Talk:Tropical year/Archive 2

Archive 1

Archive 2

Archive 3

Archive 4

Reasons for tags

The primary citation used in the article, Meeus & Savoie, gives not just one definition but many different definitions for the tropical year.

Numerous RS's (and their comparison with the data-sources on which they rely) show that for astronomical standards purposes, the number quoted for a tropical year-length, at any epoch, is usually now obtained from the inverse of the linear coefficient of the elapsed time in the adopted polynomial expression for the sun's change of mean longitude with time relative to equinox and ecliptic of date, when expressed for that epoch.

In other words, if the linear coefficient in the expression for mean solar longitude w.r.t. equinox and ecliptic of date (starting from epoch X) is x degrees/day, then the tropical year length (at epoch X) is 360/x days. (Inverting instead the 1st derivative of the entire polynomial gives the variation of year-length with time.) The numbers given in the cited Meeus/Savoie source for Leverrier and Newcomb's estimates of the tropical year numerically match that, even though their verbal description is not so clear.

The reasons for the other tags arise from the same basis. It needs to be explained which definition is being used in which context. Terry0051 (talk) 20:15, 22 January 2010 (UTC)

I am working on this. You can see what I've don so far at User:Jc3s5h/sandbox3. I've gone through as far as the 18th and 19th century history. Let me know if you think I'm headed in the right direction. --Jc3s5h (talk) 20:55, 22 January 2010 (UTC)

Thanks. If it's ok with you I'll post on your sandbox3-talk page. Terry0051 (talk) 22:42, 22 January 2010 (UTC)

Agreed. --Jc3s5h (talk) 23:13, 22 January 2010 (UTC)

• You probably have this all in hand, but apropos of the "dubious" tag against the opening definition, and the above discussion, we need to make sure that said definition remains intelligible to ordinary readers. For example, we cannot lead off with an explanation that involves "linear coefficients", "first derivatives of polynomials" and so on. 99.9% of readers will not have the faintest idea what it's talking about. 81.129.128.22 (talk) 05:08, 23 January 2010 (UTC)

Terry0051: I find the "unreferenced" and "dubious" tags somewhat offensive. If you really look into it, there are infinitely many possible definitions of the "tropical year", as this article tries to explain. A conventional but somewhat naive modern astronomical definition is, the period from the polynomial expression of the Sun's mean longitude as measured from the northward equinox. However, historically a tropical year ran from one summer solstice to the next, or from northward aequinox to the next. Those periods are not equal and also not equal to the astronomer's "mean mean" tropical year, for rather arcane reasons that the article tries to explain. It is somewhat relevant because the Gregorian calendar year was defined to set and keep the vernal aequinox at 21 March; some calendar reformers claim that the calendar year could be improved by better matching it to the somewhat smaller "mean mean" tropical year, but that will make the date of the vernal aequinox drift and conflicts with the churches' Easter computus. Most astronomers don't know and don't care so you won't find a proper treatment in most astronomical text books. It appears that Meeus was the first to realize and publish about the distinction when he formulated empirical expressions for the moments of the aequinoxes and solstices, maybe only 20 years ago (in his Astronomical Algorithms; in his earlier Astronomical Formulae he used a single approximate formula for all seasons). I suggest you help improve the text rather than flag it. I think earlier versions of the article were better but the quality has eroded when people started trying to explain fragmentss they found obscure. Tom Peters (talk) 15:53, 23 January 2010 (UTC)

Tom, I am working to improve the article in my sandbox, and Terry has been helping. Any precise statement about a tropical year (T. Y.) would be dubious if it didn't identify which tropical year is being referred to, and what time scale is employed. Also, we do not rely on original research by Wikipedia editors. Taking an algorithm out of a book and using it to derive data about tropical years probably qualifies as original research, so there is a strong argument that any such results, if done by a Wikipedia editor, are unreferenced.

Meeus' could be called original research, but published on paper. The "derived" in the reference refers to taking the derivative of his polynomials to go from moments in time, to speed. This is a trivial operation for anyone who had calculus in secondary school. The "Moisson" value takes some more computation, as explained in the note; I suppose one could consider it "original research" in that the parameter that is of interest here is less obvious in the paper, but can be derived from the original data in a straightforward manner. The chances to get this computation published anywhere as "original research" are nil, so conversely I think Wikipedia should not disqualify such digestion of original data as "original research" unfit for inclusion: the values given can be verified from the sources. I think that in this form it is useful information adapted to the subject of the encyclopedic article. Tom Peters (talk) 22:56, 25 January 2010 (UTC)

It also occurs to me that the arguments about whether a calendar does a better job of tracking the mean T. Y. or the mean northern vernal equinox T. Y. have become moot because the unpredictable nature of the Earth's rotation, which has been revealed since the invention of atomic clocks, swamps the difference between these two varieties of T.Y. --Jc3s5h (talk) 17:27, 23 January 2010 (UTC)

Well, it's not entirely unpredictable, several mechanisms are well understood and can be modeled. Just because we measure time in SI seconds with atomic clocks, the rotation rate of the Earth becomes irrelevant, and we can compare a pure sidereal with a pure tropical year. And it so happens that when using a second based on the rotation of the Earth rather than the SI second (i.e. using UT rather that TDT), the date of the northward aequinox is stable over several thousands of years around present. So a case can be made to keep basing the calendar on the northward aequinox year in UT, rather than some mean mean tropical year in some ephemeris time scale. Tom Peters (talk) 22:56, 25 January 2010 (UTC)

My suggestion for the article: don't try to be exactly precise in the definition of the tropical year in the beginning of the article. The major point is the distinction between sidereal and tropical periods caused by precession. Then at closer look, the motion of the perigee also comes to play a role through the variable speed of the Earth in its orbit: but that is a second-order effect. Tom Peters (talk) 22:56, 25 January 2010 (UTC)

I concur with putting off overwhelming details until later in the article. I also suggest you read the WP:No original research article. Converting units or finding a density given a population and an area would qualify as trivial calculations; doing calculus or writing computer software would not. I grant you this does leave a gap between what can't be calculated by Wikipedia editors and what a journal would consider worthy of publication, but we have no way of telling the difference between a Wikipedia editor who is also a professional astronomer, versus one of those physics cranks who use to make the science related newsgroups nearly useless. --Jc3s5h (talk) 23:33, 25 January 2010 (UTC)

I agree with Jc3s5h's approach. I apologize if I've posted anything unduly long/complicated. I agree with keeping things as simple as the truth and sense will allow. The tags were not intended to be offensive, but I would respectfully defend their use. (Tom Peters' reaction came down to 'so fix it'. I would have started, though not immediately, but Jc3s5h immediately posted that he's working on it, it seems to me he's taking a good thoughtful approach.)

To be more specific, the first 'dubious' tag maybe could have been better placed, I defend it because it relates to the combination of the 1st and 3rd lead paragraphs together. There must be something wrong there (with all due respect to the arcane explanations), because, if it really is true that the mean tropical year-length is different between the solstices, than between the equinoxes, it would have to follow that at some time the solstice and equinox would coincide, which is physically impossible.

I suggest the existing first paragraph would become good if 'vernal equinox' is qualified (both times) by 'mean', and if the complicating reference to the solstice is left till later.

I've re-read an article by Jan Meeus about the various intervals between equinoxes and solstices. It is clear he started out by referring primarily to equinoxes and solstices based on true/apparent positions (which show effects of several kinds of periodical perturbation). He has even said this expressly, see Jean Meeus, 'Mathematical Astronomy Morsels' (1997), p.347, reprinting in translation his articles originally published many years before. (The very title of the book 'Mathematical Astronomy Morsels' conveys that there is intentionally an element of entertainment in his treatment of this subject, rather than of standard-setting. The subjects were treated as a jeu d'esprit, though in a learned and instructive way. This is meant respectfully to the author Jean Meeus, it was clearly his intent, he has been a great educator and mediator in bringing mathematical astronomy to a wide audience; and in the days when calculating/computing power was becoming available, but still expensive, he created highly ingenious intermediate approximations for astronomical theories and calculations, intermediate between on the one hand the full theories, which were still unfeasible then for the computing resources of most users, and on the other hand the more commonly-quoted crude approximations, which are/were of unusefully low precision.)

All of the considerations based on true, perturbed, positions of equinoxes and solstices seem to be at some distance away from the big first encyclopedic point about the tropical year length. This is already present in effect in the 1st paragraph (arguably confused by other material). It is the year length that is locked in sync with the seasons. That is a physical reality, and even those who are content with equinoxes defined to the nearest day can be interested in a good precise long-term measure of that reality. It results from the relation between the sun and the reference-frame defined by the equinox, and although both of these move with irregularities, a mean can be found that represents the long-term physical reality. (If there are competing measures or definitions, all of them that are valid will converge to represent that reality.)

(Also, if there is any connection between on the one hand Jan Meeus' jeux d'esprit about equinoxes and solstices, and on the other hand the medieval/renaissance debates that took place about year-length before the 1582 calendar reform, it seems a reliable source has not yet been cited to show that. Among other points, the exact times of solstices and equinoxes were difficult to observe and to measure. There is much good information in "Astronomical aspects of the calendar reform" (J Dobrzycki), though there may also be other and even controversial sides to the questions treated.) With good wishes. Terry0051 (talk) 14:18, 26 January 2010 (UTC)

Dubiosity tags

1. Def of tropical year: the tropical year is defined as the time passing of Sun's passage throught the point of vernal equinox, until the next such passage, as seen from earth. That is the tropical year, and that is irrespective of eccentricity of Earth's orbit. A mean tropical year, could however be said to compensate for the eccentricity. There's no meaning with looking it up in Meeus, because he doesn't provide definitions, and is not using mathematical definitions derivations as much as he should. The tropical year is never defined by any other point than by vernal equinox. In older times certain years might have been defined by choosing other points, but tropical year is an astronomical term. Rursus dixit. (^mbork³!) 17:03, 27 January 2010 (UTC)

The term tropical year is not a name for a year determined by any reference point, but those who make that mistake do so by using it as the vernal equinox year. Actually using Meeus's Astronomical Algorithms is very informative here. Differentiation of the formulas for the mean equinoxes or solstices gives formulas for the mean vernal equinox, September equinox, June solstice, and December solstice years. Adding those formulas and dividing by four gives a formula that calculates the tropical year value given on page 408, and that matches the value gotten through differentiating the mean longitude formula given on page 183. Saros136 (talk) 07:12, 20 September 2010 (UTC)

Quite incorrect. You should try finding a book defining tropical year. My book Astronomi och Astrofysik, by Gunnar-Larsson Leander is in Swedish but it says "the time that sun needs to move anticlockwise along the ecliptic from the vernal equinox and back to that again ... one calls tropical year" (literal translation –> weird syntax), i.e. the same as Fact-index.com: "Tropical year". My objection stand. Rursus dixit. (^mbork³!) 07:06, 21 September 2010 (UTC)

I found the ultimate source. I'll read it and then answer. However: there are enough examples defining it as the full turn backward eccliptic movement from vernal equinox to vernal equinox, to use that definition as a starting point in the text. Either one can provide the very generalized, intransparent definition first, or one can start with the vernal equinox tropical year and expand to a generalized notion. Either way, multiple sources refers to the vernal equinox year as being equal to the tropical year, that's no mistake. Rursus dixit. (^mbork³!) 07:25, 21 September 2010 (UTC)

That was Meeus and another guy named Savioe, making a very confused appearance. They claim that there's no coherent definition. Then they claim that the tropical year of antiquity was defined as the turn of sun from one tropos (any equinox or ecliptical longitude) to the same one 360° on, and that modern authors claims so too. After that, they claim that it's easy to see that the tropical year is not the same as that turn along the ecliptic because of nutation and planetary perturbations. There's no order in their text! They are making the objection, not the various authors. They're not distinguishing unnutated and unperturbed ecliptic from the perturbed one, they're not introducing deviations after the main definition, they're starting with the deviations and then trying to define everything at once in a confused verbal mess that explains nothing. I now understand why Meeus never provides derivation in his books: it is because he cannot write explaining discourses.

The best thing is to stick to the original defining sources of antiquity: the tropical year is the time of the anticlockwise movement of sun along the ecliptic from one tropos to the same one next time, (in modern times usually vernal equinox) and then add complications such as nutation and planetary perturbations afterwards as is customary in scientific pedagogy, not bash with all complications at once like Meeus, and then deny that there is a definition. Rursus dixit. (^mbork³!) 07:47, 21 September 2010 (UTC)

Well, I wasn't using Meeus and Savioe for my post. A book by Meeus. The Meeus and Savioe article says the definition has changed. I thought it wasa fairly good although somewhat messy. They do not claim there is no coherent definition, now. It has changed over time. The definition is very simple-it is a way of expressing the rate of change in the sun's mean longitude at an instant. But it didn't seem confusing to me because I was familiar with the subject, having first read about the history and distinctions in Marking Time, by the astronomer Duncan Steel, who covers it quite thoroughly in his appendix, and is correct.

It's true that most who write consider the tropical year to by synonymous with the vernal equinox year. But what's interesting is that everyone agrees about the length of the tropical year, even though the different definitions lead to different lengths. If you take the vernal equinoxes times of, say, 1900 and 2100 (true equinox) and divide the difference by 200, you'd get a figure about a second different from that figured using modern value for the vernal equinox. I got 365d,5h,49m,2.34s, using the dates generated by Solex 11.0. The figure given by Meeus and Savioe, for J2000 vernal equinox year ends with 1.11s (although they didn't use the min-sec form). Other sources come very close if not the same. But the figure everyone agrees that the tropical year equals ends with 45 m45.2s, which is what one would gets from the equation given by Meeus&Savioe, and is the average of the four equinox or solstice years. So there is a contradiction for those who say the tropical year is the VE year, yet give the modern value for the tropical year (which is 16 s shorter)

As far as which is correct...the atomic second was set to be equal to ephemeris second, which was officially defined as the fraction 1/31 556 925.9747 of the tropical year for 1900 January 0d 12h ephemeris time. The y-d-m-s form ends with 45.9747 seconds, the modern one with 45.7 just a fraction of a second different. Because they used the same definition. Saros136 (talk) 10:19, 22 September 2010 (UTC)

The lead of the article should present the current definition. It doesn't really matter if you don't like the way Meeus and Savioe wrote their article, because others agree with them as far as the current definition is concerned. For example, see "year, tropical" in the glossary of the Astronomical Almanac Online. —Preceding unsigned comment added by Jc3s5h (talk (talk • contribs) 12:35, 21 September 2010

The "tropos" in "tropical year" means turn, and refers to the turning back of the Sun in its motion at the solstices. So the tropical year need not be measured from the northward aequinox by definition. And the length of the period from the tropic of Cancer to the next event, is on average different from the period of the aequinox to the next. That difference is the second-order effect due to the long-term motion of the perigee with respect to the aequinox.

But again, the major distinction should be with the sidereal year. For either one, all short-periodic perturbations like elliptic terms, planetary, and nutation, can and should be ignored: only the long-period precession matters. Tom Peters (talk) 22:16, 1 February 2010 (UTC)

Yes, right! Tropical year is generally contrasted with sidereal year, and that difference neatly connects to precession. Rursus dixit. (^mbork³!) 07:11, 21 September 2010 (UTC)

2. Alternate def in second paragraph is perfect only if the sun starts at degree 0 and runs 360° degrees forth.

3. The third paragraph might be explained if preceeded by: "because of the eccentricity of earth's orbit around the sun, and the displacement of sun due to gravitational influence from Jupiter, and less so by other major planets, the time from one passage of the vernal equinox to next such passage, might vary from year to year". Don't use the argument of choosing any other point than vernal equinox, first it has nothing to do with the tropical year, secondly it confuses.

4. I think an unqualified "tropical year" can be said to refer to the mean tropical year, but citation is needed, as asked for.

IMHO. Rursus dixit. (^mbork³!) 17:03, 27 January 2010 (UTC)

I'm afraid the 'definition' offered by Rursus has multiple ambiguities. First, the true or apparent sun can have up to about 1" latitude north or south, which makes the passages across the zero lines of ecliptic longitude, right ascension and declination happen at three different times. Second, the inequalities of the true/apparent sun in ecliptic longitude are not only due to the orbital eccentricity, but also to the lunar and planetary perturbations. Third, the inequalities of the true equinox (the nutation) are different from year to year. In short, and in addition to the multiple ambiguity, the period referred to is never the same from one 'year' to the next. This seems hardly a definition. "The vernal equinox" is ambiguous until one has specified either mean or true equinox of date, the difference at any time being defined by the value of the nutation either in longitude (for the ecliptic longitude) or in right ascension (for measurements parallel to the equator).

In view of all these factual considerations, it seems that the matters put forward in my previous post still hold. Terry0051 (talk) 22:27, 28 January 2010 (UTC)

Nothing to be afraid of ;-), but you're right. 0° to 360° refers to ecliptic longitude, nothing else. Then it is perfectly unambiguous. Rursus dixit. (^mbork³!) 06:52, 21 September 2010 (UTC)

The definition of the ephemeris second in The explanatory supplement to the Astronomical Almanac (1992/2006) p.80 clarifies "The tropical year was defined as the interval during which the Sun's mean longitude, referred to the mean equinox of date, increased by 360°." Earlier in the paragraph "the tropical year was understood to be the mean tropical year". This definition is loaded with hidden meaning. "mean" means that all periodic terms are ignored (deleted), including terms defining the orbital ellipse and its movement, hence the periodic terms (the equation of the center) needed for the vernal equinox year are not included. However, polynomial terms are retained, hence Newcomb's linear decrease in the length of the mean tropical year is retained, so the [instantaneous] tropical year at noon Greenwich mean time on 1900 January 1 differs from the [instantaneous] tropical year on 1900 February 1, etc. "of date" means that general precession is included (no periodic terms are needed) but nutation is ignored (periodic terms would have been required).

Even though "year, tropical" in the glossary of the Astronomical Almanac correctly includes the phrase "the tropical year comprises a complete cycle of seasons", the hyperlinks incorrectly lead, via "ecliptic longitude", "dynamical equinox", and "true equator" to the "true equator and equinox", which is affected by nutation, so it is not the "mean equinox". Confirming that the Astronomical Almanac uses the mean tropical year we find "tropical year is $360^{\circ }/{\dot {\lambda }}$" on page L8, where λ is defined on page C1 as 279°.319067 + 0.98564736 d, hence the tropical year is 365.242190 days when limited to the eight significant digits in the coefficient of d, which is the same value given for the "tropical year" on page C2. — Joe Kress (talk) 02:26, 28 September 2010 (UTC)

Proposal of new sub-section

I would propose to add the following table as a new sub-section after the sub-section "Mean tropical year current value"

Any protests? Any questions? Other comments?

+++++++++++++++++++++++

Variations of the individual tropical years from the mean value above

Because of the gravitational attraction to the other planets of the Solar system the orbit of the Earth around the Sun will vary somewhat between different years depending on the constellation of these planets. The difference between the times from solstice to solstice for an individual year will therefore deviate with a few minutes from the mean value 365.2421897 given above.

Using the JPL planetary ephemeris and a standard model for the precession of the Earth axis the following deviations were found:

Start of year (Atomic time)	Offset from 365.2421897 SI days (minutes)
1990/12/22 2:59: 2.1	-10.89
1991/12/22 9: 0:24.5	12.62
1992/12/21 14:35:52.6	-13.29
1993/12/21 20:28: 7.8	3.50
1994/12/22 2:19: 4.9	2.20
1995/12/22 8: 8:58.0	1.13
1996/12/21 14: 2:58.4	5.25
1997/12/21 19:51: 7.3	-0.61
1998/12/22 1:51:31.3	11.65
1999/12/22 7:25: 0.6	-15.26
2000/12/21 13:26: 7.0	12.35
2001/12/21 19: 7:58.9	-6.89
2002/12/22 0:55:50.2	-0.90
2003/12/22 6:57:44.1	13.15
2004/12/21 12:23:55.9	-22.56
2005/12/21 18:31:27.1	18.77
2006/12/22 0:12: 6.5	-8.10
2007/12/22 6: 4: 4.2	3.21
2008/12/21 12: 3:19.7	10.51
2009/12/21 17:40:13.2	-11.86
2010/12/21 23:44:53.2	15.91
2011/12/22 5:21:41.8	-11.94
2012/12/21 11:14: 1.9	3.58
2013/12/21 17: 5:38.3	2.85
2014/12/21 22:55:15.2	0.86
2015/12/22 4:44:29.3	0.48
2016/12/21 10:28:12.6	-5.03
2017/12/21 16:22:18.6	5.35
2018/12/21 22: 2:52.6	-8.19
2019/12/22 4: 8:18.1	16.67
2020/12/21 9:47:46.7	-9.28
2021/12/21 15:42: 6.9	5.58
2022/12/21 21:42:35.6	11.73
2023/12/22 3:10:37.1	-20.73
2024/12/21 9:18:53.8	19.53
2025/12/21 14:53:32.3	-14.11
2026/12/21 20:47:37.8	5.34
2027/12/22 2:41:37.0	5.23
2028/12/21 8:13:52.5	-16.50
2029/12/21 14:19:45.1	17.12
2030/12/21 20: 0:48.9	-7.69
2031/12/22 1:58:26.5	8.87
2032/12/21 7:49:15.7	2.07
2033/12/21 13:38:28.5	0.46
2034/12/21 19:29: 5.7	1.87
2035/12/22 1:13:54.4	-3.94
2036/12/21 7: 6:22.3	3.71
2037/12/21 12:47:12.9	-7.91
2038/12/21 18:51:44.3	15.77
2039/12/22 0:25:56.5	-14.55
2040/12/21 6:17:35.0	2.89
2041/12/21 12:12:42.6	6.37
2042/12/21 17:47:45.5	-13.70
2043/12/22 0: 0:44.2	24.23
2044/12/21 5:34: 0.7	-15.48
2045/12/21 11:33:48.3	11.04
2046/12/21 17:28: 8.2	5.58
2047/12/21 23: 2:31.1	-14.37
2048/12/21 5: 7:41.4	16.42
2049/12/21 10:43:23.7	-13.05

The mean of the durations of these 60 tropical years was 0.62 minutes longer than the theoretical value 365.2421897 SI days specified above

Stamcose (talk) 15:35, 13 June 2011 (UTC)

It would be more appetising to present this information in a bar diagram. And modify in the last sentence, the presumptuous "was" longer. −Woodstone (talk) 11:12, 14 June 2011 (UTC)

Are we to understand that you, Stamcose, derived these numbers from the JPL ephemeris? Such a synthesis is against the rules, I believe. — And I agree with Woodstone that it's inappropriately bulky. I'd make it a graph of cumulative offsets; a graph of year-lengths would (I imagine) look like white noise. —Tamfang (talk) 18:33, 14 June 2011 (UTC)

Why is this table important?

The section Mean tropical year current value says:

The mean tropical year, as of January 1, 2000 was 365.2421897 or 365 days, 5 hours, 48 minutes, 45.19 seconds. This changes slowly; an expression suitable for calculating the length in days for the distant past is

365.2421896698 − 6.15359×10^⁻⁶T − 7.29×10^⁻¹⁰T² + 2.64×10^⁻¹⁰T³

The "mean value for January 1, 2000", how this now should be understood, is given with an accuracy of 1/100 seconds!

The formula for the "mean value" is even given as a function of time with an accuracy of about 1/100000 second!

With normal concepts one would talk about a mean value for 60 consequtive years (what I do) or possibly for 1 million consequtive years if a sensible analysis for this at all is possible! Sure, there is a theoretical model where "mean" for one single specified year is defined (in some special meaning). But instead of entering into complicated discussions/explanations about this it is more useful to generate such a tabel that explicitly shows how the durations of the individual years vary with many minutes! It is all a matter of many minutes, values with accuracy of 1/100 seconds or even 1/100000 seconds give a completly wrong impression of the accuracies involved. But with the table this is all clear and the many decimals make no harm anymore and could stay. But by preference be explained better!

Stamcose (talk) 22:33, 14 June 2011 (UTC)

References and notes

Please use numbered references with <ref> as all other Wikipedia articles. Notes can use letters. 167.107.191.217 (talk) 17:15, 14 March 2011 (UTC)

Please see Wikipedia:Citing sources, especially the statement "Editors are free to use any method for inline citations; no method is recommended over any other." Jc3s5h (talk) 18:17, 14 March 2011 (UTC)

Jc3s5h, you seem to support this method of referencing sources. I just want to point out that the vast majority of the readers of this article do not care from which page of which book the information he is reading comes from. I have no idea why you would support cluttering the article with that information. Could you please explain your thinking? Dave3457 (talk) 23:00, 9 September 2011 (UTC)

The method is effective when different parts of the same source will be cited many times. It is also easy to understand, so future editors will not have trouble figuring out how to add new citations. Also, readers who are familiar with the literature will recognize the sources immediately, without having to click to go to the footnote. These reasons are sufficient to cause a significant number of scholarly publications to use parenthetical citations. Jc3s5h (talk) 00:20, 10 September 2011 (UTC)

I can definitely appreciate why scholarly publications whose readers are familiar with the literature might use this form, and I can also appreciate that this is somewhat of a "specialized" subject. But Wikipedia is targeted at the general public not academics. I can't help but feel that we should be making Wikipedia as accessible as possible and the citations add clutter and a bit of confusion. I don't know what the "rules" are concerning this method, but may I suggest a compromise between the two points of view where we have the font of the references be at least reduced in size. It would make things clearer and less distracting for the general reader. Below is an example using the "small font" option at the top of the editing window.

... early astronomers did so by noting the time required between the appearance of the Sun in one of the tropics to the next appearance in the same tropic. (Meeus & Savoie, 1992, p. 40)

I personally think that it is a substantive improvement. Dave3457 (talk) 02:05, 11 September 2011 (UTC)

Irrespective of whether consensus ended up being reached regarding the referencing style, this is not a proper use of an editnotice (they go on the edit page, by reference to a special subpage). They're not supposed to be used as cleanup tags, and we're not supposed to add permanent disclaimers. I'm excising the editnotice, without implying an opinion on the style of referencing currently used here. TheFeds 06:57, 5 September 2012 (UTC)

The template does indeed seem to not be working. I don't know if a template can provide an edit notice. But the template is not being used as a cleanup tag. If it were working, it would provide a reminder to editors who might be more accustomed to seeing other citation styles. It seems to me this issue should be dealt with at the template, not in individual articles. If the goal is beyond the capabilities of templates, delete the template. If it is never appropriate to remind editors that an article uses a style that they might not be used to, delete the template. If it could work, and if reminders are appropriate, find someone to fix it. Jc3s5h (talk) 13:35, 5 September 2012 (UTC)

After further investigation I see the template won't work when it is added to the text of the article, it would have to be added as an editnotice by an administrator or account creator. Since I am neither, I've just restored TheFeds' deletion. As an aside, I don't agree with TheFeds that the edit notice is a disclaimer. The disclaimers page is all about providing warnings or labels regarding article content; that page does not address providing technical hints for editors on how to edit the article. Jc3s5h (talk) 14:30, 5 September 2012 (UTC)

Please see the referencing method of Mayer–Vietoris sequence for perhaps a compromise that all parties will be satisfied with. I can add an editnotice to Template:Editnotices/Page/Tropical year if required. Just use {{editprotected}} to attract the attention of an admin. — Martin (MSGJ · talk) 15:40, 5 September 2012 (UTC)

It would be easy to overlook the year in the last post that questioned the citation style: 11 September 2011. That edit suggested reducing the size of the inline citations. I would oppose that because I think the default font size in articles is too small, and I have my browser set to zoom in on all Wikipedia articles. So obviously I oppose shrinking anything but the most useless text. Jc3s5h (talk) 15:55, 5 September 2012 (UTC)

I'll add that I think the present form of citation is suitable for this article because there is a lot of misinformation about the tropical year. It's literally a religious conflict. Many Orthodox churches follow the Julian calendar, which tracks the tropical year more loosely than the Gregorian calendar or several proposals to reform the calendar. Much of the calendar reform literature was written before the invention of atomic clocks. So this is a topic where who made a claim and when they made it is likely to be on the mind of readers, and providing a short summary of this information inline is helpful. Jc3s5h (talk) 16:11, 5 September 2012 (UTC)

Maya versus Gregorian

I find it interesting that the northward equinox of March agrees with Mayan-Amizaduga figures of 1507 years (365.2422 = 1508x365 =1507 tropical) while the southward equinox of September supports the Gregorian 1600 years (and 400) figure of 365.2425 days showing two cultures can both be precise from their viewpoint rather than slam the Catholics as not having Mayan genius. — Preceding unsigned comment added by 98.144.71.174 (talk) 01:42, 11 October 2012 (UTC)

Year "0"?

What is this year 0 referred to in two of the tables? Our calendar runs like this Dec.31st in year 1 BCE , and the next day is Jan 1st, in year 1 CE (supposed year of the birth of Christ). Of course, this standard was introduced som 600 years later (rulers first year of reign was used in,before and after the time of birth of Christ), and most continued to change years in March, even though Gaivs Ivlivs Cæsar decreed Jan 1.st as new years day from the year 44 BCE.

However, there has not been a year 0, not even in calculation, so why use this as anything? — Preceding unsigned comment added by 94.234.170.181 (talk) 04:30, 19 February 2013 (UTC)

See Astronomical year numbering. Also, this usage is consistent with the sources that the tables were based on. Further, astronomical year numbering is more convenient for use with the equations that are included in the article. Jc3s5h (talk) 12:46, 19 February 2013 (UTC)

Not designed for tropical year

I don't agree that the Gregorian calendar was that it is designed to maintain synchrony with the tropical year, as the article says. The church didn't make a statement that (in modern terminology) they wanted to match the tropical year, or any average. It is just the modern way of thinking that judges it by secular standards. What is clear is that the Catholic Church's concerns were religious, and especially concerned Easter. The main issue was that the vernal equinox had been coming earlier in the year, and they wanted to keep it within a small range of days. How long the calendar does so depends on the vernal equinox year more than any other. And the Gregorian calendar article doesn't claim that it was designed for either the tropical or vernal year—it makes comparisons for both. Saros136 (talk) 06:51, 23 June 2014 (UTC)

Saros136 is quite right that the Gregorian calendar was designed to keep the astronomical vernal equinox close to March 21. The time between vernal equinoxes is one form of tropical year, although not the form used by modern astronomers. So the Gregorian calendar was designed to maintain synchrony with one form of the tropical year. Jc3s5h (talk) 12:13, 23 June 2014 (UTC)

The sentence I question referred to the tropical year, not a tropical year. The difference is crucial. The first normally means the mean tropical year. The writer or speaker has in mind a standard with a definite length, the one currently 365d5h48m45.1s long. I was judging the default meaning of the words, and using it myself.

The VE year is actually calculated by formula now, but it still represents closely a real interval, as opposed to an average. It is not just another kind of tropical year, it's more like the solstice years or the September equinox one.

Saros136 (talk) 03:23, 24 June 2014 (UTC)

The Alfonsine tables, first printed in 1483, were in general use in Europe at the time of the calendar reform. Dobrzycki critisizes the geometrical structure implicit in these tables as being "incoherent". A competeting hypothesis, published in the midst of the reform, was Copernican heliocentrism, and Dobrzycki considers an important improvement in the Copernican hypothesis to be "unequivocal definition of all the elements in the system of celestial coordinates". (p. 123) A new set of astronomical tables, based on the Copernican hypothesis, was the Prutenic Tables, which were used by the spokesman for the Gregorian reform, Christoph Clavius to investigate the actual and mean tropical years based on the vernal equinox, and decided the mean tropical year would be satisfactory.

So the design of the Gregorian calendar was based on the mean tropical year between vernal equinoxes, rather than the modern mean tropical year which is based on the mean elements of the Earth's orbit, and using calculations based on those elements, the time it would take for the Earth's ecliptic longitude to increase 360 degrees.

Work cited:

Dobrzycki, J. "Astronomical Aspects of the Calendar Reform." In G.V. Coyne, M. A. Hoskin, and O. Pedersen. Gregorian Reform of the Calendar:Proceedings of the Vatican Conference to Commemorate Its 400th Anniversary 1582&ndash 1982. (Vatican Observatory, 1983) p. 117–125. Jc3s5h (talk) 12:45, 24 June 2014 (UTC)

I have added a footnote to the article to indicate the exact type of tropical year used in the design of the Gregorian calendar. Jc3s5h (talk) 13:10, 24 June 2014 (UTC)

I'd recommend not using that guy for a source. He, like everyone else at the conference, thinks the vernal equinox year is the mean tropical year. Tom Peters :wrote about it on Calndr-L that "I found it striking that all of the authors of the conference equate (sometimes explicitly) the vernal equinox year with a (mean) mean tropical year of 365.2422 days. Apparently this distinction has not become generally known before Jean Meeus published expressions for the times of aequinoxes and solstices in his Astronomical Algorithms in 1991 (Chapter 26). However anyone looking for regularity or predicting of these events could have known." Saros136 (talk) 16:20, 26 June 2014 (UTC)

There's still usage issues here. Writing that the Gregorian calendar was designed for the tropical year, given common usage, is taken to mean the mean tropical year. Your footnote will be overlooked by most.

I still don't think we should say what the calendar was designed for. There were other factors, but we will never know all. They did not pick the most accurate they knew of.

What would be better would be a mention of the complications her in judging the calendars.

• Most people think the mean tropical year should is that standard (and believe that 365d5h48m45s value represents that average gap between vernal equinoxes).
• For those who know the modern language many just compare it to the MTY standard. Duncan Steel, in Marking Time: the Epic Quest for the Perfect Calendar is an astronomer who argues emphatically the in the spirit of the Catholic Church's main goal it should be compared to the VE year. (like most, he does not add tropical qualifier.) But probably many more others who may will continue to judge it by the MTY.
• Because the tropical year with no other qualifier is not the VE year, those of us referring to it need to make it clear right away that we're writing about the latter. Most (like Tom Peters above) do not add that's it is a tropical year, probably because it's unnecessary.

Saros136 (talk) 16:42, 26 June 2014 (UTC)

(edit conflict) The archive of calndr-l you provided does not contain the words "found", "striking", or "Peters", so I please provide a locatable position in that document so I can see what you're writing about.

Dobrzycki makes it clear the year used by Christoph Clavius was the mean vernal equinox year, and that he consulted both the Alfonsine tables and the Prutenic Tables. In the same book North on p. 79 states "Finally, for future reference, I note that Clavius claimed that for the Gregorian reform the mean of Copernicus' maximum and minimum values for the tropical year, namely 365d 5 h 49m 16.4s, the mean of 365d 5h 55m 37.7s and 365d 5h 42m 55.1s. I think it should be obvious that this is a method of finding a mean vernal equinox tropical year, and since the reader knows the Gregorian calendar was designed in the 16th century, the reader will understand the method of calculation will not be the same as today. Is this article really the place to go into the detailed history of the design of a calendar that is over 400 years old? Jc3s5h (talk) 16:46, 26 June 2014 (UTC)

We're using words differently. The four years defined by one of the equinoxes or solstices all have different lengths. The tropical year, or mean tropical year, is the average of those four, although it is not defined as such. The writers at that conference did not recognize the difference, and this is why what they wrote does not make it, as you say, obvious that this is a method of finding a mean vernal equinox tropical year , or that Copernicus was printing data with that in mind. Clavius and the others then did know that the measurements were not simply intervals of the vernal equinox. Copernicus had already decided that the tropical year should be measured by the sidereal year and precession, according to a source in the article. And I gave the wrong link last time. Now it's right.

This messyness is why we shouldn't make such definite statements about the design.

At any rate Clavius should not be taken at face value. He was under attack, and by his own account, they judged what the most accurate numbers were and almost perfectly matched it. The most accurate proposal made (eight of 33 years a leap one), known of long before the reform, was rejected. Because of the smaller cycle of 33 rather than 400 years, it doesn't wander as much from its own target.

The problem with the article is still that it says the tropical year, which always refers to the one that is the average of the equinox and solstice years. The one that ends with either 45s of 46s in a time citation. The one that's the subject of equations in the article. If you want to have that footnote, either change the text to a tropical year, or even better put the VE reference in the text. Saros136 (talk) 19:53, 7 July 2014 (UTC)

Calendar Year Fixing

If math people and astronomers would just think a little, just a little, they would have get the right answer for the Julian year calendar:
The reason for the day off every 128 years - not to be believed - is adding an extra day every 128 years!

Here:

365.242189... * 128 = 46,751.000192... days.

365.25... * 128 = 46,752 days.

As I said, extra day all along.
And here I read about ideas of disadd a Febuary 29 every year which is divided by 3200 - 775 leap years instead of 776. No need!

Here:

775/3200 + 365 = 365.2421875

The idea of this long period is a bummer and... unnecessary. why?
Because - if you divide both numbers of the 775/3200 fragment, you get: :31/128 = 365.2421875. This means 31 leap years (instead of 32) in a 128 year period. That's all! (יהודה שמחה ולדמן (talk) 19:00, 27 February 2014 (UTC))

The purpose of this article is to discuss improvement to the article. I can't figure out what the post of יהודה שמחה ולדמן is about, but it does not seem to be about improving this article. Jc3s5h (talk) 15:42, 28 February 2014 (UTC)

Do you have any compliments to say? Did you read anything here? Focus... יהודה שמחה ולדמן (talk) 23:27, 1 March 2014 (UTC)

יהודה שמחה ולדמן is arguing for a revision of the Gregorian calendar based on the mean tropical year. This was never the purpose of most calendars: they aim to match the vernal equinox year of 365.2424 days. No-one yet knows whether an adjustment will be necessary during the next 3200 years. See John Herschel's correction. Dbfirs 08:32, 16 January 2015 (UTC)

Introduction of changes by 156.61.250.250

I will make one final attempt to explain the nature of the errors being introduced by 156.61.250.250. My next step will be dispute resolution.

First, this is the main article about the tropical year. It is an appropriate place to discuss historical definitions of the tropical year, or alternate definitions used for particular purposes. In other articles, such as "Leap year", it would be wrong to write as if any of these historical or alternate definitions are the main value of the leap year adopted by the scientific community. It was wrong to remove an alternate definition that is useful for some purposes, such as understanding why the design goal of the Gregorian calendar is slightly different than approximating the tropical year (as defined by 21st century astronomers).

Also, if one reads page L8 in the "Notes and References" section of the Astronomical Almanac for the Year 2011 it explains how the tropical year value printed in the almanac (on page C2) is calculated. Note that the heading for the table of year lengths on page C2 is "The lengths of the principal years at 2011.0 as derived from the Sun's mean motion are:". This makes it clear the interval is not between the equinox crossing (or some kind of "mean equinox crossing" however that might be defined) some time in 2011 and the next equinox crossing some time in 2012. No, the duration of the tropical year is calculated at 2011.0.

This calculation is found by using the mean orbital elements of the earth (specifically the mean geometric longitude λ) and calculating the angular velocity of the Earth, that is dλ/dt. Then the time to cover 360° is found by calculating 360°/(dλ/dt). So the length of the tropical year is the length of time it would take for the mean geometric longitude to increase 360° if the rate of change of that remained constant. For practical purposes it doesn't matter over a few years; the rate of change in both the 2001 and 2011 almanacs (p. C1) was 0.98564736 degrees per day. But we should not misstate the current definition just because our definition is "close enough" to the correct definition. Jc3s5h (talk) 15:02, 9 March 2015 (UTC)

I agree that we should emphasise the current scientific definition, but we should also retain the calculation on which the Gregorian calendar was based (as we do). Both values are important. I don't understand why 156.61.250.250 removed the table with the separate calculations. Dbfirs 20:08, 9 March 2015 (UTC)

I have further examined the need to introduce a passage from Borkowski. I made up a spread sheet based on equation 3 in his paper, and found that to the 9 significant figures given in the Astronomical Almanac, Borkowski's equation gives the same length for a tropical year (365.242190 days of Terrestrial Time for any year between 2000 and 2003). Since the values agree, and the Astronomical Almanac is more prominent, and intended for a more general audience, than Borkowski's paper, I see no need to include the passage from Borkowski's paper. Jc3s5h (talk) 03:51, 10 March 2015 (UTC)

I supported your recent restoration, but I see that Woodstone doesn't like it. I assume his argument is that the difference was not perceived at the time the calendar was devised, which is a fair viewpoint, even though it was the vernal equinox that was being matched. I'm happy to leave things as they are, rather than revert, but I hope no-one starts removing further information. Dbfirs 17:51, 15 March 2015 (UTC)

Once again Jc3s5h emphasises we should be using official definitions:

The prestige of the United States and United Kingdom Nautical Almanac Offices is infinitely superior to an anonymous internet editor

[2].

The official terminology is "interval between mean equinoxes". 156.61.250.250 (talk) 16:58, 10 April 2015 (UTC)

I'm unhappy with your continuing campaign to remove the calculations of Jean Meeus from all Wikipedia articles. I agree that it would be useful to know the exact details of the calculations, but one has been verified by your own method, and the others could be similarly verified. Wikipedia does not require that all sources provide full details of all calculations. Meeus cites the exact data used in his calculations, and the values are cited elsewhere. It is not fair to remove referenced data just because you don't like it. Dbfirs 14:27, 7 May 2015 (UTC)

I too would prefer to keep the Jean Meeus references. His calculations are cited in many publications and he is always careful to provide reliable references to the astronomical literature. AstroLynx (talk) 15:10, 7 May 2015 (UTC)

On Talk:Year I see that an average length of the vernal equinox year over two millennia 1000 - 3000 is 365.242 360 days. Meeus and Savoie gave a "mean time interval between two northward equinoxes for the year 2000" of 365.242 374 days. If they can't be bothered to explain how they get that figure why should we quote them? "Providing reliable references to the astronomical literature" is a joke: Wikipedia requires author, title and page number. If Meeus cites the numbers he actually crunched perhaps you could pass the information on so that we can see if he did the calculation right. 156.61.250.250 (talk) 14:20, 8 May 2015 (UTC)

If you had taken the trouble to actually read the Meeus-Savoie paper, online here, you can see that the numbers were derived from the planetary theory VSOP87 of P. Bretagnon and G. Francou. The small difference with the value you cited from Talk:Year is probably not significant as the latter computation neglects higher order terms (T^3, T^4, etc.) in the polynomials representing the planetary motions. AstroLynx (talk) 14:53, 8 May 2015 (UTC)

That calculation of the average over 2000 years just verified the accuracy claimed by Jean Meeus for his year 2000 estimate. He didn't calculate his figure that way, of course, but used a refinement of the formula for mean tropical year, using ephemeris data from "Numerical Expressions for precession formulae and mean elements for the Moon and planets" - a paper by J L Simon, Pierre Bretagnon, J Chapront, M Chapront-Touze, G Francou and Jacques Laskar (whose formula you use). I agree that we would like to know exactly how he modified Laskar's formula for the separate equinoxes and solstices. If we can't find the detail, perhaps we should write to him, or perhaps Jacques Laskar can explain if you know him personally. See our article VSOP (planets) for the data used by Jean Meeus. Dbfirs 15:35, 8 May 2015 (UTC)

Meeus has published a few editions of a book, Astronomical Algorithms, and I have seen hints in internet searches this book includes information on year length. If someone has a nearby library with this book, perhaps you could take a look and see if it gives more details about his method. Jc3s5h (talk) 15:25, 8 May 2015 (UTC)

The formulae used for the four separate calculations are given in chapter 26 of Jean Meeus' "Astronomical Algorithms" (1991) according to one account, but I don't have access to a copy of the book. Dbfirs 16:25, 8 May 2015 (UTC)

The full details on how this is computed (again from VSOP87) is indeed found in Jean Meeus, Astronomical Algorithms: Second Edition (Richmond: Willmann-Bell, 1998), chapter 27 ("Equinoxes and Solstices"). See also Jean Meeus, More Mathematical Astronomy Morsels (Richmond: Willmann-Bell, 2002), chapter 63 ("The Gregorian Calendar and the Tropical Year") for even more detail. AstroLynx (talk) 16:39, 8 May 2015 (UTC)

(ec)Bouasse, cited by Meeus and Savoie, doesn't appear to know much. He thinks "the true tropical year is the time interval between two successive passages of the Sun through the vernal equinox" and "the mean tropical year is the mean of a large number of true tropical years". Yes, about 25,000 of them (using his definition) but does he know that? I see that VSOP 87 provides the mean tropical year. On page 41 Meeus and Savoie appear to have overlooked the fact that "the vernal point" is also subject to the equation of the centre. The claim that "it was the length of the tropical year as derived from" the Alphonsine Tables is wrong. The astronomers averaged three sets of tables, because they all gave different longitudes for the sun and there was no reason to trust one more than the others. [156.61.250.250 - please sign your contribs correctly!]

On page 42 there is another blooper: "It should be noted that the tropical year is not equal to the (mean) time interval between two successive spring equinoxes". They then say that the equation of the centre affects the length of the mean tropical year. That's like saying the equation of the centre affects the length of the mean sidereal month, so that the sidereal month is not 27.32166 days at all, but variable depending whether you start from the ascending node, or the descending node, or the perigee, or the apogee, or some other point. [156.61.250.250 - please sign your contribs correctly!]

So if the mean time interval between two successive equinoxes or solstices (same season) is found to be different from the mean tropical year we know they calculated wrong. We don't know how Meeus deduced the figures from VSOP 87, and until we do we can't use them. 156.61.250.250 (talk) 17:33, 8 May 2015 (UTC)

All I can track down is [3]. They appear to be playing around with formulae for the elements of the planetary orbits. The only thing you can derive from that is the instant of any given equinox or solstice. Unless they can say which equinox or solstice they used we can't use their values. Presumably these are formulae which we have to put the arguments into to get a value, and they won't say which arguments they put in and what the result was. 156.61.250.250 (talk) 17:58, 8 May 2015 (UTC)

This series of edits introduces numerous errors so I have reverted them. I'll mention a few of the errors:

"Since antiquity, astronomers have progressively refined the definition of the tropical year. Meeus and Savoie, 1992 p. 40 define it as the time required for the mean Sun's tropical longitude (longitudinal position along the ecliptic relative to its position at the vernal equinox) to increase by 360 degrees". Meeus and Savoie use numerous definitions, historical as well as current. In the lead it is essential to inform the reader of the current meaning, rather than obscuring it with names of authors.

"The mean tropical year (averaged over equinoxes and solstices) on 1 January 2000 was 365.242189 days according to the calculation of Laskar (1986), each day lasting 86,400 SI seconds." No, it is the time required for the mean ecliptic longitude of the Sun to increase by 360°.

"Values of mean time intervals between equinoxes and solstices (the mean tropical year) were provided by Meeus and Savoie (1992, p. 42) for the years 0 and 2000." The current meaning of mean tropical year (the word mean being optional) is the time required for the mean ecliptic longitude of the Sun to increase by 360°. The mean interval between a given equinox or solstice is different.

This was inserted into the lead:

Ancient tables provided the sun's mean longitude. Christopher Clavius, the architect of the Gregorian calendar, noted that the tables agreed neither on the time when the sun passed through the vernal equinox nor on the length of the mean tropical year. Tycho Brahe also noticed discrepancies. The Gregorian leap year rule (97 leap years in 400 years) was put forward by Petrus Pitatus of Verona in 1560. He noted that it is consistent with the tropical year of the Alfonsine tables and with the mean tropical year of Copernicus (De revolutionibus) and Reinhold (Prutenic tables). The three mean tropical years in Babylonian sexagesimals as the excess over 365 days (the way they would have been extracted from the tables of mean longitude) were 14,33,9,57 (Alphonsine), 14,33,11,12 (Copernicus) and 14,33,9,24 (Reinhold). All values are the same to two places (14:33) and this is also the mean length of the Gregorian year. Thus Pitatus' solution would have commended itself to the astronomers.

This is utterly unsuitable for the lead of the article. Indeed, it is unsuitable for this article; that sort of discussion, if it belongs in an encyclopedia at all, would belong in the "Gregorian calendar" article. But there are no citations, and I recall reading several different points of view about why the reformers adopted the value they did.

There is one change I see that, while not required, may be helpful to some readers: "The Gregorian calendar, as used for civil purposes, is an international standard. It is a solar calendar that is designed to maintain synchrony with the mean tropical year. I will add that change. Jc3s5h (talk) 23:37, 8 May 2015 (UTC)

The current meaning of mean tropical year (the word mean being optional) is the time required for the mean ecliptic longitude of the Sun to increase by 360 degrees. The mean interval between a given equinox or solstice is different.

How so? The interval between two mean occurrences of a given equinox or solstice is a direct function of the increase in the mean ecliptic longitude. 156.61.250.250 (talk) 11:38, 9 May 2015 (UTC)

No, as the times of the equinoxes and the solstices also depend on the eccentricity and the line of apsides of the apparent solar orbit which slowly vary. Only over very long periods will the various tropical years (mean, vernal-equinoctial, summer-solstitial, autumn-equinoctial & winter-solstitial) be equal. AstroLynx (talk) 11:51, 9 May 2015 (UTC)

If you're adding a function which corrects for the equation of the centre you are applying a term to the mean value. So your mean value becomes actual. It is no longer mean. 156.61.250.250 (talk) 12:03, 9 May 2015 (UTC)

To get the actual values of the equinoxes & solstices you also have to add the numerous planetary perturbations, the correction for the earth-moon barycentre and nutation. In the various equinoctial and solstitial tropical years discussed by Meeus these are neglected (i.e. "averaged-out"). AstroLynx (talk) 12:23, 9 May 2015 (UTC)

You're supposed to be a professor of mathematics but you're making a mistake that a secondary school mathematics student wouldn't make. As I understand it, you start with the mean then you concoct a suitable sine curve function to get the first approximation, then the second and so on. It's best to start with the correction that best matches the actual value then refine with successive functions. Some changes are believed to be very long periodic functions but it's not possible to separate the periodic from the secular. In the theory, correcting for the equation of the centre is done first, to get as quickly as possible very near to the actual value - these other corrections are just icing on the cake. The initial correction is the most significant adjustment to the mean - if you told a twelve - year old mathematics student that after doing that you still had a mean value she wouldn't believe you. 156.61.250.250 (talk) 12:45, 9 May 2015 (UTC)

Your response tells me that you have no clue how these phenomena are routinely calculated. Perhaps you should first read the books of Jean Meeus and do some of the computations yourself before you criticize his methods. You are very quick in criticizing the works of others but what have you ever published on this topic?

I should furthermore correct you: although I do a lot of computing on a daily basis, I never claimed nor am I a professor of mathematics. AstroLynx (talk) 13:11, 9 May 2015 (UTC)

The word mean is meaningless (sorry) unless you specify over what values the average is being taken. Usually it is obvious, so there is little need to specify, but here we have various possibilities. In the case of the mean tropical year, the average is taken over perturbations in the orbit and is calculated for a particular point in time. There is no logical reason why one particular perturbation cannot be taken into account when calculating the mean time between vernal equinoxes on a specified date. The fact that the calculation agrees almost exactly with the mean over time (over both 2000 years and 200 years) suggests that the method has merit. Dbfirs 13:07, 9 May 2015 (UTC)

(Edit conflict). What AstroLynx said. "Mean" has many meanings in astronomy. 156.61.250.250's reference to the equation of the center is apt; the mean anomaly is similar to mean longitude (although I'm still checking some subtleties like the distinction between the Earth and the Earth-Moon barycenter). Periodic terms such as the annual variation in angular speed due to the elliptical orbit have been removed; it is almost equivalent to treating the orbit as circular with the same period as the elliptical orbit.

We don't know the exact procedure Meeus and Savoie used, but they may very well have used the mean orbital elements; the orbit is treated as an ellipse. Periodic disturbances have been smoothed out, but the orbit is an ellipse and the changes in angular velocity due to the position of the Earth in its orbit will cause different lengths of the tropical year. Mean orbital elements are available in papers by J. Laskar ("Secular terms of classical planetary theories using the results of general theory", Astronomy and Astrophysics, v. 157 pp. 59-70, 1986) and J. L. Simon et al. ("Numerical expressions for precessional formulae and mean elements for the Moon and planets", Astronomy and Astrophysics, v. 282 pp. 663-683, 1984). Simon's results are used for the tropical year length printed in the Astronomical Almanac.

Another meaning for "mean" is the position of a celestial object (or plane) taking into account precession, but not nutation. So the true equinox would be the intersection of the true celestial equator of date and the true ecliptic of date. To have a mean equinox, one must be using a theory of planetary motion and Earth orientation that separates precession and nutation; the mean equinox is the intersection of the mean celestial equator of date and the mean ecliptic of date. For this meaning, the only difference is nutation; the Earth would have its true position in its orbit, affected by perturbations due to gravitational attraction by other planets. Such perturbations are smoothed out in the mean elements computed by Laskar or Simon et al, so the meanings of "mean" are different. Jc3s5h (talk) 13:23, 9 May 2015 (UTC) Added corrections & clarifications 20:21 UT.

The flaw in Jc3s5h's argument is that since the equinox precesses the "mean equinox" must be related to that movement. The technical term is "mean equinox of date". The "mean tropical year" is likewise the mean tropical year referred to a specific epoch (e.g. J2000). Astronomers specifically exclude terms relating to the equation of the centre in their definition of the mean tropical year. In the same way, effects due to obliquity and eccentricity are excluded from the definition of Greenwich Mean Time. 156.61.250.250 (talk) 13:57, 9 May 2015 (UTC)

I apologize for not remembering that while the instantaneous equator is affected by nutation, the instantaneous ecliptic is not, so I should not have applied the terms "true" or "mean" to the ecliptic, and should have applied the term "of date" since I was referring to the instantaneous planes. I agree with what 156.61.250.250 wrote at 13:57, 9 May 2015 (UTC). However, the mean vernal equinox tropical year does involve the equation of the center, and so is different from the mean tropical year. The mean vernal equinox tropical year is not normally used by modern astronomers (but Meeus and Savoie decided to discuss it their paper, and others, such as Richards ("Calendars" in Explanatory Supplement to the Astronomical Almanac, 2013, pp. 586) and McCarthy & Seidelman 2009 (full citation in article), p.18, have cited this paper.

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