here that explains my calculations: Would it be acceptable to use that link as the citation? I don't know the policy on citations very well - it has been several years since I edited anything on Wikipedia and we were much looser back in those days :-). I would be happy to make the edit but I don't know how to cite correctly and the full explanation with conservation of angular momentum won't be as concise as the current note. Thanks for your help. FrankH 12:08, 1 October 2012 (UTC) — Preceding unsigned comment added by FrankH (talkcontribs)

That section suffered from an egregious lack of citations. It also suffered from a total lack of meaningful organization. It appeared that some editor, qualified or not, searched through a drawer and tossed in some scattered "facts" with no concern about what was significant, what was possible to confirm experimentally, or what was important enough to be in an encyclopedia article. I deleted the section.
FrankH should not cite his own calculations unless
  • He has published in the general area in reliable publications (usually, peer-reviewed).
  • The calculation he wants to put in is available in a publication, which could be a personal web site or Quora.
  • There is a way to reliably determine that the Frank Heile who wrote on Quora or a personal website is the same person who published in the reliable sources. The most direct way to accomplish this would be if a personal website had been mentioned in a peer-reviewed article. Jc3s5h (talk) 13:47, 1 October 2012 (UTC)
The section "Sidereal, tropical, and anomalistic years" contains a reasonable summary of verifiable or common-knowledge information from the deleted section, or in the "Sidereal year" and "Sidereal year" articles. I would suggest if more material is to be added about other, that would be enough to make articles about the affected years (anomalistic, eclipse, or Gaussian year) and just mention in the "Year" article that details on variation can be found in the newly-created articles. Jc3s5h (talk) 14:09, 1 October 2012 (UTC)
LeadSongDog's decided to restore the section and try to find sources. But the citation to the glossary of the Online Astronomical Almanac does not say anything like "The exact length of an astronomical year changes over time." Only someone who does not need to read this article could infer a change in the length of an "astronomical year" [sic] from the glossary entry. Jc3s5h (talk) 20:03, 1 October 2012 (UTC)
Yeah, I'm still working on that. The full almanac's more detailled, but the web glossary's more accessible. Perhaps the book preview for the explanatory supplement is a better basis.LeadSongDog come howl! 20:09, 1 October 2012 (UTC)
One could describe the variation in the last 20 years or so by going to a decent college library and transcribing the lengths of the various kinds of years from whichever almanacs they have on hand. So far as I've noticed, the 2nd edition of the Explanatory Supplement really only addresses variation in the tropical year. Moments ago I ordered the newly-published 3rd edition; maybe that will say something helpful. Jc3s5h (talk) 20:53, 1 October 2012 (UTC)
Ok, I'll bite. What was wrong here? Is the conversion of units from 59 years/trillion centuries to 51 nanoseconds/year too obscure? It seems like basic arithmetic, which is exempt from wp:NOR. LeadSongDog come howl! 13:39, 2 October 2012 (UTC)
That section in the Explanatory Supplement is about sidereal time, which is measured with respect to the vernal equinox, and is subject to precession. The sidereal year is measured with respect to the so-called fixed stars, so is not subject to precession. Check the Online Astronomical Almanac glossary entry for Year. Jc3s5h (talk) 14:02, 2 October 2012 (UTC)

Thanks Jc3s5h. I get that I cannot use my own writing on Quora as a cited source. I am FrankH and I am also the Frank Heile of Quora. I do have a Ph.D. in particle physics but I have not published any papers about planetary orbits. However the calculations I've done just use elementary algebra and High School level physics. Since the original "citation" just calculated the result in line, I would propose to just show my calculations in line also. The current number and citation state:

...(approximately an extra 1.25 microsecond per year). REF: Solar mass is ~2×1030 kg, decreasing at ~5×109 kg/s, or ~8×10−14 solar mass per year. The period of an orbiting body is proportional to \tfrac{1}{\sqrt{M}}, where M is the mass of the primary. :ENDREF

I would propose that this change to:

...(approximately an extra 5.0 microsecond per year). REF: Solar mass is ~2×1030 kg, decreasing at ~5×109 kg/s, or ~8×10−14 solar mass per year. Consider a circular orbit of radius r, velocity v, period T and primary mass M. Orbital angular momentum is  \propto r v \propto r^2/T and the orbital angular momentum must be conserved which implies r \propto \sqrt{T}. Kepler's Law says that T \propto \sqrt{r^3/M} and therefore to conserve orbital angular momentum T \propto 1/M^2. :ENDREF

Since the incorrect dependence of period on mass was 1/sqrt(M) instead of the correct 1/M^2 the resulting correct answer is 4 times the incorrect answer. If there is no objection, I will make the edit tomorrow? Is that OK? FrankH 23:42, 1 October 2012 (UTC) — Preceding unsigned comment added by FrankH (talkcontribs)

I'll take your word that you've researched it; my knowledge of angular momentum for orbits is a little rusty. I'd rather have a justified argument than an unreferenced bare claim. It would be better still if you could provide citations for the formulas you used and the rate of decrease in solar mass. Also, it would be best to state which year this would apply to; I would think it would apply to the anomalistic year, right? Unfortunately, we don't have an anomalistic year article, so I don't know if this variation compares to other variations that the anomalistic year may be subject to, so I can't judge if this variation is worth mentioning compared to the other variations. Ideally we would know if this change is experimentally verifiable. 00:09, 2 October 2012 (UTC)
Apsidal precession seems relevant, although it is poorly referenced and the definition of terms doesn't answer the questions I have. Jc3s5h (talk) 00:19, 2 October 2012 (UTC)
This [5] would appear to be a possible reference. Dragons flight (talk) 04:27, 2 October 2012 (UTC)
Thanks Dragons flight, That is an excellent reference! According to the mass loss they quote of 9.13 10^-14 and their statement that the period of planetary orbits will increase at twice that amount gives a 5.8 microsecond per year increase for the earth. That calculation is from WolframAlpha [6] . Their statement of twice the mass loss rate is exactly what I computed with conservation of angular momentum (which they also mention). So the current answer is definitely wrong since it assumes "half" the rate due to the sqrt(M) dependence.
So, I would like to fix this, (or have someone else fix it if they want). In terms of current practice is it acceptable to use an arxiv as a citation source or does it need to be MORE published than that? Also, does the conversion of "twice mass loss" to 5.8 microseconds need to be "cited" (is using the WolframAlpha link acceptable?) or can I be trusted to do that multiplication and unit conversion correctly. Advice please? FrankH 03:50, 3 October 2012 (UTC) — Preceding unsigned comment added by FrankH (talkcontribs)
The Noerdlinger paper contains this passage:

The secular effect of the Sun’s loss of mass was traditionally omitted (Guinot 1989, Newhall et al 1983, Standish 1995) or given only brief mention (Brumberg 1991)

I recognize Standish who is deeply involved with the Jet Propulsion Laboratory Development Ephemeris. If solar mass was ignored as a factor in these key ephemerides until at least 1995, and possibly to this day, that suggest to me that loss of solar mass is unworthy of mention in an encyclopedia article on such a broad topic as the year. I think we should just remove it, at least we can identify for sure which kind of year it most directly applies to, and whether it is significant compared to the other variations in that kind of year.
As for the question of using an arxiv article, I think it would be ok as a convenience copy for people who lack access to scientific journals, but only if the same, or a nearly identical article, were also published in a suitable journal. Jc3s5h (talk) 12:19, 3 October 2012 (UTC)
For comparison, the tropical year is decreasing at a rate of 0.53 seconds per century (530,000 microseconds per year) due to an increasing precession rate. This is 5 orders of magnitude greater than the variation under discussion. (Dennis McCarthy and P. Kenneth Seidelmann, Time From Earth Rotation to Atomic Physics, Wiley-VCH, 2009, p. 18.) Jc3s5h (talk) 12:31, 3 October 2012 (UTC)

The Noerdingler paper has been published and is already referenced twice in Wikipedia.
In the Astronical Unit article [7] it says: "The Sun is constantly losing mass by radiating away energy,[45] so the orbits of the planets are steadily expanding outward from the Sun." [45]^ Noerdlinger, Peter D. (2008), "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System", Celest. Mech. Dynam. Astron. 0801: 3807, arXiv:0801.3807, Bibcode 2008arXiv0801.3807N
In the Solar Luminosity article [8] it says: "The major fluctuation is the eleven-year solar cycle (sunspot cycle), which causes a periodic variation of about ±0.1%. Any other variation over the last 200–300 years is thought to be much smaller than this.[3]...[3]^ a b Noedlinger, Peter D. (2008), "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System", Celest. Mech. Dynam. Astron. 0801: 3807, arXiv:0801.3807, Bibcode 2008arXiv0801.3807N
So this has been peer reviewed and is a real theoretical effect. By my reading of Noerdlingler, the effect is just on the edge of being experimentally verified. For example he says: "In the 44 centuries spanned by the DE200 ephemeris (Newhall et al 1983), the increase in amounts to 60 - 69 m, which is larger than their stated present error in the AU, 149,597,870,680 +/-30 a?m± (Newhall et al, 1983)." Also he says: "The DE406 ephemeris extends (Standish 2005a) from 3000 BC to 3000 AD with a stated interpolation accuracy of 25 m for all planets. The variation in the Earth's semi-major axis from 3000 BC to present, due to 149,597,870,687.7 1.5 m (formal error)±???µ, however, is about 68 - 78 m." He goes on to say that the angular position of the planets could give an accurate test of this effect if the mass of more asteroids could be determined with more accuracy since the other planets and even the larger asteroids can change a planet's position.
In terms of which of the various kinds of "years" this effect would apply to, I believe the answer is ALL of them. This effect is, after all, an actual change in the radius of the orbit which would therefore apply to any of the different ways a year is measured. As I understand it, the different kinds of "years" all depend on what criterion is used to start and stop the measurement of the length of a year so they all would be affected. So, even though this effect is currently to small to be measured, there is no doubt that it is a real effect which will soon be apparent as the modelling and measuring of the orbits of planets are improved. FrankH 04:48, 4 October 2012 (UTC) — Preceding unsigned comment added by FrankH (talkcontribs)
I guess what I was thinking when I asked about what kind of year it applies to was what is the most simply defined year this applies to, and for what kind of year is it most likely to be experimentally verifiable? Taking the tropical year as an example, it's definition depends on the location of the vernal equinox, which is hard to precisely locate, which is a big reason why sidereal time has been redefined in terms of earth rotation angle. So uncertainties in the definition of tropical year might swamp the effect of solar mass decrease. Other kinds of years might be more accurately measurable, so there might be a potential of experimentally verifying the solar mass effect.
Now that we have a decent citation to work with, and you have dug through it to verify the effect is not yet experimentally verifiability, but might be in the not-to-distant future, do you think it belongs in an article as general as "Year"? Jc3s5h (talk) 13:03, 4 October 2012 (UTC)
If there were a more appropriate article like "Variability of the Year" I would agree that would be the place to put this information. Failing that, I do think "Year" is an appropriate place to talk about the variability of the year. In fact I think the bullet points before the discussion of the solar mass loss should have more details - for example, how much variation does the gravitational effect of the other planets have on the typical length of the year? I know on this talk page, it is mentioned somewhere that it could be 25 minutes. I don't know any citation for that but if there is one, I think that would be relevant number to mention.
In any case, since I think we are all agreed the current number is wrong, I will make the edit. Please forgive me if I make any reference formatting error. (By the way, I sign my edits with the 4 "~"'s but for some reason the "SineBot" ends up signing it for me. Why? What am I doing wrong?) FrankH 23:05, 7 October 2012 (UTC) — Preceding unsigned comment added by FrankH (talkcontribs)

Citation style[edit]

The citation style for this article was established with this edit by LeadSongDog in 2009. The style is Citation Style 1. Since then inconsistency has been introduced.

That same month LeadSongDog established the date format for access dates as YYYY-MM-DD.

The next month LeadSongDog established the date format for publication dates as DD Month YYYY, although dates in the body of the article put the month before the day. At the same time he created inconsistency in access date formats.

In summary:

  • Spelling: American English
  • Citation format: Citation Style 1
  • Date format for article body: Month DD, YYYY
  • Date format for publication dates in citations: DD Month YYYY
  • Date format for access dates in citations: YYYY-MM-DD

Jc3s5h (talk) 20:59, 11 October 2012 (UTC)

A blast from the past! Clearly I wasn't paying much attention to consistency of format. IIRC, I was more concerned with finding some useful sources at the time. I don't really care much about dateformats, so long as the meaning is clear. No objection from me to a consistency change. LeadSongDog come howl! 01:59, 12 October 2012 (UTC)

Removed minor sources of variation[edit]

I removed three minor sources of variation from the "Variation in the length of the year and the day" section. The largest claimed variation in the removed items was 5.8 μs per year for loss of mass from the Sun. But, using the method indicated in Astronomical Almanac for the Year 2011 on page L8 to find the lengths of the mean sidereal, mean tropical, and mean anomalistic years for 0, 1900, and 2000, I saw that the year with the least variation was the sidereal year, which showed 100 μs per year on average for the period 1900 to 2000. This is nearly 20 times greater than the claimed variation for solar mass loss, so I don't feel this qualifies as one of the main sources of variation, which is what the first line of the section claims to describe. Jc3s5h (talk) 21:40, 11 October 2012 (UTC)

Numerical value of year variation[edit]

The Astronomical Almanac publishes values for the length of the mean tropical, sidereal, anomalistic, and eclipse years. The volumes I have at hand are for 2001 and 2011, and the change over that period is too small to get a good idea of how quickly the year lengths change. At least for the 2011 values, they are derived from the work by Simon et al. (1994). The 2001 volume does not say what method was used to find the year length, but it seems that even if we used the volume for 1994 and it used the same method as 2011, the change wouldn't be great enough to estimate the rate of change well.

I therefore implemented the expressions from Simon et al, and took derivatives as indicated on page L8 of the 2011 volume (actually those instructions need some improvement). I only did the mean tropical, sidereal, and anomalistic years.

Mean year lengths, truncated at minutes
Type of year days hours minutes
tropical 365 5 48
sidereal 365 6 9
anomalistic 365 6 13
Length of year, seconds portion
Type of year year (AD/BC) seconds
tropical 1 BC 55.96
tropical AD 1900 45.78
tropical AD 2000 45.25
sidereal 1 BC 9.57
sidereal AD 1900 9.75
sidereal AD 2000 9.76
anomalistic 0 BC 47.17
anomalistic AD 1900 52.27
anomalistic AD 2000 52.54

I think it would be useful to include this in the article, if no one has any objection to the method Jc3s5h (talk) 23:37, 11 October 2012 (UTC)

Hearing no objection, I have recompared my formulas to those in the Astronomical Almanac for 2011 and Simon et at. and found that Simon actually gave more than one expression for some of the quantities, so I used the ones specified in the Astronomical Almanac. I also found Taff, an older source with simpler expressions, to compare to. Finally, the 3rd edition of the Explanatory Supplement to the Astronomical Almanac has just come out and I compared to the tropical year values in that. I am now adding the results to the article. Jc3s5h (talk) 13:01, 7 November 2012 (UTC)

Numerical value of year variation: sources[edit]

  • Simon, J.L.; Bretagnon, P.; Chapront, J.; Chapront-Touzé, M.; Francou, G.; Laskar, J. (February 1994). "Numerical expressions for precession formulae and mean elements for the Moon and planets" (PDF). Astronomy and Astrophysics 282 (2): 663–683. 
  • U.S. Naval Observatory Nautical Almanac Office and Her Majesty's Nautical Almanac Office (2000). Astronomical Almanac for the year 2001. Washington: U.S. Government Printing Office. 
  • U.S. Naval Observatory Nautical Almanac Office and Her Majesty's Nautical Almanac Office (2010). Astronomical Almanac for the year 2011. Washington: U.S. Government Printing Office. pp. C2, L8. 


Isn't a year is 365.24 days, not .25 days, the reason way every hundred years we drop a leap year (but not every 400)? — Preceding unsigned comment added by (talk) 22:59, 8 January 2014 (UTC)

The average length of day in the Gregorian calendar is 365.2425. But there are many kinds of years, many of which are described in the article. Jc3s5h (talk) 23:13, 8 January 2014 (UTC)

What is a "year"?[edit]

What is a year? Is it that the earth goes round the sun by 360 degrees? Or in relativity terms, equally, the universe rotates around the solar system 360 degrees, which is essentially the same thing from out viewpoint. So a year is defined by the observable frame of reference. Or is it that the earth gets back to its same position on its elliptical orbit? Is it both? Or is the elliptical path our planet takes not 360 degrees? (presumably not as seasons don't gradually drift.) This page would also be the appropriate place on Wikipedia to cover this issue. — Preceding unsigned comment added by (talk) 23:07, 8 January 2014 (UTC)

None of the above. It's the time between corresponding solstices and equinoxes (nearly always the spring equinox). This is currently 365.2424 days, so 365.2425 is an excellent approximation, but there is the problem of Fluctuations in the length of day and ΔT. Dbfirs 22:33, 15 January 2015 (UTC)

Blurish lead[edit]

A year is today defined according to the Gregorian Calendar, a predecessor of the Julian Calendar. But also other definitions have been used through the times - from Egypt to Stonehenge and Ale stenar etc, etc - are all monuments to show the cardinal directions or where the sun rises at summer or winter Solstice. Twelve (virual) full moons have been used in order to define a year etc. The current lead is a mish-mash , for instance why involving the SI-system with the Julian Calendar ? The SI system has its first roots in the French revolution , some 1800 years before Caesar's time. From a mathematical-historical point of view should it also be mentioned that already by the time of Caesar astronomers knew that a (vitrual sun orbit) year didn't comprice an interger number of days (day=24 hrs). The Julian (Caecar's) calendar defined the year as 365 + 1/4 days. (not 365.25, the Romans didn't use the decimal commas). I think the article calls for some rewrightings. Either start with the current astronomical definition and the Gregorian Calendar, SI system etc - or begin with a historical overview which includes all known definitions. This lead starts somewhere in the middle. Combining unrelated issues as the zodiac (which has no impact on the definition at all, the time between two summer or winter Solstices or the time between two spring or autumn (=fall) eqinoxes both equal the time of a year. So why involve the zodiac at all ? And this together with the modern SI-system make's the lead blurish, atleast in my mind. Boeing720 (talk) 21:43, 14 January 2015 (UTC)

I won't try to defend the current lead. However, whenever any time is defined, or any time period is given to high precision, it is mandatory to state what kind of seconds the value is given in. The second can be an SI second (the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom), 1/86,400 of a mean solar day, or 1/86,400 of an apparent solar day. These are all different durations. Of course, one could tell a white lie in the lead and not say which kind of second is being used, and provide that mandatory information in later section; that is a matter of editorial judgement. Jc3s5h (talk) 21:44, 15 January 2015 (UTC)
Only the Julian year is defined in terms of the second (and it's the SI variety). All other years for millennia have been attempts to get a year to match the time between solstices and equinoxes. The Julian calendar got the calculation slightly wrong (though it was an excellent estimate for its time), hence the Gregorian reform which matched many other cultures in fixing a year as the time between northward equinoxes. More emphasis needs to be given to this equinox definition since it has been the most common worldwide throughout history (citations needed, but I'm pretty sure that it's true). The length of a year has varied in the number of days assigned to it, and in the length of those days, but it has always been defined in terms of the equinoxes and solstices (nearly always the spring equinox). Dbfirs 22:30, 15 January 2015 (UTC)
On second thoughts, I'm being very "earthist" in my viewpoint. For other planets, the term "year" is used in different ways. Dbfirs 23:05, 15 January 2015 (UTC)
Modern astronomers define the tropical year as time for the Sun's mean longitude to increase by 360°. The process for finding an expression for the length of the tropical year is to first find an expression for the Sun's mean longitude (with respect to ♈), such as Newcomb's expression given above, or Laskar's expression (1986, p. 64). When viewed over a 1 year period, the mean longitude is very nearly a linear function of Terrestrial Time. To find the length of the tropical year, the mean longitude is differentiated, to give the angular speed of the Sun as a function of Terrestrial Time, and this angular speed is used to compute how long it would take for the Sun to move 360°. (Meeus & Savoie, 1992, p. 42). Jc3s5h (talk) 23:11, 15 January 2015 (UTC)
Yes, I wasn't suggesting that we should delete the record of what modern astronomers have measured, but their measurement of the "mean tropical year" is not actually used for any purpose other than defining their particular year (and perhaps for making predictions about rates of change of rotation). Actual calendars are not based on this "year". Dbfirs 00:02, 16 January 2015 (UTC)
You're being disingenuous with your edit summary. It is evident from the above post that you know exactly what the mean equinox is. You insist on inserting an undefined year length which you claim to be accurate to six places of decimals, which is about a twentieth of a second. (talk) 18:24, 23 April 2015 (UTC)
No, I'm simply recording what has been measured. Astronomers have measured both the mean time between northward equinoxes and the mean year averaged over both equinoxes and solstices. I accept that, at the time the Gregorian calendar was constructed, they might not have known that there was a difference (though I'll look for evidence), but now that we know the separate figures, I see no reason to suppress them. The addition which you last reverted was in fact a rounded figure, not to the six decimal that you previously reverted, but the figure has been measured to the same accuracy as your figure for the mean tropical year (which I have never disputed). Why are you edit-warring over this? Isn't there room for both figures? Dbfirs 19:22, 23 April 2015 (UTC)
So can you please explain how this value was measured to an accuracy of 1/20 second? (talk) 08:14, 24 April 2015 (UTC)
The same way that the mean tropical year was measured. These values are constantly changing, so any quoted figure must be an average of measurements. I agree that it is spurious accuracy to give any of these figures to 1/20 second. Dbfirs 09:13, 24 April 2015 (UTC)
No, you have this completely wrong. The measurement for the mean tropical year is the formula contained in Newcomb's Tables of the Sun (1898). You're saying that this figure accurate to 1/20 second is an average of measurements. What measurements exactly? (talk) 09:37, 24 April 2015 (UTC)
Yes, I thought you were going to say that. You will be aware that your formula was not available to the originators of the Gregorian calendar who used the Alfonsine tables and Prutenic Tables which gave the value of the seasonal year as 365;14,33 (Babylonian sexagesimal notation) i.e. 365.2425 days. The more accurate and more recent calculation for the mean interval between vernal equinoxes around "era 2000" was calculated using Newcomb's or Laskar's formula, taking into account the precession of separate equinoxes (similar to the calculations in this paper). Perhaps you have access to the details of the calculation, or are able to do it yourself from published parameters. The precise figure of 365.242374 was calculated by Jean Meeus using data from the Bureau des Longitudes. Dbfirs 12:13, 24 April 2015 (UTC)
Well, that paper you quoted is straightforward celestial mechanics, such as used in SOLEX to pinpoint the future position of planets (claimed to predict simultaneous transits of Mercury and Venus hundreds of thousands of years into the future). Your reference to "the precession of separate equinoxes" is a joke. If you're calculating the length of the vernal equinox year the only equinox whose precession you are interested in is the March one. (talk) 13:12, 24 April 2015 (UTC)
I'm actually interested in both equinoxes: northward equinoxes 365.242374 days in a year and southward equinoxes 365.242018 days. The vernal one is of most interest because many calendars are based on this. Dbfirs 14:09, 24 April 2015 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────Let me start with a simple comment. Recent versions of the article gave the mean interval between vernal equinoxes to four decimal places, which is a precision of about 9 seconds. Currently the difference between the UT1 day and the SI day is around 1.5 ms, which over the course of a year would accumulate to about 0.5 s. Thus, we can get away with giving the length of a tropical year to 4 decimal places without specifying which kind of day we are using, but any further precision will require that the timescale be given.

The only source I have seen for the mean interval between vernal equinoxes is the 1992 paper by Meeus and Savoie; they don't give a specific explanation of how they calculated the mean interval between vernal equinoxes.

For most of the 20th century the mean tropical year (or just "tropical year") used by astronomers was that derived by Newcomb in the 1998 (Vol. 6, "Table of the Four Inner Planets", Astronomical Papers Prepared for the Use of the Astronomical Ephemeris and Nautical Almanac, Washington: Bureau of Equipment, Navy Department). This book can be found on Google Books. On page 9 he states the latest equation for the mean longitude of the Sun, and on page 10 he states he derived the length of the tropical value from the mean longitude. The method of deriving the length of the tropical year from the mean longitude is fairly obvious and is explained on the Astronomical Almanac for the year 2011 page L8, among other places.

More recent values for the mean longitude of the Sun are given in Laskar's paper mentioned above by Dbfirs, specifically on pages 63–64. It is also explained in a similar, but updated, paper by Simon, Bretagnon, Charpont, Chapont-Touze, Francou, and Laskar in 1994 ("Numerical expressions for precession formulae and mean elements for the Moon and planets", Astronomy and Astrophysics, v. 282, pp. 663–683). The paper is available through the NASA Astrophysics Data System, and is the one currently used by the Astronomical Almanac for the tropical year. The latter paper contains in § 5 "Mean elements of the planets" an explanation that the mean longitude is based on the long period perturbations, that is, those with periods on the order of 10,000 years, and that the analysis uses Fourier series. I have used Fourier series professionally in electronics; they are useful for separating short-period fluctuations from long-term trends. Jc3s5h (talk) 13:51, 24 April 2015 (UTC)

Of course they don't give an explanation of how they calculated the mean interval between vernal equinoxes. There's only one way to do it - the method explained by Newcomb and refined by later celestial mathematicians. Meeus and Savoie's value is too far from Newcomb's to be correct. (talk) 14:33, 24 April 2015 (UTC)
Well Newcomb's method gives 365.24219294 days for the mean tropical year in the epoch J2000 (compared with 365.24219023 for the Leverrier formula) whilst the Meeus and Savoie value for J2000 is 365.242189623 ephemeris days (i.e. mean solar days for the 1900 epoch). I agree that this accuracy is spurious, but I don't understand your claim that the value calculated by the VSOP87 method is "too far out". We seem to be arguing at cross-purposes and discussing different calculations. Dbfirs 17:10, 24 April 2015 (UTC)
The value that was in the article till I removed it on Wednesday was 365.242374 days. (talk) 17:28, 24 April 2015 (UTC)
The Meeus and Savoie value (p.42, middle of right column) is for 2000. I interpreted's post of 14:33, 24 April 2015 (UTC) to mean that because Meeus and Savoie's value (six lines above the value for the mean tropical year at 2000), which is 365.242374 ephemeris days, is too far from Newcomb's value to be correct. But Meeus and Savoie, as well as astronomer Duncan Steel (Marking Time: The Epic Quest to Invent the Perfect Calendar (Wiley, New York, 2000), pp. 381–2) indicate that calculating the mean interval between vernal equinoxes is a method, although not the method currently used by astronomers, of calculating the tropical year, and it does give a different result from the current astronomical definition of the tropical year. Jc3s5h (talk) 18:08, 24 April 2015 (UTC)
Yes, we are talking about different calculations. The Meeus and Savoie value for the mean tropical year is just an update of the Leverrier and Newcomb calculations using slightly more accurate modern data. (I've clarified that their calculations are for the J2000 epoch.) All of these calculations of the mean tropical year are averaged over all points of the tropical zodiac. This averaging is inherent in the method. Meeus and Savoie also calculate times between individual equinoxes and solstices for the J2000 epoch, and this separate calculation is the 365.242374 days that objects to. They explain: "The vernal equinox slowly regresses along the ecliptic (precession). When ... the sun returns to the vernal point it has not made a complete circuit with respect to the stars ... This small arc is described with a somewhat different speed, according to its position with respect to the perihelion of the Earth's orbit. Depending on the starting point adopted for the 'year', one complete circuit in tropical longitude will have a somewhat variable length.". I have no reason to doubt the accuracy of the Meeus and Savoie calculations, and I see no reason for suppression of their figures, especially as they are cited in other publications, but I agree that it would be good to see the details of the method and to have the figures checked independently. Dbfirs 18:45, 24 April 2015 (UTC)
Indeed it will, but we are talking about the mean here, from which these variations have been ironed out. (talk) 08:54, 25 April 2015 (UTC)
We need to consider over what variables the mean is taken. In the case of the Newcomb and similar equations, it is the mean over all points of the tropical zodiac. You are correct that if the year length is averaged over 25,771(and about a half) years, then the vernal equinox mean will match the tropical year, but that's a very long period of time, and by then some of the constants will have changed, including our definitions of days and seconds if humans are still around. Meanwhile, averaged over a couple of thousand years centred on J2000, the vernal equinox year is 365.2424 years. Dbfirs 11:20, 25 April 2015 (UTC)
In this country, the phrase "a couple" means two - some languages are more relaxed. An equinox is scheduled for 28 February 3000 (Julian) at 16:27:21. There was one on 14 March 1000 at 23:11:47. The date difference is 15 days 6:44:26. 2000 Julian years are 73 050 days. Subtracting the date difference, the interval is 73 034 days 17:15:34. Converting the time to days the interval is 730 34.719 144 days. That gives a vernal equinox year averaged over the period of 365.173 596 days. Of what possible use is this value? (talk) 12:49, 25 April 2015 (UTC)
Actually, the difference between the two equinoxes is 730484.719144 days, resulting in a mean vernal equinoctial year of 365,242360 days. AstroLynx (talk) 13:43, 25 April 2015 (UTC)
Thanks, AstroLynx, I was trying to work out what was wrong with's arithmetic. Dbfirs 13:47, 25 April 2015 (UTC)