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Talk:Axial precession

/Archive 2005–2008

Does a Precession Formula Exist?
The astronomical formulas I have seen appear to be based on working back from known observational data (e.g., the earth's precession around the Ecliptic Pole, the Anomalous Precession period, the Lunisolar Precession period, Apsidal (Perihelion) Precession and the "Mercury Question", etc.).

Is there an actual standard formula that exists to calculate precession? Specifically, one that allows the user to enter applicable values (mass of the bodies, distance, orbital period, rotation period, obliquity, etc.), and come up with the precession value? Such a formula should work with any given value (including values given for any hypotheical planetary system).

Unless such a formula exists in the scientific community, I tend to agree with those who hint that determining Precession remains an open-ended mystery (at least regarding both its cause and its affect outside calculations based on direct observation).

Granted, any standard formula would only be accurate to so-many decimal places (due to not being able to account for ALL the multitude of minor gravitational influences from lesser bodies throughout any given system and beyond). Nevertheless, if science has determined the true cause and affect of precession, then a standarized formula (with known-body input values)should exist. Otherwise, any questioning mind may be justified in questioning the existing theories.

The many with greater knowledge may know of such a formula. If so, may it be included on the Wiki page? Oh ... and it would be super if it was written in a manner that is can be interpreted by mathematically limited individuals (who, me?!). --Tesseract501 06:10, 12 October 2008 (UTC)

 * My dear Tesseract501, thank you for understanding so well the problem of precession and I wish you a lot of success in your future researches. The fact that in front of this problem I am not alone anymore gives me a soul peace that will help me in my own researches. --Abel Cavași (talk) 08:03, 25 October 2008 (UTC)

 * I am adding a set of equations. — Joe Kress (talk) 17:18, 24 December 2008 (UTC)

Yes, there are many precession nutation models, the most comprehensive is the 2000A model with almost 1400 terms. The problem is the models are "not consistent with dynamical theory" according to the International Astronomical Union (IAU 2006 P03). Also, while the models find a value close to the observed rate they have been unable to predict "changes" in the precession rate (such as the constant increase in the rate over the last few hundred years). Consequently, the models are revised or modified every few years to better match precession observations. This has been going on since d'Alembert substantially modified Newton's formula which did not work. Of course the changes keep getting smaller but one has to wonder if many of the unknown dynamic assumptions (concerning the shape and viscosity of the earth's core, etc.) are included to make the model fit the observable. Interesting area of study. —Preceding unsigned comment added by 69.234.46.179 (talk) 21:33, 16 November 2009 (UTC)

Precession of the equator
The section referring to precession of the equator should be deleted ASAp unless a reference supporting the assertion that `precession of the equinoxes' has been replaced by 'precession of the equator' Terry MacKinnell (talk) 22:52, 27 February 2009 (UTC)

 * I'll add the official IAU 2006 resolution recommending that lunisolar precession be replaced by precession of the equator and that planetary precession be replaced by precession of the ecliptic. The sum of lunisolar precession and planetary precession was called general precession, which has not changed. I checked the IAU 1938 resolutions, and they refer to lunisolar precession, planetary precession and general precession, so those terms are at least that old. These terms also appear in Simon Newcomb's A Compendium of Spherical Astronomy (1906) who does mention precession of the equinoxes, but only while discussing ancient astronomers. This is becoming ridiculous! How long do new terms have to be in use before the old terms are retired?

 * A much more serious problem is that the opening sentence stating that precession is the motion of the rotational axis with respect to inerital space is not quite right. That is only its major component formerly called lunisolar precession and now called precession of the equator. This ignores the motion of the reference plane itself, the ecliptic, formerly called planetary precession and now called precession of the ecliptic. — Joe Kress (talk) 01:39, 28 February 2009 (UTC)

 * I have rewritten the lead due to my concerns. The first paragraph is a bit bloated by the need to include all the various precession terms, which I have included in chronological order. Improvements are welcome. — Joe Kress (talk) 07:40, 28 February 2009 (UTC)

 * I just reordered this because it didn't flow properly in my opinion. There was an abrupt discontinuity between the two paragraphs in the lead, as if one had been written without any regard for the other. I think we need to begin with a "precession is"-type sentence, and proceed from the general to the specific, rather than launch into detail from the first sentence only to then backtrack to a layman's explanation. Personally I'm happy with the opening statement that precession is the slow change in orientation of the axis, because that gives the ordinary reader a "good enough" (at this point) picture of roughly what the concept is. Then the detail can be expanded (as it is). 86.138.104.133 (talk) 02:58, 2 March 2009 (UTC)

 * ... but bearing in mind your concerns, I just tweaked it again to try to give a more general opening definition that covers all the bases. Please make any necessary changes, but I really do think we need to start with "precession is... ". That's my view anyway. 86.138.104.133 (talk) 03:11, 2 March 2009 (UTC).

 * I have no objection to your reorganization, although I still have more tweaking to do as a result of more research. I've traced the earliest use of the trio lunisolar precession, planetary precession, and general precession back to 1863. Earlier, planetary precession had other names like planetary perturbation, although both lunisolar precession and general precession were in use. I suspect that equivalent German terms were in use as early as 1830. — Joe Kress (talk) 14:38, 2 March 2009 (UTC)

What pre-modern astronomers called it
It's not very clear who these 'pre-modern' astronomers are supposed to have been, who called it the 'precession of the equinoxes'. Plenty of sources show that up to about the end of the sixteenth century AD, which is pre-modern if you like, it was often called 'the motion of the eighth sphere' (e.g. 'De motu octavae sphaerae', I.Werner, Nuremberg, 1522). 'Precession of the equinoxes' is a _relatively_ modern term.

It's also not very clear that the term 'precession of the equinoxes is out of date, either. It's not equal to either the 'precession of the equator' or the 'precession of the ecliptic' -- it's the combined effect of the two of them together. Is there a replacement terminology for that? —Preceding unsigned comment added by 86.14.225.140 (talk) 18:15, 1 March 2009 (UTC)

 * You are correct that in non-technical discussions (no detailed mathematics), precession of the equinoxes is still in use, which is one of the tweaks I am making. All of the terms now in the lead are in current use, but the motion of the eighth sphere, trepidation, and similar terms are not, so I don't think they belong in the lead. Of course, they do belong in the historical section. The technical replacement for precession of the equinoxes is general precession which is the combination of precession of the equator and precession of the ecliptic. It was not changed in 2006, so it was also the combination of lunisolar precession and planetary precession. — Joe Kress (talk) 14:38, 2 March 2009 (UTC)

Precession direction
Isn't the direction of the precession wrong in the picture? The angular momenta is supposed to be conserved and thus the precession must be in the same direction as the body is spining. Besides I actually found another copy of the same image on the internet with the correct direction of the precession.

Samuel —Preceding unsigned comment added by 83.250.175.92 (talk) 22:23, 5 March 2009 (UTC)

No! Precession is in the opposite direction to the spin - otherwise it would be called PROcession of the equinoxes! TomNicholson (talk) 15:33, 18 November 2009 (UTC)

Question
If the Earth's axis of rotation is orthogonally projected to the plane of the solar system, is the projected direction parallel to the major axis of the orbit? If so, is there an explanation of such a phenomenon in gravitational terms? 132.70.50.117 (talk) 10:23, 5 May 2009 (UTC)

 * The two are not parallel because the two precessions discussed in the article have different periods, the precession of Earth's rotational axis in inertial space and the precession of the major axis of Earth's orbit, also known as anomalistic precession (the last section in the article), which is the advance of the line of apsides (perihelion and aphelion). The projection of Earth's rotational axis onto its orbital plane is from/to the solstices (winter/summer), now about December 21/June 21. Conversely, the major axis of the orbit is from/to the apsides (perihelion/aphelion), now about January 3/July 5. The Gregorian calendar is "tuned" to the equinoxes and solstices, so their dates remain relatively fixed, even though their precession is 50.3"/year in inertial space. But the dates of the apsides move forward in the Gregorian calendar because they advance 11.6"/year in inertial space. The sum of 61.9"/year causes a relatively rapid calendrical advance. In terms of years, the average length of the Gregorian year is 365.2425 days which is nearest the vernal equinox year of 365.242374 days. The anomalistic year at 365.259636 days is even longer than the sidereal year. The lines were parallel about the year 1225 when the length of autumn equalled that of winter and spring equalled summer. The lines will be perpendicular about 3825 causing spring to equal autumn and causing the lengths of winter and summer to be maximally different. This is discussed in The Lengths of the Seasons (on Earth) by Irv Bromberg. — Joe Kress (talk) 03:12, 6 May 2009 (UTC)

 * Thanks, that's very interesting. Which of the two precessions is supposed to be explained by the equatorial bulge? 132.70.50.117 (talk) 11:46, 6 May 2009 (UTC)

 * Earth's equatorial bulge interacts mainly with Moon, because its declination alternates between being north of and south of the equatorial bulge. This both causes and stabilizes the Earth axial wobble and tilt as well as the lunar orbital tilt. Lunar precession is much larger than planetary precession. Kalendis (talk) 03:30, 5 March 2017 (UTC)

Current precession cycle?
When does the current precession cycle finishes? Echofloripa (talk) 23:14, 16 July 2009 (UTC)

 * Precession never ends. It takes about 26,000 years for the vernal equinox to precess completely around the ecliptic (the apparent path of the Sun on the celestial sphere). At the same time Earth's axis precesses causing the celestial north pole to trace a circular path on the celestial sphere. So we can say that our current north star, Polaris, will cease to be the north star in only a thousand years and will not be the north star again until 26,000 years from now. You may be thinking of the position of the vernal equinox in specific zodiacal constellations. Because the ecliptic is astrologically divided into twelve constellations, the vernal equinox spends roughtly 2,150 years in each constellation. While the vernal equinox was in the constellation of Pisces, we were in the Age of Pisces. When precession causes the vernal equinox to move into the next zodiacal constellation, Aquarius, the Age of Aquarius begins. Astrologers differ on when this occurs, varying from 1447 AD to 3621 AD, although many think we entered the Age of Aquarius during the 20th century. Also see astrological age. — Joe Kress (talk) 02:33, 17 July 2009 (UTC)

Name change
Zbayz changed the name of this article from "Precession (astronomy)" to "Axial precession (astronomy)" without any discussion whatsoever. His stated reason was "This article only discusses precession of the rotational axis. It says nothing about perhelion precession." both of which are wrong. Although the dominant focus of the article is 'axial precession' it does mention "planetary precession" now renamed "precession of the ecliptic" and "anomalistic precession". The proper name for 'axial precession' is either the old name "lunisolar precession" which was used for at least two centuries or its new name, since 2006, "precession of the equator". Furthermore, this article mentions "planetary precession" now renamed "precession of the ecliptic" which is the gradual change in the inclination of Earth's orbit relative to the invariable plane of the solar system and the combination of "precession of the equator" and "precession of the ecliptic" which is called "general precession" and has been so named for at least one and a half centuries. This article also has a section on "anomalistic precession" at the end of the article, which Zbayz calls "perihelion precession", but refers to an article named apsidal precession.

Zbayz also did not follow Wikipedia naming conventions for disambiguating articles. Do not use a parenthetical qualifier unless two or more articles have the same name. — Joe Kress (talk) 22:42, 25 August 2009 (UTC)

 * I think that the different motions should have their own articles. Then we can call this one "precession of the equator". Zbayz (talk) 12:35, 26 August 2009 (UTC)

 * Other thoughts: Since "ecliptic" is about the Earth, "precession of the ecliptic" doesn't seem a very good name for variation in the orbital inclination of celestial objects in general. Also the phrase "anomalistic precession" seems to be hardly used at all. Zbayz (talk) 16:30, 26 August 2009 (UTC)

Astronomy/Astrology splitting suggestion
I suggest to split out astronomic scientific material of this article and through out pseudoscience astrological data. There is no reasons to cover both this topics in the article. Astrology - is a cultural phenomenon, not the science. Thank you. —Preceding unsigned comment added by 95.133.136.138 (talk) 14:14, 7 September 2009 (UTC)

Are you suggesting that science is not a cultural phenomenon? TomNicholson (talk) 15:36, 18 November 2009 (UTC)

Astrology was (and for a long time) the reason for astronomy. I notice it has lost cultural colective favour (except in Biblical instances such as the star of Bethlehem, kings choosing when to procreate etc - where it is regarded as a part of gods plan) When you say ' through out' pseudoscience astrological data. I presume you mean - 'throw out'. This vandalism you blithely propose is just that. 188.220.186.57 (talk) 15:29, 30 August 2011 (UTC)

20 minutes per year - is that right?
From the Effects Para: Thus, the tropical year, measuring the cycle of seasons (for example, the time from solstice to solstice, or equinox to equinox), is about 20 minutes shorter than the sidereal year, which is measured by the Sun's apparent position relative to the stars. Note that 20 minutes per year is approximately equivalent to one year per 25,771.5 years, so after one full cycle of 25,771.5 years the positions of the seasons relative to the orbit are "back where they started".

I calculate that 20 minutes per year gets 360 degrees of precession in 72 years not in 25,771.5 years. What's going on here? Who did this math?Lkoler (talk) 04:53, 16 October 2009 (UTC)

 * From Values, the constant rate of precession is 5,028.796195"/Julian century or 50.28796195"/Julian year. A Julian year is 365.25 days. The number of arcseconds in 1° is 3600".
 * 72 years is only 1° of precession via $$\tfrac{3,600}{50.28796195} = 71.58770927$$
 * Multiply by 360° to get 25,771.5 years via $$360\times 71.58770927=25,771.57534$$
 * Calculate 20 minutes via $$\tfrac{50.28796195}{1,296,000} \times 365.25 \times 24 \times 60 = 20.40853122$$
 * — Joe Kress (talk) 06:21, 16 October 2009 (UTC)

 * Thanks for responding so soon. I'm sorry but, I calculated the precession to be 3.34 seconds per year and not 20.4 mins. If you look here in the Journal of Theoretics, you will see how I got there. The problem in your calculations is that you are assuming that the tropical year (365.25631 days of 86400 secs. each) and the sidereal year (366.25631 days of 86164.0905 secs. each) are not the same. But, because of the extra rotation for the sidereal year (see Donald Sauter’s brain teaser at  to find out why), you will see why you were wrong. Don't be surprised about this: almost all textbooks and astronomical references are wrong on this point, too. Lkoler (talk) 22:42, 16 October 2009 (UTC)

 * Wikipedia does not allow fringe theories in its articles. It only allows what "almost all textbooks and astronomical references" state. — Joe Kress (talk) 08:58, 17 October 2009 (UTC)

 * It's not a theory to state a fact. 366.25631 sidereal days is exactly one (1) day longer than most people use in their calculations (note that calculations are also not theories) for the sidereal year. Please get your definitions correct if you are going to quote Wikipedia rules.Lkoler (talk) 15:27, 17 October 2009 (UTC)

 * Lkoler, the number of days (sidereal or otherwise) per year (sidereal or otherwise) has no bearing on the statement, "20 minutes per year is approximately equivalent to one year per 25,771.5 years" which can be verified using basic high school maths of proportion and ratio, as patiently demonstrated by Joe Kress above. TomNicholson (talk) 16:13, 18 November 2009 (UTC)

I agree with Lkoler. Common sense indicates otherwise. 20 extra minutes per year? There are 24 hours in a day. 20 minutes is 1/72 of 24 hours. Certainly, the stars(celestial sphere) are not adjusting 1/72 every year. That would put precession at super speed and we would be cycling through the constellations every 72 years. Something is wrong in the math. Common sense just doesn't support it.

If time passes by, then the celestial sphere moves. Actually, the celestial sphere moving is the cause of the time measurement, not the other way around. So, if the celestial sphere moves 20 extra minutes from what it was the year before, it must move 1/72 of the angle of the sky. 360 degrees multiplied by 1/72 is 5 degrees of the sky every year. And (divide 5(18,000 arcseconds) degrees by 365 days)would have to move about 50 arcseconds every day. This does not happen.

Remember, an extra 20 minutes per year would mean the celestial sphere shifts 5 degrees every year, and 50 arc seconds per day. It's not 50 arc seconds per day, it's 50 arc seconds per year. Hipparchus could tell you that. It's obvious, but a lot of people are getting it wrong for some reason.--Markblohm (talk) 18:10, 8 December 2009 (UTC)

 * The math is fine. The difference of 20 time minutes between the tropical and sidereal year means an adjustment in the sky of (20 minutes) / (1 year) or ~0.0038% of the sky, or ~0.86 arc-seconds / year.  Dragons flight (talk) 18:29, 8 December 2009 (UTC)

An extra 20 minutes causes the earth to point 5 full degrees different in relation to the stars. Just like an extra 12 hours would cause a 180 degree change. Think about it. 1 tropical year is when the sun is back to the same position in relation to the earth. A tropical year plus 12 more hours would have us facing the opposite way. Likewise, 20 extra minutes would have us facing 5 full degrees off from the previous. Say at time zero you are facing 0 degrees angle. 1 day later you are also facing 0 degrees angle. 100 days later, still 0 degrees angle. 1 tropical year later exactly, and you are facing 0 degrees angle. But what is being said is that 20 more minutes is being added to the tropical year. That is 5 full degrees extra of the celestial sphere(because we have a 24 hour day). 1 tropical year later, the sun is in the same position. The shift is 50 arcseconds of the celestial sphere/year(this shift of 50 arcseconds has been observed for a long time, and is much less than 20 minutes.--Markblohm (talk) 21:06, 8 December 2009 (UTC)

I now understand why the time of around 20 minutes is being found. The math is not wrong. The equation is wrong. Precession is independent of the spin of the earth, so to account for the total seconds of the spin of the earth in a year when finding the real time change of precession is incorrect. Even if we say that it is wobbling, the wobbling is occurring independent of the spin. The "wobble" is only about 50 arcseconds, and is independent of the spin of the earth. We add the extra wobble time onto the total spin at the end of the year. After all, 50 arcseconds of angle(or 3.3 seconds of real time) is the change each year, which is clear to observing astronomers in the past and present.--Markblohm (talk) 01:47, 9 December 2009 (UTC)

 * Everyone agrees that precession is about 50"/yr, but some disagreement exists concerning its equivalent time per year. The value of 3.34 seconds per year which Houmann and Lkoler use was apparently obtained by multiplying 9.12 ms per sidereal day by the number of sidereal days in a tropical year, which disagrees with the value of 20 minutes per year usually quoted. A solution is to obtain both from angular precession.

 * In 1900, precession was specified as 50.265"/tropical year, which decreased slightly since then. Since 1984, precession has been specified as 50.29" per Julian year because the length of the Julian year (365.25 days of 86,400 SI seconds each) is known with ultimate precision and it never changes. In astronomy, unlike geometry, any 'year' or 'day' is always 360° or 1,296,000", regardless of its length. Thus a sidereal year, a Julian year, a tropical year, a sidereal day and a solar day all have an angular duration of 1,296,000". To shorten the equations, I'll use 'd' for the dimension of a sidereal day of 86,164 seconds and 'D' for the dimension of the slightly longer solar day of 86,400 seconds. Both the numerical values and their dimensions are critical in this analysis.

 * First determine the time per sidereal day using the new value of precession:
 * $$50.29\text{/yr}\tfrac{86,164\ \text{s/d}}{(365.25\ \text{D/yr})(1,296,000\text{/D})}=9.154\ \text{ms/d}$$
 * Then determine the time per Julian year also from that precession:
 * $$50.29\text{/yr}\tfrac{(365.25\ \text{D/yr})(86,400\ \text{s/D})}{1,296,000\text{/yr}}=1225\ \text{s/yr}=20.42\ \text{minutes/Julian year}$$
 * To convert time per sidereal day into time per Julian year, combine the conversion factors by rearranging the first equation so that it can replace the angular precession in the second equation:
 * $$9.154\ \text{ms/d}\tfrac{(365.25\ \text{D/yr})(1,296,000\text{/D})}{86,164\ \text{s/d}}\tfrac{(365.25\ \text{D/yr})(86,400\ \text{s/D})}{1,296,000\text{/yr}}$$
 * $$=9.154\ \text{ms/d}\tfrac{(365.25\ \text{D/yr})^2}{\ }\tfrac{(1,296,000\text{/D})(86,400\ \text{s/D})}{(1,296,000\text{/yr})(86,164\ \text{s/d})}=1225\ \text{s/yr}=20.42\ \text{minutes/Julian year}$$
 * Time per sidereal day must basically be multiplied by the square of the number of days per year, not by just the number of days per year (other terms eliminate the square dimensions). So 3.34 s/yr is wrong, whereas 1225 s/yr is correct. — Joe Kress (talk) 21:26, 9 December 2009 (UTC)

No matter what equations you throw up, 50 arcseconds can never be anything other than 3.3 seconds of real time, just as 180 degrees can never be anything but 12 hours of real time. The spinning earth arcseconds do not get factored into the precession equation. You have made the very common error.--Markblohm (talk) 01:58, 10 December 2009 (UTC)

 * It is much simpler to find the difference between the tropical and sidereal years. According to the Useful constants of the International Earth Rotation and Reference Systems Service (IERS), the sidereal year is 365.256363004 days and the tropical year is 365.242190402 days, where both are in mean solar days of 86,400 seconds each at 2000 January 1 noon Terrestrial Time. Their difference is 0.014172602 days or 20.408547 minutes.

 * If the Sun was directly overhead (0°) at the beginning of a tropical year, the only way it could be directly overhead (0°) at the end of one tropical year is if that tropical year had a whole number of days. But a tropical year is 365.2422 days. The extra 0.2422 days beyond an integral number of days means the Sun must be near the western horizon near sunset. — Joe Kress (talk) 05:06, 10 December 2009 (UTC)

It appears to me that Lkoler and Markblohm are consistently confusing two kinds of circular motion. 50 arcsec of daily rotation takes 3.3 sec "of real time", but 50 arcsec of annual revolution takes 365 times as long. But that's so obvious that someone ought to have pointed it out by now, so have I missed something? —Tamfang (talk) 06:04, 10 December 2009 (UTC)

 * Good point. If the 365.25 D/yr term is removed from my second equation immediately above, then the remaining equation is
 * $$50.29\text{/yr}\tfrac{86,400\ \text{s/D}}{1,296,000\text{/yr}}=3.35\ \text{s/D}$$
 * Because this result is 3.35 seconds, albeit per day rather than per year, it implies that Lkoler and Markblohm have overlooked a term. I find the term "of real time" unnecessary and mysterious. — Joe Kress (talk) 08:37, 10 December 2009 (UTC)

Ah, but we're not measuring 50 arcseconds of annual revolution. If we measure 50 arcseconds of annual revolution(earth's orbital circumference) then we do get 20 minutes. It indeed takes 20 minutes for the earth to travel 50 arcseconds of the orbital circumference. But the observed 50 arcseconds of celestial sky movement is 1/365 of that. Because the earth spins 365 times in its orbital revolution. That is what the famous 50 arcesonds is, 50 arcseconds of celestial sky displacement viewed from the earth every year, cumulative for the whole year. An ancient astronomer like Hipparchus only observed 50 arcseconds of celestial sky displacement per year. He could not have observed 50 arcseconds of the orbital circumference.--Markblohm (talk) 15:26, 10 December 2009 (UTC)

 * Why do you say "the observed 50 arcseconds of celestial sky movement is 1/365 of that"? You seem to be saying that the annual change in the position of the equinoxes affects the length of the day rather than the length of the (seasonal) year.
 * As for what an ancient astronomer could have observed — Is it possible now to observe directly when the equinox occurs? —Tamfang (talk) 18:37, 10 December 2009 (UTC)

Hi Joe(Kress.) May I ask, why are you multiplying 50" by 365?--Markblohm (talk) 16:07, 10 December 2009 (UTC)

 * Because the relevance of the angle is its relation to the year, not the day. As a thought experiment, consider how the length of the seasonal year would be affected if, leaving everything else unchanged (the amount of tilt, the precession rate, the size of the orbit and so on), the rotation period were doubled. —Tamfang (talk) 19:17, 10 December 2009 (UTC)

Dear Tamfang, You have highlighted the problem exactly. I assume by double rotation period you mean two times faster. But even if you mean two times slower it doesn't matter. If the earth were spinning(rotating) at double it's current speed(and precession rate remained the same), the precession rate would be exactly 3.3 seconds. The seasonal year would still be the tropical year length PLUS the 3.3 seconds. The spinning earth doesn't multiply the precession, which is what is being said in these equations above. You are multiplying the precession time by the amount of days. That is incorrect. The precession movement is independent of the spinning, so you must ADD the extra precession time onto the length of the tropical year.

The sun "travels" in the sky 473040000arcseconds(365(roughly) x 360 degrees) in one year. The celestial sky travels 473040000arcseconds PLUS 50 arcseconds. In other words, the sun travels 31536000 time seconds(525600 minutes) in one year. It then takes 3.3 seconds(50 arcseconds) to catch up on the vernal equinox. These arcseconds/time seconds have been accumulating all year. On the half year the sun would take only 3.3/2 seconds(25 arcseconds to catch up). The sun travels through the sky roughly 473040000arcseconds in one year, the celestial background is travelling 473040050arcseconds.--Markblohm (talk) 20:23, 10 December 2009 (UTC)

 * The daily rotation needs to catch up SIX HOURS at the end of the year, not 3.3 seconds! The axial precession is about seasons, not days, so it's the yearly motion (not the daily motion) that needs to catch up to it. —Tamfang (talk) 23:02, 10 December 2009 (UTC)

 * The equinox is the moment when the plane of Earth's equator crosses the center of the Sun. That plane is independent of the phase of the daily rotation.  —Tamfang (talk) 05:56, 14 December 2009 (UTC)

Markblohm: My equation for the annual precession time is independent of Earth's rate of rotation. If Earth rotated twice as fast, its day would be half as long, 43,200 seconds, but the number of those shorter days in a year would be twice as many, 730.5 days, so there would be no change in the precession time in a Julian year, 20.42 minutes. The angular speed of the Sun in its apparent orbit around the Earth can also be used to determine the time it takes an equinox to precess along the ecliptic in one year. The Sun moves at an average speed of (1,296,000"/yr)/(365.25 days/yr) = 3548"/day. Hence the annual precession time is (50.29"/yr)/(3548"/day) = 0.014174 day/yr = 20.4 minutes/yr. You agree that this is correct via your statement "It indeed takes 20 minutes for the earth to travel 50 arcseconds of the orbital circumference." But you then state "An ancient astronomer like Hipparchus only observed 50 arcseconds of celestial sky displacement per year. He could not have observed 50 arcseconds of the orbital circumference." To Hipparchus these were a single concept. A little history is warranted:

Hipparchus and Ptolemy regarded the Universe as the stars, five planets and the Sun and Moon all revolving around a motionless Earth at their center. The orbit of the Sun around Earth (the mirror image of Earth's orbit around the Sun) marked the ecliptic, which was also the center of the zodiac, a band which contained the orbits of the Moon and the five planets. But the dominant motion (now known to be due to Earth's own rotation) was parallel to the celestial equator, which was inclined to the ecliptic by 23.5°. Hipparchus discovered that the stars had an additional motion parallel to the ecliptic called precession. A ring mounted in the plane of the equator was used to determine the date/time of the equinoxes, which occurred when the shadow of the Sun cast by the upper part of the ring fell on its lower part, meaning that the Sun was crossing the equator from south to north or vice versa. The location of the equinoxes and solstices among the stars was determined using the Moon as an intermediary because it was visible both during the day and night.

Hipparchus determined that the ecliptic longitude of Regulus, a star within 0.4° of the ecliptic, was 29$5/6$° east of the summer solstice (119.8° east of the vernal equinox) in 129 BC. Ptolemy determined that the longitude of this same star was 32$1/2$° east of the summer solstice (122.5°) in AD 139, so Ptolemy noted that the star had moved 2$2/3$° in 265 years (we now say the summer solstice moved, not the star). From this he concluded that precession was 1° in 100 years or 36"/yr, the same precession that Hipparchus had deduced (precession is now known to be 1° in 72 years or 50"/yr). Today (J2000), Regulus has a longitude of 150.2°, so the solstices and equinoxes have precessed 30.4°, about one zodiacal sign, in 2,129 years, a precession of 51.4"/yr (using Hipparchus' imprecise position), about the same as the modern value. Hipparchus and Ptolemy used twelve zodiacal signs of 30° each to measure longitude. Precession measurements never used or depended upon either the solar day or the sidereal day. They also determined the angular distances (called declinations) of those stars north or south of the equator. They noted that stars near the autumnal equinox which were north of the equator later moved south of the equator (south to north near vernal equinox). Both methods resulted in the same precession. This "celestial sky displacement" was along the ecliptic, which was the "orbital circumference" of the Sun's orbit.

By the 18th century, astronomers no longer needed to use ancient observations, but were able to determine precession by comparing the positions of stars determined at times less than a century apart. These modern astronomers also discovered that some stars had large proper motions (Sirius moves about 1.3" every year), which had to be excluded from those stars used to measure precession. The pointing accuracy of the largest telescopes is now about 5", so precession is observeable within one year and must be considered to even locate stars at high magnifications if a star catalogue several years old is used.

Although you state that the spinning Earth does not multiply the precession, that is exactly what you do via "(365(roughly) x 360 degrees)". — Joe Kress (talk) 22:35, 15 December 2009 (UTC)

Image: Earth_precession.svg
This image, currently shown at the top of the page, is confusing in that the rotation of the axis is shown to be in the same direction as the spin of the planet. A reading of the description (click on the image to go to the image page and see the summary below) reveals that the axial rotation shown in this image is "relative to the direction to the Sun at perihelion and aphelion", (ie. it relates to orbital precession - even though the orbit is not shown), rather than axial precession, the title of this page. The commonly understood meaning of the unqualified term "precession" is axial precession relative to the fixed stars, where it moves counter to the spin (hence the term PREcession, rather than PROcession).

This image appears here: http://earthobservatory.nasa.gov/IOTD/view.php?id=541  with the words "orbital precession" at the top. Why have these words been removed? Is someone purposefully trying to confuse here? TomNicholson (talk) 16:57, 18 November 2009 (UTC)

 * The image Earth precession as originally uploaded in 2008 showed the correct CW precession, but Mysid thought it wrong so he uploaded an incorrect CCW image in 2009. I reverted to the original image for the reason I explained at File talk:Earth precession.svg, so the image at the top of this article now shows the correct CW precession. I have also corrected the file's description, which was indeed wrong, because axial precession has nothing whatsoever to do with orbital precession, also called apsidal precession. I don't know why NASA Earth Observatory has an erroneous CCW precession image on its site. Ironically, the associated animation shows a correct CW precession. — Joe Kress (talk) 02:38, 15 January 2010 (UTC)

Errors in the "Cause" section of the article (still!)
I would edit this section directly if it were not for the fact that the image has errors, and I don't have a replacement.

The vertical cyan (pale blue) arrows and the yellow arrows (shown at the equator) indicating the torque should not be present at the equinoxes - the symmetry of the earth-sun relationship at the equinoxes (and hence the lack of torque) is more clearly seen if the orbital motion (which is irrelevant) is ignored, or with reference to the first equation in the following section where it is seen that the torque vanishes at the equinoxes when delta (and sine delta) become zero. This is mentioned in the text: "The magnitude of the torque from the sun (or the moon) varies with the gravitational object's alignment with the earth's spin axis and approaches zero when it is orthogonal" - that is, at the equinoxes.

Is anyone else bothered by the statement, "This average torque is perpendicular to the direction in which the rotation axis is tilted away from the ecliptic pole, so that it does not change the axial tilt itself"? It is the axis of the average torque which is perpendicular to the direction in which the rotation axis is tilted away from the ecliptic pole, and I don't believe it is obvious why this does not change the axial tilt itself. Actually, the "force" of the torque tends to "want" to lessen the axial tilt - a tendency which is thwarted due to the (counter-intuitive) properties of spinning objects. If at this point you think I'm completely crazy :) then try the following ...

Take a bicycle wheel (minus the bike) and hold the spindle in your hands so that your arms are like the front forks of the bike. Spin the wheel. Now (carefully!) try and change the axis of rotation. Weird, isn't it?!

TomNicholson (talk) 18:07, 18 November 2009 (UTC)
 * Yeah, the image is wrong. The cyan arrows are all wrong, too. I think the author of the image had a misconception of how precession works. I'll try to get the image deleted for now, but it would be nice to have a replacement. ErikHaugen (talk) 19:41, 9 June 2010 (UTC)

On the Introduction
The Introduction mentions a period of 26,000 years and a cone of unspecified size and direction.

A cone is not necessarily circular.

I think that it would be well to indicate, in the introduction (but not necessarily in these terms), that the direction of the Earth's axis of rotation moves in a circle of radius 23.5° about the Earth's orbital axis ; and that the current direction of motion is approximately along a line from Polaris towards some other well-known star. The one which it will be near in AD 4000 might suit ; perhaps in Cepheus, probably Gamma, I think - or maybe use the Great Square.

The circularity and size are present, buried lower down.

82.163.24.100 (talk) 14:33, 24 November 2009 (UTC)

Great Year
Could someone perhaps take a look at the related Great Year article? A number of questionable edits have been made recently. The new "Confusion of the Platonic Year with Precession" section may be of particular concern. Pollinosisss (talk) 07:20, 14 December 2009 (UTC)

Date of vernal equinox inquiry
In 12,850 years, will the date of the vernal equinox in the Northern Hemisphere still be March 20th or will it be October 20th? Why has the date decreased from March 22nd a century ago to March 20th now? Keraunos (talk) 16:14, 1 January 2010 (UTC)

 * See Gregorian calendar for information on how accurately that calender preserves the position of the vernal equinox. The Gregorian calendar corrects the problems with the Julian calendar by omitting a leap year in centurial years, unless the centurial year is evenly divisible by 400. So this correction was done in 1900, but not in 2000. If you only look at the period between 1910 and 2009, the Gregorian calendar behaves like the Julian calendar. --Jc3s5h (talk) 18:54, 1 January 2010 (UTC)

 * Does this chart help? —Tamfang (talk) 03:58, 2 January 2010 (UTC)

Thank you so much for the clarification. I had always wondered about that problem. Happy New Year 2010! Keraunos (talk) 11:06, 2 January 2010 (UTC)

 * Irv Bromberg (Sym454.org) has calculated the drift of the equinox for several calendars (many proposed) at Leap cycle drift relative to the northward equinox, where the upper black line is the equinox drift of the Gregorian calendar. Assuming it continues linearly (a dangerous assumption), there will be about eight days of drift, meaning that the vernal equinox will occur eight days earlier than it does now, about March 12, in 13,000 years. The almost vertical dashed red line shows the rapid drift of the equinox in the Julian calendar, which drifted about ten days in only 1,300 years between roughly AD 300 and AD 1600. This shows that any fixed arithmetic calendar, that is, a calendar that adds a day, week or month at regular intervals, is useless beyond a few thousand years, at least for keeping the vernal equinox near some spcific date. — Joe Kress (talk) 04:19, 15 January 2010 (UTC)

Additional relevant astrology links
If the article is going to discuss Mithraism in detail, it might as well give a nod to "tropical astrology" vs. "sidereal astrology" and the so-called "Age of Aquarius"... AnonMoos (talk) 13:03, 15 January 2010 (UTC)

Voting for Simplified Introduction
The Articles INTRODUCTION is overly complex and therefore poorly explained .The diagrams a bewildering to none-astronomers.Is this the object of wikipedia? A celestial sphere, the sun at the centre with a zodiac ring drawn as a band on the sphere, would be a better introduction.This would: (a)  Root the observations to a fairly universally known (and therefore familiar) set of coordinates. (b) Remove the visual confusion (c) Allow for a clear intersection planes to be inscribed on the sphere. I would butte in a fix it myself but its really up to those most impassioned in this debate.Anyway were does a layman get the computer program to generate the diagrams?Ha! —Preceding unsigned comment added by Chasludo (talk • contribs) 23:55, 16 January 2010 (UTC)

Modern estimates of precession
I moved Cuvier's 1825 estimate (recently added by Hmschallenger) to the Middle Ages onwards section, at least temporarily. It certainly does not belong in the Hipparchus section just because it uses observations by Hipparchus. It should be in a "modern estimates" section which currently does not exist. A good start would be Evolution of adopted values for precession by Jay H. Lieske. — Joe Kress (talk) 23:54, 24 January 2010 (UTC)

Article used without reference or credit
I cannot see a credit at http://www.crystalinks.com/precession.html to this article.

There is a simple one link on a line by itself that is labeled "wikipedia" but no indication that the article is copied. The link is not labeled "orginal wikipedia article" or the like. I cannot see that the mere label "wikipedia" constitutes either a reference or credit and the owner appears to have a commercial site (psychic this or astrological that)

In the case of  http://encycl.opentopia.com/term/Precession_of_the_equinoxes there is a fine print credit to wikipedia without actually naming this article. —Preceding unsigned comment added by Grshiplett (talk • contribs) 00:52, 4 March 2010 (UTC)

 * Many sites that use material from Wikipedia do not give adequate credit to Wikipedia. Both of the sites you mention give at least some credit to Wikipedia. The Crystalinks site used the images from an old version of this article but the text is mostly their own. The Wikipedia link they give is to the current version of this article. The Opentopia site is basically a Wikipedia mirror. They also give a pointer to the current version of this article. — Joe Kress (talk) 02:14, 4 March 2010 (UTC)

Strange reference
In the section about Mayans it states that professional scholars do not hold the opinion that the Mayans where aware of precession. The reference is written by a Mayan scholar who does hold that opinion and states her opinion uncategorically in the article by saying... "The end of the baktun on the winter solstice is not a coincidence, and this mathematical feat is certainly a sign of a sophisticated link between Maya astronomy and mathematics."Yourliver (talk) 14:46, 11 May 2010 (UTC)
 * The sentence you quote does not show she thinks that they were aware of the precession of the equinoxes (and is replying to a rather different claim). The cited article goes no further than to say that it is not impossible that the Mayans were aware of this precession and that some of their records could have been useful in calculating it. A better reference would be good (such as to that author's book) but the current claim is reasonably well supported by this citation, I believe.
 * All the best. –Syncategoremata (talk) 20:30, 11 May 2010 (UTC)
 * Actually, you are quite correct. I have reread the article several times.  Oddly, she holds the opinion that the Maya were aware that the seasons of winter and summer moved through the solar year and calibrated their calendar to reflect this.  However she does not believe that spring and fall could be calculated with any precision at all. I withdraw my statement that Miss Milbrath even remotely can be considered a scholar.Yourliver (talk) 00:37, 12 May 2010 (UTC)
 * The citation specifically rebuts the claim it is being proposed as evidence of. "I discuss Maya records of long cycles of time that might have been useful in calculating the precession of the equinox.[...]In the book, I even refer to a record of a long cycle of 30,000 years involving the Pleiades that may have been an effort to calculate the precession of the equinox." I'm pretty sure if Milbrath states the long count was "an effort to calculate the precession" then it follows that she believes the Maya were "aware" of the precession. Her contention seems to be only with claims of their accuracy in predicting it. Boatscaptain (talk) 05:55, 1 January 2012 (UTC)

Cause
There's some dispute here about what causes precession of the equinoxes. I got rid of the picture, which I think is misleading. My edits have been largely reverted here:. There is more discussion here: if anyone is interested. ErikHaugen (talk) 23:03, 14 June 2010 (UTC)

Here is the summary, as I see it: There are two competing explanations for precession of the equinoxes. At least one is totally bogus. The first considers the "vertical"(north/south) and "horizontal"(sunward) components of the forces on the halves of the bulge by the sun - the vertical components point in opposite directions and cause a torque. The second, (which I assert is right), is that the difference in magnitude, due to the difference in distance to the sun, causes a torque, since the sun pulling on the closer half of the bulge causes a torque in one direction, and the sun pulling on the far half of the bulge causes a torque in the other direction - the close half wins since the distance to the sun is closer. Note that the two explanations disagree on basic things like "At the solstice, in what direction is the torque caused by the sun pulling just on the far half of the bulge?" And also note that the first explanation does not have anything to do with the inverse square law and gravity getting weaker with the difference in distance. Please say if you do not agree with this assessment. To resolve, can we cite sources? ie, can someone suggest a particular page of a particular astronomy book? (I'd sure appreciate one that freely available online.) I'll offer:
 * Encyclopedia of planetary sciences By James H. Shirley, Rhodes Whitmore Fairbridge, p.657 - "Except for twice a year at the vernal or the autumnal equinox when the Sun crosses the equator, there is a tendency for the gravitational attractions of both the Sun and Moon to pull the Earth's equatorial bulge into alignment with their respective planes"
 * The ever-changing sky: a guide to the celestial sphere By James B. Kaler p.159 - "the Moon and Sun are continuously moving back and forth across the terrestrial rotation bulge. The force acting to produce precession is at a maximum when these two bodies are at the solstices, and are zero when they are at the equinoxes and in line with the Earth's bulge and center." ErikHaugen (talk) 00:42, 15 June 2010 (UTC)
 * Also consider Axial_precession_(astronomy) and its references - the torque varies with the angle of declination, etc. ErikHaugen (talk) 00:53, 15 June 2010 (UTC)

I still think you are mistaken, and so are many others, and in fact it is very difficult to find any literature about precession which try to explain the cause. Most quickly pass this part and then directly jump to the results. There are some however: Looking at this picture we see the vectors of the differential gravitation for different angular distances from the disturbing body. It is true that there is no tangential component whatsoever if the sun/moon are on the equator, so no precession takes place. But that does not mean that there is none at the equinoxes. Because the equatorial bulge is not a single point, it is still a whole ring. That is the crucial issue. Even if during the equinoxes the point of the bulge 'under' the sun is on the equator and not doing anything, the extreme (solstice) points are then on the terminator, and they still are subject the tidal force towards the equator. In fact it does not matter where the sun is somewhere, equinox, solstice or somewhere in between, that part of the bulge north of the equator experiences a force to the south (strongest at the northernmost part, going down to zero to the equator) and vice versa for the southern half. The two forces of course are part of a torque, and there the precession begins. It also means that the precession force is always the same, the whole year around (or the whole month around if you talk about the moon). How otherwise could the precession speed of 50" per year be a constant (ignoring secular changes and the several magnitudes smaller irregularities of the nutation) as everybody agrees ? No astronomer has ever observed that precession would come to a standstill at the equinox and reach full speed at the solstice; it just progresses at a constant rate during the year (and the month).
 * 'Note that the net gravitational force on any portion of the earth’s ring is toward the ecliptic plane, producing a torque in the equatorial plane.' (page 12, physnet2.pa.msu.edu/home/modules/pdf_modules/m77.pdf) It is not for nothing they spell out the idea of the ring.

So the torque does not change over time. What does change on the bulge when the sun (or moon) appears to go round the ecliptic plane is the strength of the radial component, the difference being largest at the equinoxes. But a radial component does not contribute to a torque. If there is anything 'bogus' there is that.

Please restore the picture. It is still correct.

What about the quote of Kaler and others above? I am sorry, no doubt dr Kaler is an excellent astronomer, but he is specialised on stars and nebuale, and therefore less at home in celestial mechanics. His statement on variable precession is utterly wrong. --Tauʻolunga (talk) 08:51, 15 June 2010 (UTC)
 * Thanks for your response. This quote does not conflict with my (the second above) explanation: 'Note that the net gravitational force on any portion of the earth’s ring is toward the ecliptic plane, producing a torque in the equatorial plane.' Like many quotes that one finds when trying to explain this phenomenon, it is pretty vague. You say "it is very difficult to find any literature about precession which try to explain the cause" and "(Kaler's) statement on variable precession is utterly wrong." - Can you find _any_ that are "right?" It is really problematic to have one unsourced explanation for astronomical phenomenon on Wikipedia when it is a different explanation that is carried in books/etc written by astronomers. ErikHaugen (talk) 13:59, 15 June 2010 (UTC)
 * Here I'll try to answer some of your points, although ultimately this is beside the point; it doesn't really matter if we "convince" each other, we need to find sources. "How otherwise could the precession speed of 50" per year be a constant" - it's essentially constant from year to year, but during the year it varies. The average over any given 6 month period is always about the same :). "No astronomer has ever observed that precession would come to a standstill at the equinox and reach full speed at the solstice" - I have no idea if this sinusoidal variation can be observed or not; precession happens at a very small rate - again, do you have a source that analyzes this? I want to go back to something I mentioned above - your explanation claims that the torque on the far-side bulge is pulling the far side of the bulge down toward the ecliptic. But, think about what would happen if the ring/donut (consider the bulge in isolation) were fixed about a point in the very center (via tiny spokes of insignificant mass). Now, tie a string to the far side and pull. Does this pulling cause a torque on the donut pulling it toward the plane of the ecliptic? No, it pulls it away from that plane, so that the far side of the donut will go away from the ecliptic. My point is that the way you are breaking down the force arrow components is not right. ErikHaugen (talk) 16:13, 15 June 2010 (UTC)
 * I already quoted the lab exercise of Physnet. Admittedly not too clear, indeed some more literature would be welcome. I shall keep my eyes open.
 * 50" per year, which is more than 0.1" per day, is a huge value for positional astronomy, where an accuracy of 0.01" is possible. An astronomer who does not correct for precession on a daily basis commits a major error. Any supposedly seasonal variation would have been discovered centuries ago, especially since it is accumulating. None has ever been found. (There is a yearly nutation term with an amplitude of 0.1261", but that is another story).
 * Field_tidal.png Pull? Which direction do you want to pull? You are not doing the pulling, gravity does, and gravity can only pull in the directions given in the picture again. They all, no exception, have a component towards the equatorial plane, and not away from it. Sorry, you are erring, not me. --Tauʻolunga (talk) 03:42, 16 June 2010 (UTC)
 * As I explained above, the Physnet quote is totally consistent with my explanation; it is too vague to be useful in this particular discussion. wrt consistent or not observations: "None has ever been found" - do you have a citation? wrt my example: "You are not doing the pulling, gravity does" - the pulling with a string was supposed to be analogous to the Sun's gravity, so I mean, you would stand as if you were the Sun and pull on the far side of the donut with a string - because the far side of the donut appears to you to be above the fixed pivot point (center of the earth), the torque you cause will pull the far side of the bulge up away from the ecliptic. I was just trying to demonstrate, through a simple example, the intuition behind why the Sun's gravity pulling on the night side of the bulge will result in a torque pulling the night side of the bulge away from the ecliptic, but I see it was not clear enough. I said ecliptic, not equatorial plane, and that picture appears to be about tides, not the subject at hand. Unless you find this profitable, let's let it go, since really what we need here for the article is sources, not to convince each other. You keep saying things like "you are erring, not me," but you can not find any sources. I'm not sure what else I can do; I have found quotes from books written by astronomers that clearly contradict your explanation and support mine. ErikHaugen (talk) 05:48, 16 June 2010 (UTC)
 * That picture belongs to differential gravitation which explains the tides and the precession, and therefore it belongs here too. But what do I care? Have it your way. Apparently we cannot convince each other, and at the end, yes, verifyable sources is what really counts for wikipedia. Without access to libraries it can take a long time before I find one. Until then. --Tauʻolunga (talk) 07:40, 17 June 2010 (UTC)
 * For what it's worth, I would have to say the Erik is correct in the above discussion. The simplest way to determine this is to simply plug the numbers into the torque equation seen in the article:
 * $$\overrightarrow{T} = \frac{3Gm}{r^3}(C-A)\sin\delta\cos\delta\begin{pmatrix}\sin\alpha\\-\cos\alpha\\0\end{pmatrix}$$
 * Notice that one of the terms is declination (δ). At the equinox, the sun's declination is zero so sinδ = 0. Last time I checked, multiplying any vector by a scalar with a value of 0 gives... $$\overrightarrow{0}$$! So at the equinox, there can be no torque caused by the sun's gravitation.
 * To think of it another way (one that requires neither derivation of a torque formula nor the assumption that the one given is correct — which it is, by the way), at the equinox, the center of the sun lies IN THE EQUATORIAL PLANE. Since gravitational forces are directed toward that center, they MUST lie in that plane. Since no component of that force can be orthogonal to the equator, there is no resultant torque.
 * The source of the error lies in confounding two different frames of reference: the equatorial and the ecliptic. At the equinox, there is indeed a small component of the gravitational force that is orthogonal to the ECLIPTIC, but that component is entirely an artifact of the incongruence between the equatorial and ecliptic planes, and it DISAPPEARS when you transform these vectors into the EQUATORIAL plane.
 * I've tried to be both clear and succinct in this explanation, but if there is any misunderstanding (and any contention must be a misunderstanding), I'll try to clarify. Wilford Nusser (talk) 01:52, 4 July 2010 (UTC)

 * This disagreement is resolved by noting that torque is not directly related to precession. Instead, torque is directly related to the rate of change of precession+nutation, their derivative. Hence torque must be integrated to find precession+nutation. Precession is separated from nutation by decomposing the torque's sine squared term $$sin^2\,l$$ into $$\tfrac{1}{2}(1-cos\,2l)$$, where $$l\,$$ is the ecliptic longitude of the Sun, its angular position in its apparent orbit around the Earth relative to the vernal equinox. Note that the torque has a constant term and a periodic term with a semi-amplitude equal to the constant term, so the torque is zero at the equinoxes. Replace $$l\,$$ with $$n't\,$$, where $$n'\,$$ is the angular velocity of the Sun around the Earth, about 3,548"/d. Now $$\textstyle\int_t\tfrac{1}{2}(1-cos\,2n't)=\tfrac{1}{2}(t-\tfrac{1}{2n'}sin\,2n't)$$. Thus precession increases linearly throughout any and all years, while nutation is smaller than the torque's corresponding term by $$\tfrac{1}{2n'}$$. Solar precession is about 16" per year, while the semi-annual nutation term has a semi-amplitude of about 1.3". See C.H.H. Cheyne, The Earth's motion of rotation including the theory of precession and nutation (1867) page 41. — Joe Kress (talk) 07:38, 8 July 2010 (UTC)
 * Thank you all so much pointing out the solution. --Tauʻolunga (talk) 07:13, 10 July 2010 (UTC)

 * sinAcosA = sin(2A) ie twice the frequency; this expression involving declination angle has a zero at the solstices too! This is less intuitive but should be added to article. — Preceding unsigned comment added by 78.218.206.61 (talk) 21:01, 2 October 2018 (UTC)

Move
Right now, this page redirects from Axial precession. But since there is no other type of axial precession, there doesn't appear to be a need for a qualifier at the end.  Serendi pod ous  18:07, 10 April 2011 (UTC)

 * There may be no other article, but a gyroscope on a stand will precess. —Tamfang (talk) 19:05, 10 April 2011 (UTC)

 * This article was entitled precession of the equinoxes by Ewlyahoocom when he separated it from precession (where it still has a section now entitled Axial precession (precession of the equinoxes)) on 7 April 2006. On 8 May 2007 The way, the truth, and the light moved it to precession (astronomy) before he renamed the section climatic effects to anomalistic precession. (Where is the move log?) I added several related terms to the lead on 28 February 2009 (general precession, lunisolar precession, planetary precession, precession of the ecliptic, precession of the equator). Zbayz then moved this article to axial precession (astronomy) on 23 August 2009 because he said that it said nothing about perihelion precession. After I noted that both precession of the equator and anomalistic precession were discussed, he moved the anomalistic precession section to apsidal precession). I objected to his move of this article at Name change above, but I couldn't think of a better name so I did not attempt to move it again. Even though I prefer one of the other names I added, a Google search shows that precession of the equinoxes is far and away (100 times) more popular than any other term. Because this article is overwhelming about that part of the astronomical subject, I recommend that it be moved back to precession of the equinoxes. — Joe Kress (talk) 20:50, 10 April 2011 (UTC)

Southern Cross reference
By consequence, the constellation is no longer visible from subtropical northern latitudes, as it was in the time of the ancient Greeks.

How are we defining 'subtropical northern latitudes' here? Because I'm at about 25N, and I can see the top half of the Southern Cross from my driveway, 'in the city', when it's a sufficiently clear night. Around March, to be specific. I imagine it's a much better view in the Keys, with the clearer horizons.

I am hesitant to revise that line without either the original justification for it referenced, or what documentation on my part would be appropriate.

Corgi (talk) 14:28, 15 July 2011 (UTC)

Ecliptic reference
What is the tilt of the precession central axis with reference to the ecliptic of the sun, seeing that tidal torque forces from the moon are stronger than the sun's tidal forces, and the moon's orbit is not aligned with the solar ecliptic, defined by earth's orbit about the sun? The precessional central axis should be on a tidal torque coordinate that is a mathematical mix between the stronger lunar orbit tidal torque, and the weaker solar ecliptic tidal torque, and as such would also shift solar and lunar positions on horizon reference points, with the precession period over the approximately 30,000 year period. With an ecliptic-reference tilted central precession axis, these precession effects would misalign the claimed thousands of year old monuments based on the precision of solar and lunar horizon reference points on claimed ancient precise stone monuments like Stonehenge, and other ancient horizon reference stone marker systems. At least hyperbole, in media claiming such monuments still have "exact" alignments, whatever the word "exact" means in media. Only monuments aligned to the earth's own axis, like The Giza Pyramids, would remain constant, of course pointing to a moving pole, as the star charts show with Polaris today, or Thuban, or Vega, at other points on the precession path. Not to mention systems of stellar alignment, like claimed Nazca Lines, pointing to Sirius and Orion, seem to be media hype, having nothing to do with the Ecliptic, and claims of ancient formation toward these alignments, which will definitely not hold over thousands of years. LoneRubberDragon 76.166.233.62 (talk) 06:54, 5 August 2011 (UTC)

 * I don't understand your question wrt the moon's orbit. Any astronomical use of the Nazca lines or Stonehenge seems to be theoretical; I don't know what "precision" you are referring to exactly. Can you be more precise? ErikHaugen (talk | contribs) 17:00, 5 August 2011 (UTC)

 * The orbit of the Moon wobbles around a line perpendicular to the plane of the ecliptic in only 18.6 years, so the average lunar plane is identical to the plane of the ecliptic. Similarly, the average lunar torque has the same direction as the average solar torque so they simply add—the "precessional central axis" does not change direction over thousands of years, so there is no additional effect on archaeological sites. The components of both lunar torque and solar torque in other directions are lumped together under the term nutation because they have no effect over thousands of years. The limits of the tilt of the lunar orbit can be observed and is called lunar standstill which does affect archaeological sites. — Joe Kress (talk) 20:45, 7 August 2011 (UTC)

 * I found the answer on Wikipedia, too, that the axis of precession in the heart of Draco, is also virtually the north ecliptic pole. en.wikipedia.org at wiki at Ecliptic_pole contains the page with that chart, virtually matching your chart on precession. 76.166.237.179 (talk) 09:48, 25 August 2011 (UTC)

 * And agreed, with the given data pages and charts of reference, with precisely no axis tilt of the precession circle relative to the solar ecliptic, as shown, will produce solar-lunar monuments that will not have precessional effects, but stellar monuments like some Nazca claimed references, Will suffer general stellar precessional misalignments over thousands of years. 76.166.237.179 (talk) 11:38, 25 August 2011 (UTC)

 * But Furthermore, looking at the forces, relative to masses and distances, relative to earths oblateness (ellipticity), it shows the sun with 0.5:1 times the precessional gyroscopic torque than the moon, oddly resulting in the precession's central axis at virtually 90 degrees on the heliocentric ecliptic coordinate system. Given: sun 333,000 earth mass, 92,800,000 miles distance, moon 0.0123 earth mass, 238,900 miles distance, earth radius differential 4000 miles radius (approximately).  With the given, I get 179:1 gravity force ratio on earth from the sun:moon.  And for the earth radius gravitational radial differential effect to distance I get 374:1 for the moon:sun on earth.  And if the products are appropriate, that produces the 0.5:1 effect of solar precessional torque to lunar precessional torque, similar to the moon having double the tides compared to the sun's effect on earth. 76.166.237.179 (talk) 14:09, 25 August 2011 (UTC)

 * As the moon's orbit does gyroscopically precess like the earth, an 18.7 year precession period is impressive, given earth's 28,000 year precession, producing a minor angular 18.7 year Nutation in the precession. The article Nutation does include a paragraph on earth nutation from that lunar 18.7 year cycle that you mention, so perhaps a paragraph to emulate in this article, to go from general precession of the equinoxes, to a more complete specific precession of the equinoxes.  To show wikipedia weakness, the moon article does not even directly mention that its orbit plane precesses in 18.7 years, only that it precesses in ambiguous reference, lacking the Saros Cycle being mentioned or that 18.7 year value being given.  76.166.237.179 (talk) 11:38, 25 August 2011 (UTC)

 * It is interesting, given Saturn's own heliocentric tilt, that Saturn's rings have not differentially precessed from solar gravitational differentials at different radial distances, along with all of its satelite orbits, not being a shambles of inclinations outside of Saturn's rotation axis. Saturn's rings are nearly perfectly flat, which "apparently" indicates their extreme youth, to not have precessed in any percievable way, since their formation.  Saturn's moons are another story, and strange, being relatively coplanar.  Wiki says "Twenty-four of Saturn's moons are regular satellites; they have prograde orbits not greatly inclined to Saturn's equatorial plane.", and Saturn is tilted to its own orbit 27 degrees like Earth.  If the entire Saturn system is young, like its rings, that is odd. 76.166.237.179 (talk) 14:09, 25 August 2011 (UTC)

 * Nutation is negligible relative to precession. The precession angle of 23.5° is 5000 times larger than the largest nutation component of 17". Nutation is so small that it cannot be observed with the naked eye. So the precession of the Moon's orbit cannot have any observable affect on archaeological sites.

 * True. 76.166.237.179 (talk) 10:44, 26 August 2011 (UTC)

 * On the other hand, precession has two components. The largest component is lunisolar precession due to the Moon and Sun. The smaller component is planetary precession where the other planets cause the ecliptic itself to precess (actually advance) around the pole of the invariable plane of the Solar System. This distinction is mentioned at the beginning of this article. The ecliptic wobble is about 2° over a period of about 100,000 years, so it's about 9% of lunisolar precession, which is easily observable and will affect archaeological sites. See Invariable plane.

 * Good point. I should not have said that the moon has no precession effect, but like you say, an averaged precession effect, from the moon's own Saros Cycle Precession on the earth sun plane. 76.166.237.179 (talk) 10:44, 26 August 2011 (UTC)

 * The orbits of the satellites of a planet precess around the poles of the Laplace plane of that planet. This is a warped plane that coincides with the planet's equatorial plane for satellites close to the planet, while it coincides with the orbital plane of the planet for satellites far from the planet. The large inner moons of the gas giants precess around their planet's equatorial plane whereas the small outer moons of the gas giants as well as Earth's Moon precess around their planet's orbital plane.

 * Yeah, I thought about that, too, quite true. With extremely near satellites, the satellite's orbit angular momentum increases, reducing the precession rate effect from the sun for a spehrical main planet, and planetary oblateness effects of the planet itself are increased by that slowness of precession.  And with reduced satellite orbit angular momentum at further distances, that solar gyroscopic precession effects increase, as the dipole like dropoff of oblateness effects sharply drop off.  Though, it matters not whether the satellites are large or small.  If you consider that Saturn's Oblateness effect on extremely near satellite precession, is approximately a sine angular force of the satellite's orbit inclination (zero force at Saturn's Equator leaves solar precession still perfect dominant, and approximately sine, for it is also zero effect for a perpendicular orbit to Saturn's Equatorial Plane), and Oblateness is a differential force based on near bulge torque in difference compared to the opposing far bulge anti-torque-effect at 1/R^2 differences, and Saturn's increased density with depth shrinks the profile of Mass Oblateness Distribution from Optical Oblateness, that it is still odd looking for many of the satellites to be less than 0.5 degrees off Saturn's Plane, many within a tenth of a degree, some within a hundredeth of a degree off Saturn's Plane, all with Saturn's own Precession over millions of years.  *Sighs*  I'd really need to run a numerical simulation to see the balance of how strong Saturn's Oblateness would modulate solar caused precession, with Saturn 10 times farther, and 100 times more massive than earth, and Saturn Itself precessing over millions of years. 76.166.237.179 (talk) 10:44, 26 August 2011 (UTC)

 * Spending an hour looking at the dynamics without numerical simulation, further, I note that for a satellite initially on Saturn's Equatorial Plane, it would precess about the Saturn Orbit Normal Axis exclusively according to Solar Gravity Differentials on the satellite orbit with respect to the sun's distance. Then, as the satellite's inclination to Saturn's Equatorial Plane increases, that sine of the inclination approximation starts to work of Saturn Oblateness Gravitational Differentials (near and far oblateness differential distance pull), causing another effect of precession of the satellite orbital plane about the Saturn Rotation Axis.  And so the two precessions of Solar Gravitational Differentials on the satellite orbit, and the Saturn Oblateness Gravitational Differentials, work in a Superposition, and get into complex dynamics that go beyond basic paper analysis without Numerical Simulation of rate regiemes of dynamics.  76.166.237.179 (talk) 13:01, 26 August 2011 (UTC)

 * Saturn's rings are quite close to Saturn so Saturn's equatorial bulge would cause any moonlet whose orbit was inclined to Saturn's equatorial plane to precess around it. But it cannot precess because if its orbit was inclined it would collide with other moonlets whenever it attempted to pass through Saturn's equatorial plane, so all moonlets must lie quite close to Saturn's equatorial plane. — Joe Kress (talk) 04:53, 26 August 2011 (UTC)

 * For satellites within the ring plane, I assume, colliding with ring chunks, conservatively dragging them into the ring's plane. 76.166.237.179 (talk) 11:41, 26 August 2011 (UTC)

PROcession
User:TomNicholson would have us believe that precession and procession are opposites, which is news to me. The two words come respectively from (the Latin ancestors of) precede, 'go before (something else)', and proceed, 'go forward'. Let's either have some support for the claim or delete the new section asserting it. —Tamfang (talk) 21:13, 24 December 2011 (UTC)

 * It is probably best to delete the entire section added by Polestar101. The first part is Ptolemy's view, so it really belongs in the Ptolemy section, but without the neologism "procession" and provided that it is mentioned that Ptolemy regarded the equinoxes as fixed points on the celestial sphere, causing the stars to move toward the rear compared to their diurnal motion. The last part is wrong. I checked several mechanics and physics texts and all agree, without exception, that precession in the motion of the axis of rotation, that is, the "observable". None regard precession as either a "cause" or "mechanical process". — Joe Kress (talk) 08:28, 25 December 2011 (UTC)

New graphics
I'm replacing a couple of the graphics with some animations - in particular, the two depicting "inside the celestial sphere" and "outside the celestial sphere". We will need to update the text immediately under them to reflect the new graphics. Tfr000 (talk) 18:34, 9 May 2012 (UTC)

 * I've noticed you've been putting in a lot of animated graphics. I have not examined the latest ones, but in general, I hope you will try to avoid animated graphics except when they really make the material more comprehensible. My objections to animation are
 * the pace and flow of the animation may not match up well with the reader's mental processes; static images let the reader examine the parts of the image at the pace, and in the order, he prefers
 * teachers putting the material in paper handouts won't be able to use animations.
 * Jc3s5h (talk) 20:01, 9 May 2012 (UTC)

 * Understood. On the other hand, it is difficult to explain many astronomy subjects in words. The talk pages of some of the articles contain thousands of words (basically, "hand waving") of attempted explanation.
 * Manual_of_Style is relatively mute on the subject. Is anyone aware of similar discussion in another article?
 * If anyone has an opinion, please add it here. For geometric subjects like certain parts astronomy, in other words, those that involve the depiction of moving, rotating, intersecting lines, planes, spheres, and so on, would you prefer to see:
 * 1) animations
 * 2) animations that are less obnoxious - they stop moving after a time, or pause occasionally
 * 3) both animations and still graphics
 * 4) as few animations as possible
 * Tfr000 (talk) 13:51, 10 May 2012 (UTC)

 * Answering my own question, several discussions of this exact sort turn up in this search:

 * http://en.wikipedia.org/w/index.php?title=Special:Search&limit=20&offset=80&redirs=1&ns1=1&search=~animated+images

 * in particular,

 * http://en.wikipedia.org/w/index.php?title=Wikipedia:Village%20pump%20%28proposals%29&oldid=136544556#Avoid_movement_in_pages

 * There doesn't seem to be any real consensus, but it seems the majority just plain dislike moving images. I will keep this in mind. I have been trying, for the most part, to replace only images that are confusing and hard to interpret. Tfr000 (talk) 15:06, 10 May 2012 (UTC)

angle of precession-cone
What angle is the cone made by Earth's rotational axis in the first illustration? The article begs the question. Maybe add it to that first illustration. I'm still not sure, my best guess is 23DEG based on the article.

Pb8bije6a7b6a3w (talk) 23:23, 27 February 2013 (UTC)
 * Yeah, the article says: The rotation axis of the Earth describes, over a period of 25,700 years, a small circle (blue) among the stars, centered on the ecliptic north pole (the blue E) and with an angular radius of about 23.4°. Please feel free to edit the article to make this more clear, if that is what you meant. ErikHaugen (talk | contribs) 17:42, 28 February 2013 (UTC)

Equations
I think the section called Equations is unclear. You see equations but it is not at all clear how they were derived. The reason for choosing an ecliptic plane coordinate system is unclear, An earth center fixed, non-rotating coordiante system with x and y in the equatorial plane, z along the earth polar axis positive north and with x pointing in the vernal equinox direction positive seems to be much better. The derivation in Meirovitch's "Methods of Analytic Dynamics" is much clearer in my opinion.

Cuneiform claim is unsourced
From the introduction: "...although evidence from cuneiform tablets suggest that his [Hipparchus'] statements and mathematics relied heavily on Babylonian astronomical materials that had existed for many centuries prior..." It'd be great to have a source for this to reference. The History material later in the article doesn't provide a source for this either. Any ideas anyone? Bob Enyart, Denver radio host at KGOV (talk) 17:18, 29 June 2013 (UTC)

Precession Equations Dubious, topic spill
Please split topic.

This section is about precession whatis and maybe short cause with lead to other topic: the usual.

It's not a topic to cut and paste earth moon / earth body formulas (and words) from likely copyrighted books ! that MIGHT contribute to precession. MIGHT.

Please create a new topic for that. I vote: split

BTW. current theory is moon hit earth which would give it INITIAL precession. the equations are paste they assume no initial precession and do not imply whether or how precession would continue or balance if the newtonians frame forces were removed.

another concern the equations mention forces two non-parallel as contributing (didn't cancel.) HOWEVER. it said nothing about, say, 250000 (or any) yrs later when THE OPPOSITE SIDE would get the same treatment thus almost wholey cancel the unbalanced forces mentioned

Formula the above talk asked for...
the formula is there (needs many conversions to use: T). and the precession itself is bound to be constant rate and rate (like a top) and is tabled in article.

but for an easier to use formula for effect on season length, see tropic year in wikipedia it has a good equation and tables

Rotation
The illustration shows the axial precession of the Earth. Looking at it it would appear to me that half way through, the Earth is tilted the opposite way from the beginning of the circle and in that case summer would be reversed (if at the beginning of a cycle, summer is June 21 - Sep 21 or so in the northern hemisphere, then half way through the cycle June 21 - Spe 21 would be winter in the northern hemisphere). I suppose that is not true but that is how it looks doesn't it?

== tc

 * The reason it doesn’t is that the calendar is designed to keep pace with the Sun’s apparent motion with respect to the Earth’s axis. If we referred it to the fixed stars instead, the situation would be as you describe: a 29-ka ‘great year’ marked by a creeping rotation of the seasons through the whole calendar. What does happen is that the seasonal ‘starscape’ slowly changes with the precession cycle; around the XIII millennium BCE, from a given latitude, the present-day summer constellations were most prominent in the winters.—Odysseus 1 4 7  9  00:26, 28 June 2014 (UTC)

OK. But it is true then, right, that the perihelion (now in winter) and the aphelion (now in summer) will at times be switched (perihelion in summer and aphelion in winter)? I think I got those terms right. There is also apogee. — Preceding unsigned comment added by 63.84.231.3 (talk) 13:08, 2 July 2014 (UTC)

 * Yes, according to our article on the topic, Apsis. Jc3s5h (talk) 13:21, 2 July 2014 (UTC)

Blending of art and science
The blending of art and science greatly hinders each and every scientific discipline that is contaminated. I wish there was a more gentle word, other than "contaminate," because imagination and creativity are crucial traits for a species to have, however, when the line that separates what we know from what we think, gets blurred, we eventually get flat out false assumptions accepted by the masses as truth. The precession of Astronomers and Astrophysicists from sort of right to completely wrong and then back to almost accurate observations is the only thing that occurs. And if Astronomers and Astrophysicists could be honest enough to just admit the things that we don't know with scientific certainty, so that it doesn't get confused with things we know with certainty, We wouldn't be so lost and argumentative with Our knowledge of how things work. Scientists do not debate like this, peer review does not mean hold a debate to discern the Truth. And this subject is a perfect example of the nonsense that gets accepted as fact. These subjects are why the world still, to this day, believes the Moon causes the tides of Our Oceans, or that Our Solar System is hurdling outward in a straight line which fools somehow think proves the expansion of space. The ego of men and the feeble minds which encourages arguing for one exaggerated false claim over another, and Our allowing foolish men and their false theories to be accepted as facts, has severely hindered humane beings' ability to understand this world. And that is sad. -Dirtclustit (talk) 13:14, 21 August 2014 (UTC)

@Dirtclustit: Nice. Far too much certainty given to hypotheses in most sciences.

Where is a derivation?
In the section 'equations' there is:

T = 3GM/r^3 ...

I don't see any support for that not other result, and none of references to this solution also. What this is a pseudoscience or religion? — Preceding unsigned comment added by 217.99.107.103 (talk) 00:06, 12 December 2014 (UTC)
 * That equation appears in the James Williams paper from JPL cited at the end of the paragraph immediately above: (2) on page 712, under “Fundamentals”. It’s apparently derived from an expression for the gravitational potential energy of an external body WRT the Earth.—Odysseus 1 4 7  9  04:37, 12 December 2014 (UTC)

17:38, 28 December 2014 (UTC)17:38, 28 December 2014 (UTC)83.26.156.68 (talk) 17:38, 28 December 2014 (UTC)
 * You told about this?

http://adsabs.harvard.edu/abs/1994AJ....108..711W

I don't see there any derivation, just this same formulas - the final. BTW. The suppositin the potential of an oblate spheroid is responsible for a precession of the same spheroid is wrong, because the momentum can be conserved in other way, for example the orbital momentum can change accirdingly.

The method of solution and these formulas are adequate for a satelite's orbital precession of the Earth, but not for the Earth itself.
 * Are you saying the Williams article is wrong? Can you find a source that says otherwise?  The suppositin the potential of an oblate spheroid is responsible for a precession of the same spheroid is wrong, because the momentum can be conserved in other way — Can you rephrase this?  I'm not sure what you're saying.  In particular, are you suggesting a change to the article?  Can you be more specific about the change you'd like to see? ErikHaugen (talk | contribs) 19:16, 30 December 2014 (UTC)

00:50, 7 January 2015 (UTC)217.99.238.57 (talk)
 * It's possible the solution is wrong, because there is no a solution, but just the final results.

"The term (C−A)/C is Earth's dynamical ellipticity or flattening, which is adjusted to the observed precession because Earth's internal structure is not known with sufficient detail."

So, it's rather evident it's just a manipulation of numbers, not any real solution.

What is a precession speed of a massive ring or disk inclined at angle i, and spinning with speed w?

Axial Precession Theory
No valid observation has been made across 26,000 years yet. It is unproven, so the title of the article must be presented as an experiment in vitro. All information should be re-evaluated in this regard. The article must be changed to "Axial Precession Theory", as written in heading of this new section. — Preceding unsigned comment added by 72.94.152.209 (talk) 12:18, 26 February 2015 (UTC)

Mithraic question
It seems to me very questionable if the section "Mithraic question" belongs here at the present length, or at all. At least most of it is wholly outside the topic. It is not even known whether Mithraic Mysteries had anything to do with the precession at all; it is just the wiev of one scholar. It belongs rather to the article Mithraic Mysteries, which this question actually is handled. In this article, a much shorter mentioning of this hypothesis would be enough, but of course, there should be a link to the article Mithraic Mysteries. Indeed, that section could be replaced with a more general one, with headline "Astrological, mythological and religious interpretations", or "Effects on astrolgical beliefs and religions", or something like that. There namely are (or have been) quite a few religious beliefs which have at least sometimes been interpreted as inspired by the fact of precession; Mithraic mysteries are just one example among others. According to some scholars (as I have somewhere read, I do not remember where), even the fish (Ikhthus) as an early Christian symbol, generally thought to be just an acronym, might have been inspired by the fact that what astrologers call "Age of Pisces" (Fishes) had begun just a little before the time of Jesus. -KLS (talk) 11:23, 14 January 2016 (UTC)
 * In this article, such beliefs are mentioned briefly at the end of the section Effects and handled in detail in the article Astrological Age, which, of course, is where they belong. But in this article there was no link to that article, and so I added one. Although such beliefs are fully unscientific, they have been and still are so widespread that they should be mentioned even here, at least briefly. But I think the section "Mithraic question" is still out of place here, but the question could be handled in Astrological Age, maybe in the section "Age of Pisces" or as a separate section. -KLS (talk) 12:45, 14 January 2016 (UTC)
 * Many unscientific beliefs such as Mithraic beliefs etc are studied by academics (archeo-astronomers, cultural historians, religious historians etc) and many people are interested in subjects like these, but I agree that such topics do not belong on this page and should either be included in the Astroligical Ages and/or other pages. Terry Macro (talk) 22:31, 15 January 2016 (UTC)
 * I'm totally with you here. One could boil down all of this to one or two sentances IF it really relates significantly to this subject at all.

IceDragon64 (talk) 23:02, 15 July 2018 (UTC)

Precession and Poleward Pointing to the Star Vega
I would like to see some graphic which depicts the Earth's inclination in relation to the sun when Vega is the pole star in another 12,000 or so years. Vega will have scarcely changed its relation to our solar system in this time (in fact, it is reputed to be moving directly towards us, and we towards it). But Vega lies (now) at a current astronomical latitude of about 39°N., some 50+° away from Polaris. Given that the angle of obliquity, when doubled, equals this 50° more or less, and Vega is completely on the other side of the path through the heavens described by the polar axis, my comment could perhaps be labelled correctly as an inability to visualize what the future inclination of the planet will be. However, I can conceive that significant changes in which areas of the Earth would come directly under the sun, and also that the yearly periods of their being under the sun would change drastically. Would the angle of obliquity of the axis always remain between ~24° and ~21°? Obviously the apparent positions of the stars in the skies will change, as they have changed before, but I would like to read something from a knowledgable source about what this means in relation to apparent latitude of the sun as seen from different areas of Earth. A good graphic would help. Not meant to be a criticism of any one or any theory. — Preceding unsigned comment added by Daniel Sparkman (talk • contribs) 09:58, 11 May 2016 (UTC)

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Period and precision
There are many statements in the article about the period of precession. The last section gives a general discussion of the fact that different models are designed to maximize accuracy over time periods chosen by the modelers, and those periods may be much less than one precession cycle. I would like to see various precession values made consistent throughout the article when they are valid for the same time span. I also think that the more general, introductory statements should use values that are valid for at least one full cycle, because that is how non-specialist readers will think of a precession cycle, not a small fraction of a cycle centered around AD 2000. Jc3s5h (talk) 20:56, 18 May 2018 (UTC)

 * An equation for general precession valid for millions of years (–15Ma to +2Ma) is given by Laskar et al. in "A long term numerical solution for the insolation quantities of the Earth" (±250Ma), Astronomy and Astrophysics, 428/1 (Dec. 2004), p. 16:

 * ψ = +49086 + 50.467718t – 13.526564t$2$ + 42246($0.1500192⁄(0.150019 + 2(–13.526564)t)2$)cos(0.150019t – 13.526564t$2$ + 171.424°)

 * where ψ is in ", and t is in yr. If desired, the roots of this complex equation at 0" and 1296000" (360°) can be determined using the SOLVE function on a pocket calculator. Online equation solvers were useless. The cosine term is due to the effect of the Jupiter/Saturn resonance on the precession of the ecliptic (planetary precession). It oscillates around the line of the polynomial terms. Although it is significant in this equation, producing ten cycles in the current precession period, no evidence of it exists in the IAU precession model, so it can be safely ignored. The paper's actual model was calculated numerically—this equation was only a short term (17Ma) analytical simplification. The constant offset can also be ignored because it does not appear in the IAU model. The remaining two polynomial terms yield 25,680.0 years for the current precession period, accurate to six significant digits. The average over ±5 periods yields the same precession period, only the accuracy drops to five significant digits, 25,680 years. The period determined by using only the first term of the IAU model, 25,772 years, is false precision because it cannot be that accurate for any period beyond that of the JPL DE406 ephemeris, –5000 to +1000 years from the present, upon which it was based. Note that the JPL ephemeris was also calculated numerically. — Joe Kress (talk) 19:02, 22 May 2018 (UTC)

 * I found two grave errors in my previous solution to the megayear equation (Laskar 2004, p. 275, ψ = accumulated general precession, Fig. 3.) First, I forgot the parentheses in the denominator of the cosine coefficient. This erroneously generated a pair of vertical asymptotes that prevented Solve functions (Newton-Raphson method requiring derivatives) from working properly. I use Solve to find the value of the independent variable (t) when given the value of the dependent variable (ψ), for example ±180°, instead of hunting for it. Second, I failed to convert the arcseconds in the cosine argument to degrees, erroneously generating a sinusoid with a much higher frequency, several cycles per precession cycle. The cosine term in the corrected equation (valid for −15 Myr to +2 Myr) generates about one fourth of a sine wave in ±2,000,000 years, including 0° near year −1,700,000 and a peak of −15.5° near year +1,350,000 (see Fig. 16). For the earlier period, −15 Myr to −2 Myr, the sinusoid is smaller, so the cosine term could then be neglected. The corrected cosine term has a asymptotic peak at +5,545,347.7 years, when its coefficient reaches division by zero, so Laskar's equation does not attempt to model the future.

 * His Fig. 14 shows that we have just entered a 20 Myr period when the Jupiter-Saturn resonance will cause the obliquity of the Earth (now 23.44°) to decrease by 0.38° before resuming a slow linear increase of 2°/Gyr caused by tidal dissipation (pp. 273−4). This relatively large affect on planetary precession is not modeled by his equation. Over a much longer period the precession frequency p drops steadily from 58"/yr near −250 Myr to 45"/yr near +250 Myr due to the Moon receding from Earth and Earth's rotation slowing (pp. 264, 276−7, Fig. 19). Laskar models this with two polynomials, one for negative time and one for positive time. This continuously lengthens precession periods from about 22,345 years to 28,800 years. Thus precession changes significantly throughout Earth's history.

 * The corrected equation generates precession periods that vary from 25,687.8 years to 25,691.6 for the 20 cycles (510,795 years) centered on the present (J2000 ±3600°), with the single cycle centered on the present (±180°) being 25,689.8 years. Thus the approximation 25,690 years is accurate to four significant digits over 20 cycles. Of this the polynomial contributes 25,680 years while the cosine term contributes 10 years.

 * The P03 solution of the IAU 2000 precession (Capitaine 2003, p. 581, p$A$ = general precession, § 4.3.) is
 * p$A$ = 5028".796195t + 1".1054348t$2$ + 0".00007964t$3$ – 0".000023857t$4$ – 0".00000000383t$5$
 * This equation is fitted to the JPL ephemeris DE406 whose time span is 3000 BC to 3000 AD, beyond which it is invalid. Nevertheless, if her equation is extended forever it forms a cubic "S" with a nearly linear section from a negative peak at year −59,334 (−764°) to a positive peak at year +33,148 (+375°) (+2000 has not been added to these years for the J2000 origin), beyond which the angle increases without limit in opposite directions, positively for negative years and negatively for positive years. A single precession cycle centered on the origin (±180°) from years −13,150 to +12,677 is 25,627 years versus the "instantaneous period" of the linear term, 360×3600/5028.796195 = 25,772 years, neither of which is valid. — Joe Kress (talk) 19:16, 2 November 2018 (UTC)

 * Another model, valid for ±200,000 years, is Vondrak 2011 (p. 5):
 * p$A$ = 8134.017132 + 5043.0520035T − 0.00710733T$2$ + 271×10$−9$T$3$ + ∑$p$
 * Where p$A$ is in ", T is in Julian centuries since J2000, and ∑$p$ represents 10 cosine/sine periodic terms. Accuracy varies from a few milliarcseconds for 20 centuries centered on J2000 thus matching Capitaine 2003, to a couple of arcminutes near ±200,000 years thus matching Laskar 1993. Unfortunately, the quadratic and periodic terms produce enough jitter that it must be included with the linear term, so the 15 precession cycles within ±200,000 years of J2000, ±2700°, are 25,700±400 years in length. The exact sequence of lengths depends on their starting point because 10 periodic cycles, with a maximum amplitude of ±3.3°, occur during the 15 precession cycles. The single precession cycle centered on J2000, ±180°, is 25,784 years because the model was centered on the present, including a negative peak of the central periodic cycle (Fig. 4). Note that the linear term of Capitaine 2003 that is currently in the article, 25,772 years, is quite close to this full cycle. The linear term of Vondrak 2011 corresponds to 25,698.7 years, hence the minor rounding to 25,700 years. But over the very long term precession cycles continuously lengthen, from 22,345 years to 28,800 years over ±250 Myr. — Joe Kress (talk) 23:07, 5 November 2018 (UTC)

 * I think this is enough to reduce the precision of the statement in the article. I also plan to make an appropriate change in Year. Thanks. Jc3s5h (talk) 23:29, 5 November 2018 (UTC)

Indian Views
I think this paragraph is probably written by somebody who already fully understands the Indian references, but doesn't make much sense to me. I'm sorry I can't do it myself, but in order to gain much information from it, it needs to be fully translated into scientific English.

IceDragon64 (talk) 22:50, 15 July 2018 (UTC)

 * I thought that reviewing Hindu calendars might help, but they assume that precession doesn't exist, basing both the lunisolar and "solar" calendar years on the sidereal year. Only the 1955 reformed calendar, the Indian National Calendar, uses the tropical year, based entirely on modern knowledge. The Indian views presented in the article are those of only one writer, Bhāskar-II, which implies that Indian numerical values for precession are rare. This section comes almost verbatim from "Ayanamsha vs Precession: New Light on Ancient Wisdom". It will take a lot of research to improve this section. — Joe Kress (talk) 21:22, 18 July 2018 (UTC)

 * Bhāskar-II was an anomaly in that he believed in precession. Virtually all Indian astronomers, before and after, believed in trepidation. Wikipedia's article on Trepidation has an excellent summary of the Indian view as presented in the Surya Siddhanta (chapter iii, verses 9–12), the most respected of all Indian astronomical treatises. — Joe Kress (talk) 17:07, 22 July 2018 (UTC)

 * I revised the section on September 24, 2019. — Joe Kress (talk) 23:37, 24 September 2019 (UTC)

Standard Gravitational Parameter
The Standard Gravitational Parameter is usually given as µ (lower-case Greek mu) rather than Gm or GM.

I'm reluctant to make an arbitrary edit for fear of hurting readability/usability of the formulae.

My citation for making this statement is https://en.wikipedia.org/wiki/Standard_gravitational_parameter.

216.145.100.72 (talk) 21:40, 1 September 2018 (UTC) -- Ian Moote
 * I think you're right to make that change. Someone wishing to find how µ is derived can do so at the already-linked Standard gravitational parameter page. UpdateNerd (talk) 23:44, 1 September 2018 (UTC)

constellation List
Article missing constellation list earth precision pass trougth:

Ursa Minor Draco Hercules Lyra Cygnus Cepheus

Axet (talk) 09:39, 10 April 2019 (UTC)

Pictures are wrong for Earth
The pole does not depict the closed circle. The inclination of the Earth's axis is changed. Because the Earth’s orbit is also precessing about 4 degrees. Voproshatel (talk) 05:51, 4 September 2019 (UTC)
 * The equation required to plot your open circle is ε$A$ (obliquity) in Vondrak 2011 on page 5 of 19. It can generate up to 15.5 precession circles, J2000 ±7.75. Within that period are ten ecliptic cycles which generate a ±2° sinusoid that rides on the closed 47° diameter circle of lunisolar precession. — Joe Kress (talk) 03:01, 5 September 2019 (UTC)
 * To plot the equation as a bumpy circle use the parametric form of a circle: y = r cos 2π t/T, x = − r sin 2π t/T,
 * where r is the obliquity, t is in centuries, and T is the period of the linear term of precession, 256.98723692 cy. These [modified] equations place the present, t=0 or J2000, at the top, with the origin (unseen) in the center of the circle, directly below it, and time progressing counter clockwise. A star map could be included. — Joe Kress (talk) 22:10, 5 September 2019 (UTC)
 * Because precession is described by p$A$, not its mean, the parametric equations should be, using Vondrak's symbols:
 * y = $εA⁄3600$ cos $pA⁄3600$, x = − $εA⁄3600$ sin $pA⁄3600$
 * where 3600 is added because the arguments of cos and sin cannot be in arcseconds, but must be in degrees (or radians). It is also added to their coefficients because the declinations of stars, and often their right ascensions, are in degrees. — Joe Kress (talk) 18:19, 13 October 2019 (UTC)
 * No, p$A$ and ε$A$ are not for fixed ecliptic coordinate system. "The precession of the equator was represented by the general precession in longitude, p$A$, and mean obliquity of date, ε$A$, which are the orientation angles of the mean equator of date with respect to the ecliptic of date." Voproshatel (talk) 16:34, 11 November 2020 (UTC)

More correct trajectory http://www.astrokot.kiev.ua/slovar/images/precessiya.gif or https://rutlib5.com/book/7353/p/i_007.jpg Voproshatel (talk) 06:11, 9 November 2020 (UTC)

Yet more correct trajectory against the still sky of the epoch J2000.0 Voproshatel (talk) 18:09, 2 February 2021 (UTC)

Image illustrates Apsidal Precession over time rather than Axial Precession
The 3rd image on the page, provided by user Cmglee, appears to illustrate Apsidal Precession, the variation of Perihelion and Aphelion over an approximate 20,000 year cycle, rather than Axial Precession, which varies with an approximate 26,000 year cycle. --George Fergus (talk) 02:59, 22 December 2019 (UTC)

Actual Photo with wallclock time showing the difference for a star crossing an observer's meridian from year to year?
Has anyone a photo available to visualize the precession effect in an actual celestial observation everyone could see with their own eyes and a clock? What would be better to visualize: the change of the local solar time of the day of the midnight culmination of a star from year to year or the change in maximum elevation the midnight culmination of a specific star reaches? Stars near the celestial equator should show the largest effect and near the celestial pole the smallest in my understanding. My guess would be the time of the midnight calculation is easier to measure it should move by a maximum of 3.34s if I understand the discussion here correctly. All my consideration was of course with ignoring the individual proper motion of a star. Isenberg (talk) 04:06, 3 November 2023 (UTC)

title: Talk:Axial precession