Talk:Analemma/Archive 1

Intersection

Is the analemma the intersection of a sphere and a cone? -phma

Mercury and Venus

The last link notes, "incorrectly claims Mercury and Venus lack analemmae". The link titled 1 also makes this claim, and states why. If the author of this comment thinks that they do, what would they look like?

External link

The external link to the article by Brian Tung (currently dated and copyrighted 2002), is I think, important, because at the end it contains a link to a C program for the analemma or equation of time, which uses a more accurate formula than many use. Particularly, it is more complex than simply working out the Equation of Time due to the two components (eccentricity and obliquity) on their own, independantly of each other, then adding the two results. The movement of the Sun eastwards among the stars due to the orbital motion of the Earth, is itself uneven due to eccentricity of the orbit; this needs to be taken into account when working out the component of the Equation of Time due to the obliquity. As Brian Tung states in the last paragraph of his page, the formula which many use (working out the two effects independantly then adding them linearly) works reasonably well for small eccentricities and obliquities, but becomes noteably inaccurate for extreme orbits and inclinations. -Roo60 13:54, 2 Apr 2005 (UTC)

Axial tilt

It is not correct that the analemma would be a straight line if the orbit were circular but the axis tilted as it is. It is true that if the axial tilt were only slight, then the analemma would be almost a straight north-to-south line; but with very great axial tilts, the figure-of-eight feature would be very marked indeed.

As is explained in the article Equation of time, when the sun is crossing the equator (at the time of the equinoxes), then it is climbing/lowering at a 23.44° angle, which means that for every 1.09° of actual motion along the celestial sphere, it only moves eastwards in Right ascension by 1°. Conversely, at the solstices, the sun is cutting across meridians, meaning that for every 1° of motion along the plane of the ecliptic, its Right ascension increases by 1.09°. Thus, the Equation of time follows two cycles per year. - Roo60 20:05, 2005 Apr 7 (UTC)

Analemma Society

There's a group of amateur astronomers in Virginia called the Analemma Society. I don't know if it's wworthy of mention so I'm just putting it here: http://www.analemma.org/ --Howdybob 21:11, 16 July 2006 (UTC)

Photo of analemma

Just a comment on the photo of the analemma with the dates drawn in. The cross-over of the figure of eight is marked 15/3 and 1/9. Surely it should be 15/4 and 1/9 which is when the Equation of Time is zero (its graph crosses the x-axis). - Panus

As seen in the first diagram in the section Earth's Analemma, the solstices do not correspond to the times of zero azimuth (equation of time). The solstices correspond to maximum altitude (declination). To get a better technical understanding of this issue, please follow the many links supplied in this article. Josh-Levin@ieee.org (talk) 17:56, 3 February 2008 (UTC)

Reference to 'figure 8'

Someone please rewrite constant reference to 'figure 8'; I don't know how to do it in a plausible way. Alexander Iwaschkin 03:25, 23 January 2007 (UTC)

Can you explain why you feel it should be changed? --Lasunncty 20:36, 28 January 2007 (UTC)

DAMN!!! I'm a bloody blockhead :-))) It means symbol '8', not 'see fig. #8', as I thought :-))) Well, at least I asked before doing something stupid :-))) Alexander Iwaschkin 05:26, 29 January 2007 (UTC)

Most globes in days of yore used to have analemmas printed on them as well as an ecliptic circle printed about the globe intersecting the equator. Since most globes these days no longer come with these features, I have been looking "on line" for a good diagram of the analemma which I could print out and use to roughly detiremine the declination of the sun any time of year. I had hoped to find one here, but no. Nor, can I find a link to one! There must be a good analemma diagram somewhere to be seen, but I haven't found one yet. (By good, I mean: not distorted, and showing the months broken down to five day intrevals or less, along the line of the analemma, which would enable one, for any given date to detiremine with reasonable accuracy the declination of the sun, together with it's time ahead or behind mean solar time. I know there are tables that do this; but, the analemma is a nifty graphic tool that accomplishes this in one simple diagram. —Preceding unsigned comment added by 4.178.15.111 (talk) 21:52, 9 January 2008 (UTC)

Analemma Reversion 8 Sept 2008

"The width of the analemma is a result of the ellipticity of the earths orbit. Please explain how this relates to vibration in universal joints."

The "figure-8" related East-West motion in the analemma has absolutely nothing to do with the eccentricity of the Earth's orbit. Eccentricity causes a 12 month period East-West motion, not a 6 month period! It distorts the "figure-8". The "figure-8" East-West motion is due to the tilt of the Earth's axis. Assuming a circular orbit for simplicity, the 24 hour strobed position of the sun follows a great circle across the earth with constant velocity and one year period. During the equinoxes this sun circle crosses the equator at an angle, so it's eastward movement is slower that the 24-hour strobed rotation of the Earth. During the solstices the sun is moving parallel to the equator, and since by defintion of the solar day they must have the same yearly average, it is moving faster that the Earth's eastward rotation.

Likewise the vibration in a universal joint is due to the tilt in the coupled angular motion. The vibration also has a 2X frequency. The equations are the same! —Preceding unsigned comment added by Cloudswrest (talk • contribs) 18:31, 10 September 2008 (UTC)

Ok, hold on -

• I never said anything about figure 8, 6 month, 12 month, anything like that. All I said was that the "width is the result of the ellipticity of the earth's orbit", which is.... well its imprecise, but certainly not false.
• I never said you were wrong, I just said "please explain".
• If your explanation is that "the equations are the same", I don't think thats worth noting in the article, unless further explanation is given. A=B-C is an equation that is used to calculate my net worth (=assets-liabilities) and the Lagrangian of a particle in a gravitational field (potential energy-kinetic energy). Just because the equations are the same doesn't mean they are due to the same phenomenon.

Im still not saying you are wrong, I don't know if you are or aren't, because I cannot make any sense of your statement, even when I look at the universal joint article. You just need to give a little more detail. PAR (talk) 00:26, 11 September 2008 (UTC)

OK, fair enough. At bottom, the analemma is the projection of one angular rotation onto another, off axis angular rotation of the same frequency. In the case of the earth the two "rotations" are the yearly motion of the sun around the ecliptic, and the 24 hour strobed rotation of the earth, which also has a yearly period. The 24-hour strobed rotation of the earth is about 1 degree per day. A sidereal day (star meridian crossing to crossing) is less than a solar day, 23 hours, 56 minutes. A sidereal day is 360 degrees of earth rotation, a solar day is 361 degrees of earth rotation. The "off axis" in this case is of course the earth's tilt of 23.44°.
In the case of two coupled drive shafts, if you were to paint a dot on the rim of one, and observe this dot from the corresponding point on the rim of the other, there are two cases. In the case of a hyphoid gear coupling or CV joint, both shafts have constant rotation velocity and the dot would trace out a perfect analemma. In the case of a universal joint coupling, the driven shaft, although sychronous, has to speed up and slow down at a 2X rate in order to "cancel" the analemma. The dot appears to just move up and down from the view of the driver shaft. This is the sourse of the second harmonic vibration.--Cloudswrest (talk) 16:30, 11 September 2008 (UTC)

I'm going back to my analemma notes... A few points:

• I was wrong to imply that the width of the analemma is only due to the eccentricity of the earth's orbit, its also due to the tilt of the earth's axis, since, as you pointed out, the "figure eight" is due to the tilt of the earth's axis, and the figure eight has width.
• I think that your analogy, if it is in fact valid, must relate the universal joint to the special case where there is no eccentricity of the planet's orbit. This point was missed in the original post, and that needs to be made clear.
• I see that the two equal-period motions (the 24 hour period strobed sun and the orbital motion of the earth in one case, and possibly the two driveshafts in the other case) combine to introduce other frequencies, especially the first harmonic or 2x period.

I think if it is shown that the two equations are the same, along with a short explanation of how the two mechanisms are equivalent, that would be good. Note, that I still don't understand the universal joint equations, but I am trying to figure that out. In the orbital case, the relevant equations are the equation of time for a planet in a perfect circular orbit (but tilted on its axis), and how it is generated from the two periodic motions. Do you have a short explanation of the analogous equation for the universal joint? PAR (talk) 23:10, 12 September 2008 (UTC)

Possibly interesting: this page of mine illustrates how the interrelation of tilt and eccentricity affects the shape of the analemma. —Tamfang (talk) 04:52, 30 July 2010 (UTC)

Shadow analemma

Analemma markings traced in a public square, just visible if you zoom in

I was in a public square in Bristol some time ago and I noticed an odd pattern of marks on the ground. After wandering round puzzling about it I realised it must be something to do with the sun's shadow, probably at noon, cast from the top of a sculpture at one end that looked a bit like a spine, since there was a far off mark which looked about right for the winter solstice and a near one that looked right for the summer, and a figure of eight which crossed at where I concluded a shadow was cast at the equinoxes. After thinking this was a pretty cool thing to put in a town square I set about trying to find out more, and came across this word "analemma". My question then, is whether such a representation of the analemma from a year's worth of shadows can also be referred to as an analemma, and if so whether this example is anything notable that might merit a mention in the article, or whether there are plenty of these around the world. If anyone wants to see it, have a look at an aerial photo from Google Maps. 79.64.181.148 (talk) 19:55, 2 March 2009 (UTC)

I've just established that this is Millennium Square, which has a stub. You can see some of the analemma markings (the discs on the ground) in this photo I've found on Commons. Can someone familiar with the terminology add a note about this interesting feature of the square to its article. It might solve a mystery for anyone who looks the square up! 79.64.181.148 (talk) 20:01, 2 March 2009 (UTC)

Image size

Thumbnail size images add nothing to this article as they do not illustrate the text. I suggest this is a case where it is appropriate to force Image size as per the Manual of Style, Wikipedia:Manual_of_Style#Images . Lumos3 (talk) 23:50, 25 March 2009 (UTC)

Poem

The poem added by Mushlack on 5 December 2009 is from Analemma in Verse by Tad Dunne. Because no release from copyright is mentioned by Dunne and it was composed about 1996, the poem is under copyright in virtually all countries and it is thus a copyright violation to include it in Wikipedia. I am removing the offending poem. I am adding an external link to the poem, which is permitted for a work under copyright. — Joe Kress (talk) 20:30, 20 December 2009 (UTC)

Clarification: Even an external link is not permitted per WP:COPYLINK if an editor knows that the site violates the copyright holder's copyright. In this case, the author of the poem placed it online. — Joe Kress (talk) 06:38, 21 December 2009 (UTC)

Merger proposal for Analemmatic sundial

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

The result was do not merge into Analemma. -- DarkCrow^Caw 18:11, 24 May 2012 (UTC)

---

• I would oppose a merger. The Analemma calendar is a physical object placed in parks and gardens and although related can support an article of its own. Lumos3 (talk) 12:02, 18 January 2010 (UTC)

Comment Sorry if this is confusing. After some investigation I realised the Analemma calendar article title was at odds with its content which described the Analemmatic sundial. I have therefore renamed the Analemma calendar article as Analemmatic sundial. I have also expanded this with material from sundial. My oppose comment now applies to Analemmatic sundial. My understanding of the phrase "Analemma calendar" is that it should redirect to this article as its seems to be synonymous with Anelemma. Lumos3 (talk) 23:14, 18 January 2010 (UTC)

The application of the analemma in the analemmatic sundial still needs to be mentioned and discussed in this article per SS. I appreciate that you split the material out of another article, but it should have been split into this article, first. All good sources discuss it. Is there a reason you are trying to keep the subjects separate without discussing it here? Viriditas (talk) 12:34, 19 January 2010 (UTC)

I have removed the merger proposal since it no longer applies.--Lasunncty (talk) 11:11, 19 January 2010 (UTC)

Actually, it does apply, and the discussion is ongoing on the users talk page. The tag was added at 01:26, 18 January and you removed it at 11:05, 19 January. I've never before seen a merge tag removed that fast from any article. Is there a reason you removed it? Viriditas (talk) 12:06, 19 January 2010 (UTC)

Sorry, my mistake. Ok, in that case, I oppose a merger with this article. If anything, Analemmatic Sundial should be merged with Sundial, but as Lumos3 points out, that article is already too long. --Lasunncty (talk) 21:57, 19 January 2010 (UTC)

As I said above and on the user's talk page, the two topics of the analemma and the analemmatic sundial are related. Is there a reason both articles are separate and we have two short articles instead of one medium-size topic? I really don't see anything to oppose here. And, why would you merge analemmatic sundial into the sundial article when we have a separate article on the analemma? Viriditas (talk) 22:15, 19 January 2010 (UTC)

Sorry. was not watching this page- it was forked from Sundial as the result of that article becoming too big. The article is flawed, as an analemmatic dial, and the use of an analemma on a dial plate are not the same thing. Going back to the Greek analemma is a term for the sundials plinth. The two reference books Mayall and Mayall(Third edition only) p.186, and Waugh p.108 are hazy about the maths. The essence of an analemmatic dial is that it is a movable style (gnomon dial)- with an interesting relative the composite Foster Lambert dial. The Analemmatic calendar (a term I have not heard used by gnomonists), a noon mark, is fixed style dial that projects onto a analemma. Merger: stay well alone.--ClemRutter (talk) 09:25, 3 March 2010 (UTC)

oppose. the analemmic sundial is a sundial, this article is on the anelemmic effect. Two, related, but different things. While analemma usually refers to the apparent movement of the sun, it's not limited to the sun. If the sundial information were already in here, I'd be moving it out into it's own article just based on length.--RadioFan (talk) 14:30, 12 March 2011 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Analemma is late 17th century junk

The analemma represents a completely worthless exercise and only emerged in the late 17th century along with mechanical clocks so that giving significance to a wandering Sun 'analemma' by gauging its position using the average 24 hour day would be a harmless exercise until empiricists decided to explain the observation using the Earth's daily and orbital motions.There is only room in the celestial arena for the true 'wanderers' - the planets,and it was Copernicus who explained the 'wandering' motions including retrogrades by determining that the Earth's own orbital motion resolved the observations.The idea of a wandering analemma Sun let alone explaining it by way of planetary dynamics is hideous,don't take my word for it,extract the details from the great astronomer himself - "Moreover, we see the other five planets also retrograde at times, and stationary at either end [of the regression]. And whereas the sun always advances along its own direct path, they wander in various ways, straying sometimes to the south and sometimes to the north; that is why they are called "planets" [wanderers]. Copernicus

In short,the astronomical version of the 'Piltdown man' skull is the analemma and the reason it emerged is far more interesting,for all the wrong reasons,than this short description would imply.Oriel36 (talk) 20:11, 19 June 2010 (UTC)

• What utter nonsense. --Thorwald (talk) 00:57, 20 June 2010 (UTC)

I think it is utter nonsense too,people who believe something as childish as gauging a wandering 'analemma' Sun using a 24 hour clock and then going on to explain it using planetary dynamics may be the most stupid people on the planet. —Preceding unsigned comment added by Oriel36 (talk • contribs) 19:35, 20 June 2010 (UTC)

• No. No. You misunderstood. I was stating that your "position" was utter nonsense. --Thorwald (talk) 23:35, 20 June 2010 (UTC)

I knew what you were saying but like so many others,you have no answer to the statement of Copernicus which forbids the idea of a wandering 'analemma' Sun in the same celestial arena as the 'wandering' planets ,this wandering motion was resolved by the Earth's own orbital motion - http://apod.nasa.gov/apod/ap011220.html . If astronomy has a 'Piltdown man' skull then the analemma certainly is that, as a matter of substance ,the thing is somewhere between the Loch Ness Monster and intellectual oblivion.Oriel36 (talk) 05:29, 21 June 2010 (UTC)

The analemma has nothing to do with retrograde planets. —Tamfang (talk) 04:29, 30 July 2010 (UTC)

Ah,my Tamfang shadow,I was wondering when you would show up. I consider the analemma too embarrassing in the same way all hoaxes are,it was a means to an end in attempting to shift daily rotation away from its determination at natural noon by having the Sun wander all over the place,sideways and up and down and it would be funny only that people are dead serious about it. The determination of natural noon by the use of a shadow in reflecting the daily rotation and orbital motion of the Earth has no up and down component, just a simple alignment and a straightforward determination which Huygens relates with clarity - "Draw a Meridian line upon a floor and then hang two plummets, each by a small thred or wire, directly over the said Meridian, at the distance of some 2. feet or more one from the other, as the smalness of the thred will admit. When the middle of the Sun (the Eye being placed so, as to bring both the threds into one line) appears to be in the same line exactly you are then immediately to set the Watch, not precisely to the hour of 12. but by so much less, as is the Aequation of the day by the Table." http://www.xs4all.nl/~adcs/Huygens/06/kort-E.html Oriel36 92.251.255.11 (talk) 08:15, 31 July 2010 (UTC)

Who said the north-south motion is relevant to the definition of noon? Why do you bother denying things that no one has said, and affirming trivialities that no one denies? —Tamfang (talk) 09:37, 2 August 2010 (UTC)

The problem with "Huygens-noon" method quoted is that it produces days of inconsistent length. Correctable as your source clearly specifies in section 5, using what seems to be an analemma table.

The answer to the out-of-context misquote of Copernicus is that he is not likely to forbid an idea, and he would certainly have recognized the effect of an elliptical orbit on the apparent motion of the sun with respect to the stars. Like modern astronomers, he had no proximate visual reference (like a huge checkerboard near the plane of the ecliptic) with which to resolve the optical illusion of retrograde planetary motion, which still has nothing to do with the analemma produced by a sundial.

Wikidity (talk) 22:15, 2 August 2010 (UTC)

I have to laugh at "Huygens-noon" in inverted commas,Huygens was relating an ancient observation that the natural noon cycles vary hence the equable 24 hour day as a human devised derivative along with terms such as AM and PM that still retains the correlation between natural and 24 hour clock noon.Of course,if you are an analemma addict,you couldn't possibly comprehend what causes the natural noon cycles to vary as it shares a common mechanism with the terrestrial effect where temperatures fluctuate across the solstices.Oriel36 (talk) 17:00, 4 August 2010 (UTC)

The Aequation that Oriel mentions is of course the east-west component of the non-existent analemma. Ain't it grand? —Tamfang (talk) 07:19, 18 August 2010 (UTC)

Analemma = Earth Orbit vs Spin

. The spin of the earth during the year is fairly constant, however, the orbit around the sun is not circular, so its apparent (and actual) orbital speed varies, decreasing twice each year, for 3 months, as it 'climbs' from proximity to extremity, each followed by 3 months of acceleration back to the next proximity. As the earth recedes, the sun appears to 'fall behind in the noonday sun'. As it approaches the sun again, it catches up again, averaging out 'just right'.
. If you divide the year by the number of days (D), to get average the number of seconds per day (N), and take a vertical photo of the sky every S seconds, you would see the sun wander slightly (a couple of degrees) east & west across the sky every 6 months.
. This slight & consistent effect (nothing to do with obvious & complex 'Planetary' wandering) is not caused by any actual sun motion, and is the major cause of the analemma's width.
. While taking these photos, you might also take night photos S/2 seconds later, and see that the stars are moving across the night sky very steadily at 360/D, without E-W wander.
. I think this is the main reason and clearest explanation of why the analemma is not just a line.
. However, more subtly, the tilt of earth's axis does not align with either axis of it's elliptical orbit, and the planets also have subtle gravitational and perhaps detectable electric coupling effects, adding spice to the planetary complex.
The sun may tremble under the minuscule tugs of its planets, and its 'wanderings' are of galactic proportions, but both are well beyond the perception of all but the most extreme telescopes.
Wikidity (talk) 22:15, 2 August 2010 (UTC)

Here is what you do,there is an excellent article from about 1917 about something that was stitched together to make it look biologically feasible,the astronomical 'analemma' version doesn't even have the pleasure of being remotely elaborate but exists as something so crude that it is almost impossible to comment on other than an attempt to denote the position of the Sun using a 24 hour day and a watch. http://www.jstor.org/pss/2788903 Oriel36 (talk) 17:46, 4 August 2010 (UTC)

Wikidity - The main cause of the Earth's analemma is the tilt of its axis, not the eccentricity of its orbit. The tilt of the axis is the main course, the ellipticity is the "spice" which makes it asymmetric. I had an interesting discussion above with a user named Cloudwrest (see Talk:Analemma#Analemma Reversion 8 Sept 2008. If the Earth had a perfectly circular orbit, its analemma would be a symmetric figure 8. To the first order, the figure 8 is a combination of the apparent seasonal north-south oscillation of the sun at a particular time of day and an apparent east-west oscillation at twice that frequency. The double frequency oscillation is of exactly the same nature as the double frequency oscillation in a universal joint (I am no longer sceptical). I am trying to figure out a good way to explain this in the article without too much pain. PAR (talk) 23:43, 4 August 2010 (UTC)

Wikidity: The tugs of the jovian planets (Jupiter, Saturn, Uranus, Neptune) on the Sun are not miniscule—they are large enough to pull the barycenter (center of mass) of the Solar System outside the sun over 60% of the time, reaching a maximum of 2.2 solar radii from the center of the Sun. It exceeds 1.8 radii after recurring periods of 15 and 24 years (a year on either side of 1943, 1958, 1983, 1997, 2022, 2037, 2061).

See Jean Meeus, Mathematical Astronomy Morsels, pp.165–8. Also see Solar system barycenter 1945–1995 and Solar System Barycenter 2000–2050.

This matters because the Earth does not orbit the Sun—it orbits the barycenter (center of mass) of the Solar System.[1][2] If the equation of time and the analemma are calculated using only Earth's elliptical orbit and the tilt of its axis, as Jean Meeus does in MAM on pp.337–46 with an accuracy of about two seconds, then the barycenter shift will cause an error of about ±2 minutes whenever Earth is at a right angle to the line between the center of the Sun and the barycenter. This is a 10% error, which is just detectable using any properly constructed analemmatic sundial. — Joe Kress (talk) 19:04, 5 August 2010 (UTC)

Joe Kress - The barycenter is the center of mass. That means the Earth, the sun, and the barycenter all lie on a straight line. How can the Earth be at right angles to a line between the sun and the barycenter? PAR (talk) 14:35, 6 August 2010 (UTC)

The Solar System barycenter is not the Earth-Sun barycenter. The Earth has virtually no effect on the barycenter of the entire Solar System because the mass of Earth is negligible compared to the masses of Jupiter, Saturn, Uranus and Neptune. The Solar System barycenter is between the Earth and Sun only one day every year. — Joe Kress (talk) 07:10, 7 August 2010 (UTC)

Ah, ok. Then this is a rather complicated aperiodic error, I guess. PAR (talk) 13:50, 7 August 2010 (UTC)

Yes, if aperiodic means not yearly. But the motion of the Solar System barycenter is periodic with periods of 15 and 24 years. Wikidity assumed that these planetary perturbations were negligible. Your Analemma Earth plot for 2006 is typical for 2003–11, but includes a one minute error during this period while the barycenter is near the limb of the Sun. If planetary perturbations are totally ignored, as in the equations in the equation of time article and those given by Meeus, planetary perturbations can produce a two minute error because those equations assume that the Sun is at one focus of an Earth orbit that is assummed to be elliptical. — Joe Kress (talk) 23:24, 7 August 2010 (UTC)

I did not realize the error was that large. About the 2006 analemma, I assumed that was a measured analemma, not calculated. Are you sure it was calculated? PAR (talk) 00:52, 8 August 2010 (UTC)

I misspoke. You stated at Analemma Earth that the Sun's azimuth and altitude were generated by JPL Horizons, where all planetary positions are calculated to a precision of 16 significant digits for many centuries past and future from a few modern spacecraft missions and radar ranging measurements. That precision is impossible using any measurement. However, the positions of the Sun, all planets and many asteroids are simultaneously calculated, so the plot for 2006 includes all planetary perturbations for that year and has no error whatsoever. But the barycenter moves as the jovian planets move, so it is no longer representative of the analemmas of future years. That movement has already generated a one minute error in 2010. The error will reach three minutes when the barycenter moves to the other side of the Sun and is well outside the Sun as in 2024. Unless the analemma is recalculated for every year, some error is unavoidable. If elliptical equations are used, which ignore planetary perturbations, the maximum error is two minutes. — Joe Kress (talk) 06:33, 8 August 2010 (UTC)

I think these points would be a valuable addition to the article. Can you edit the article to include these points? PAR (talk) 11:32, 8 August 2010 (UTC)

That is my intention. — Joe Kress (talk) 18:35, 8 August 2010 (UTC)

The transition from AM to PM represents a global event along the same meridian line hence the 'M' in the abbreviation,it does not matter what hemisphere of the Earth you reside in,when the shadows align along the meridian as Huygens clearly explains, natural noon is determined the same way each cycle along with its adjustment to 24 hour noon.It is not rocket science,there is no 'analemma' feature to consider with no planetary dynamics needed to explain it - "Draw a Meridian line upon a floor and then hang two plummets, each by a small thred or wire, directly over the said Meridian, at the distance of some 2. feet or more one from the other, as the smalness of the thred will admit. When the middle of the Sun (the Eye being placed so, as to bring both the threds into one line) appears to be in the same line exactly you are then immediately to set the Watch, not precisely to the hour of 12. but by so much less, as is the Aequation of the day by the Table." Huygens Oriel36 (talk) 19:29, 5 August 2010 (UTC)

first photo

The description about the "first analemma photograph" is not quite correct. The National Geographic blurb has a couple mistakes as well. I haven't seen the original Sky & Telescope article the photo appeared in (June 1979), but I did find an annotated version of the photo here. I also found a good description here (albeit in Georgian). However, these sites are not primary sources, and I'm not sure if their source is the original S&T article or something else. --Lasunncty (talk) 06:41, 2 January 2011 (UTC)

Historical shift in meaning of "Analemma"

At the end of the article, there is a link to "The Use of the Analemma — from an inset from Bowles's New and Accurate Map of the World (1780)". This refers to the (English) meaning of "analemma" in the 18th century. At that point in time an analemma was an orthographic projection of the sphere --an entirely distinct definition (so the link probably doesn't belong here). This "analemma" could be a carefully drafted drawing or, in fact, a device for calculation, like a graphical slide rule. These "analemmas" were used to get approximate solutions to the various problems of spherical trigonometry. Only after c.1800, globe makers began placing charts of the Sun's declination on globes and labeling these as analemmas. These are the origin of the modern usage of the word analemma. Also many of these early analemmas did not include the graphing of the equation of time hence they were oval instead of "figure 8" shaped. This is described well in most early 19th century guides to the "use of globes". For example in Keith's "New Treatise on the Use of Globes" published in New York in 1819, you will find

"The analemma is properly an orthographic projection of the sphere on the plane of the meridian; but what is called the analemma on the globe, is a narrow slip of paper, the length of which is equal to the breadth of the torrid zone. It is pasted on some vacant place on the globe in the torrid zone, and is divided into months, and days of the months, correspondent to the sun's declination for every day in the year. It is divided into two parts; the right hand part begins at the winter solstice, or December 21st, and is reckoned upwards towards the summer solstice, or June 21st, where the left hand part begins, which is reckoned downwards in a similar manner, or towards the winter solstice. On Cary's globes the Analemma somewhat resembles the figure 8. It appears to have been drawn in this shape for the convenience of showing the equation of time, by means of a straight line which passes through the middle of it. The equation of time is placed on the horizon of Rardin's globes."

Keith's "Use of Globes" is available through Google Books.

As recently as 1910, some "analemmas" on globes were ovals because they only charted declination and not also equation of time. Whether the globe-maker Cary can be credited with the invention of the modern analemma (and re-definition of the word) or not, I don't know but it seems likely. Someone would have to find a source for that, so I'm just leaving on this on the talk page. 173.105.173.249 (talk) 04:56, 26 May 2011 (UTC)

Thanks to the Unknown contributor here,it may be that Cary introduced right ascension into a projection that was only meant to register declination but he was acting on an older assumption which can be found through Nevil Maskelyne -http://www.bodley.ox.ac.uk/cgi-bin/ilej/image1.pl?item=page&seq=9&size=1&id=pt.1764.x.x.54.x.343

The older (and correct) method which Maskelyne refers to can be best summed up by Christian Huygens as there is no daily geometric deviation of the Sun in right ascension,just the variation in the length of time it takes for the shadows of two threads to line up at natural noon and subsequently the application of the Equation of Time -

"Draw a Meridian line upon a floor.. and then hang two plummets, each by a small thred or wire, directly over the said Meridian, at the distance of some 2. feet or more one from the other, as the smalness of the thred will admit. When the middle of the Sun (the Eye being placed so, as to bring both the threds into one line) appears to be in the same line exactly you are then immediately to set the Watch, not precisely to the hour of 12. but by so much less, as is the Aequation of the day by the Table."Christian Huygens

http://adcs.home.xs4all.nl/Huygens/06/kort-E.html

In this respect,there is no way to reverse engineer the Equation of Time back into the Sun's position as the equal 24 hour day is drawn down from the average time of the Sun's return to natural noon where the shadows line up,nothing more or less.

There is also a fabulous letter from John Wallis to Robert Boyle in 1666 where he freely acknowledge that the explanation for the cause of variations in natural noon was still on the table while today's imaging power can provide a clear resolution however the problem is the wandering 'analemma' Sun is getting in the way -

http://books.google.com/books?id=RyBOsLIi2SMC&pg=PA219&dq=aequation+dayes#v=onepage&q&f=false

Credit where it is due to the original writer of this section as not many are versed in a more accurate view of the matter.Gkell1 (talk) 17:48, 1 July 2011 (UTC)

Did you say that the Aequation can be used to adjust from apparent solar time to mean solar time, but not the reverse? —Tamfang (talk) 04:20, 2 July 2011 (UTC)

There is just natural noon where the shadows of two threads line up hence the natural noon variations are solely in the length of time it takes to observe the event and the conversion of the natural daily inequality into a steady progression of 24 hour days.The numbers can be all negative as Huygens produced them,they can be partly negative and positive or entirely positive,the nature of the natural noon correction known as the Equation of Time relies solely on time difference,not positional differences hence its flexibility as to addition, subtraction or both as it applies to the noon observation.Huygen's spends half his treatise explaining how to center natural noon from observations of the Sun to the horizon where the equation of time can be applied in order to create the equal 24 hour day and the steady progression of days and although there are a number of points which have to be refined and cleared up,his treatise is accurate and,of course,there is no sign of a 'wandering' analemma Sun. Trying to reverse engineer observations using a 24 hour day is effectively a worthless thing to do.Gkell1 (talk) 07:40, 2 July 2011 (UTC)

Is "Gkell1" the same user as "Oriel36" (who was banned from posting on Wikipedia)? The confused, irrelevant comments here strongly suggest so. If you read comments by Oriel36 above, you will find that they are devoted to the same ecccentric concerns about the analemma which GKell1 has expressed here. None of this has anything to do with the "historical shift in the meaning of the word analemma" which is the topic of this section.24.148.57.193 (talk) 03:50, 7 July 2011 (UTC)

Elsewhere I greeted Gkell1 as "Oriel36" and Gkell1 did not contradict me. —Tamfang (talk) 01:33, 11 July 2011 (UTC)

The gentleman should be satisfied with the references which demonstrate that the 'wandering Sun' analemma was a tragic and inevitable consequence of the attempt to fit the Earth's daily and orbital motions into right ascension by guys in the late 17th century and I leave those references on the page as a resource,nothing more or less.Gkell1 (talk) 05:59, 9 July 2011 (UTC)

"Cast Away", 2000, with Tom Hanks

It would be super if this article could explain how Tom Hanks was able to make an analemma and use it to navigate off of the island! There's a link from the "Cast Away", 2000, article to the analemma article, but nothing in the analemma article explains in simple terms what a person would do to create an analemma and use it for survival navigation.

You never know when information like that will come in handy...~~

~~ — Preceding unsigned comment added by Entwhiz (talk • contribs) 11:34, 18 February 2012 (UTC)

Edit request

There is a graph supposedly showing sunrises for the month of January, 2008 for Gabon. The x-axis is date (with dates ranging from 01/01 to 01/09 then back to 01/01 !!!!). This is garbage. This graph is so flawed that it should be removed. I missed the place in the article (if it exists) where this graph was used to further the article. Assuming that the point of the graph is to show the two maxima and minima in early January, it is still completely wrong to graph a continuous line. From this graph I can determine that sunrise on 01/02 is 06:34.00 and that 8 hours later (⅓ of a day) sunrise is at 06:34.5 - This is simply absolutely wrong. (of course due to the poor quality of the graph, I do not know whether this is local time, GMT or what (ok, I admit that I don't know if Gabon is GMT or what, either)). → Please remove this graph, until it is corrected. Sunrise is a DISCRETE phenomenon (at a given location). It only happens once a day (at a given location). The graph is rubbish.173.189.74.6 (talk) 17:55, 21 September 2013 (UTC)

The problem is that you have misinterpreted the date notation. "01/02", for example, does not mean January 2. It means 1st February, using the more common international DD/MM notation. The graph therefore shows sunrise times (at daily intervals) for a whole year, not just for the month of January. It makes perfect sense, and is quite interesting. DOwenWilliams (talk) 20:13, 21 September 2013 (UTC)

Mercury's analemma

"Mercury: Because orbital resonance makes the day exactly two years long"

This appears wrong, since the resonance is 3:2 and not 1:2. The conclusion therefore also seems wrong. Can anyone with more experience in this take a look? 07:41, 7 February 2019 (UTC) — Preceding unsigned comment added by 2001:2012:406:0:60AE:6009:1576:404C (talk)

Mercury (planet) § Spin–orbit resonance gives an explanation. The 3 refers to the number of sidereal days. --Lasunncty (talk) 08:49, 7 February 2019 (UTC)

Untitled

In the second paragraph, the following sentences don't make sense: "The mean position appears to revolve around the Earth once every mean solar day, because of the Earth's rotation. This daily revolution is not considered to be averaged out to get the mean. The mean position of the Sun is therefore at the same place in the sky at the same time every day, but not at other times."

I suggest deleting them. Instead I would insert "at a fixed time" in the preceding sentence after "an observer at a fixed point on the Earth" — Preceding unsigned comment added by 137.108.145.24 (talk) 2015-01-30T14:44:24‎

I did not write the above, but I agree with it. The first 2 paragraphs are very unsatisfactory and should certainly be deleted. The last sentence of the 2nd paragraph is the only correct thing there. The reference to a mean position on the celestial sphere is entirely wrong. Whoever wrote this has a very confused notion of what the analemma is. I have therefore deleted the first 2 paragraphs, and have written an alternative. I am not a professional astronomer, so what I have written may need to be revised, but I am confident that this new lead is better than what was there before. g4oep — Preceding unsigned comment added by 77.96.58.212 (talk) 2015-05-17T02:22:27‎

Would someone like to enlarge on this : "The figure-eight form arises from the relationship between the direction of the earth's axis, and the line passing through the perihelion and aphelion of the earth's elliptical orbit around the sun." It would be interesting to know under what conditions the analemma would be a line inclined to the ecliptic meridians, and when it would be a circle. i.e. - how is the phase of the equation of time relative to the solar declination determined ? It seems to me that the analemma is an example of a Lissajous figure, the figure 8 form being related to the large 2nd harmonic content of the equation of time. How does this 2nd harmonic arise ? Under what conditions would it be minimised, and is it possible that under some conditions higher harmonics could be present, giving 3 or more loops ? g4oep — Preceding unsigned comment added by 77.96.58.212 (talk) 2015-05-18T02:04:11‎

I wrote the sentences you have seen fit to delete, and I still contend that they were more accurate and complete than your substitutions for them. However, since you found them difficult to understand, I have left your substitutions, but have added some words about the analemma's apparent motions in the sky, which are not related to the description as a set of positions of the Sun at a fixed time of day. I've also done some minor fixes which you'll see if you compare the current version with one from a few hours ago. DOwenWilliams (talk) 20:49, 17 May 2015 (UTC)

Thank you. I feel that the lead is steadily improving as these contributions accumulate. I have made a slight edit to the sentence concerning the long axis of the analemma in order to pull it into greater accord with what I think you mean. This sentence has now moved away from the idea I had when I wrote it - namely to give some meaning to the line of the long axis. Can anyone identify this line ? Is it a line of celestial longitude, for example ? Also, any comments on my immediately preceding edit on this page concerning Lissajous figure, conditions for specific phase relationships (zero phase, phase quadrature), harmonic content ? Concerning the idea of the movement of the analemma, as I see it, the analemma is a fixed pattern in the sky representing the sun's apparent motion as seen under the conditions stated in the article. The figure will appear at different positions in the sky if the chosen time of day at which the observations are made changes. I think a difficulty will arise if you attempt to define the analemma in such a way that, as a whole, it can move continuously, following the daily path of the sun in the sky, or, as was originally indicated, being fixed relative to the celestial sphere and therefore showing diurnal movement. For example, the line drawn in the sky by the sun on a particular day will be a continuous curve, and on successive days through the year discreet curves will appear. But a collection of such lines will not be an analemma, nor will the supposed problem of the analemma as a collection of discreet points be solved in this way. I would suggest that the analemma is in fact a collection of points, and the supposed continuous line of the figure exists only in the imagination. Wikki has a policy of presenting what is considered to be the usual meaning of terms, so I would like to ask "how is the analemma usually understood: as a fixed pattern of discreet points or as a moving pattern formed from a continuous line ?"

On reflection, I can see that a continuous curve would result if the analemma were defined as a plot of solar declination against the equation of time (as mentioned in the article). But it now seems that these are alternative definitions, related, but non-equivalent. Perhaps both should be given as non-equivalent alternative definitions: one a pattern in the sky, the other a plot on a graph. Of course neither would move in the sense we are discussing. G4oep (talk)

Astronomers generally think of the analemma as a continuous curve. Insisting on discrete points is oounter-productive.

Please learn the distinction between "discrete" and "discreet".

The long axis is bisected (divided into two *equal* parts) by the equator. The figure is not.

This description was getting far too long and detailed to be in the lead, so I've moved a lot of it to the "description" section.

DOwenWilliams (talk) 15:32, 18 May 2015 (UTC)

Good - the article is steadily improving. One minor point - I don't like to argue over trivia, but I think that precise use of language is desirable. This is one of the definitions of "axis" given here: http://www.thefreedictionary.com/axis. "2. Mathematics: a. An unlimited line, half-line, or line segment serving to orient a space or a geometric object, especially a line about which the object is symmetric". This is the meaning I had in mind, including the "unlimited" part. It makes no sense to me to say that an unlimited line is bisected, but I can appreciate the meaning of the bisection of the figure along an axis which is itself unlimited. You say that the figure is not bisected, so I cannot follow your meaning. I am sure that we agree that the figure has equal angular extent above and below the celestial equator. Can we find a form of words that sorts out this difficulty as well ? I would still like to include a comment about the orientation of this axis, and, if possible, its relationship to some form of recognised co-ordinate system. G4oep (talk)

The axis was originally said to be part of a line of ecliptic longitude. That was just plain wrong. I tried using celestial longitude, but that led to some awkward links to equatorial coordinate systems. So I simply used the celestial equator, which is simple and clear.

Surely, saying that the axis is bisected by the equator and perpendicular to it fully defines its orientation.

The analemma is not symmetrical in the north-south direction. The small northern loop does not match the large southern one. So an east-west line such as the equator cannot bisect it into *equal* halves.

I have put in a definition of the axis, as a finite line segment.

DOwenWilliams (talk) 18:25, 18 May 2015 (UTC)

I still think the version of 13 April is better than the more recent ones. I've half a mind just to revert to it. DOwenWilliams (talk) 18:33, 18 May 2015 (UTC)

The only reason for the figure 8 pattern is the axial tilt. The horizontal asymmetry stems from the misalignment of the solstices and apsides. It is not possible to have three or more loops.
The analemma is continuous. The discrete-point version only arises from the usual method of photographing it.
The origin of the graph is the position of the mean sun. Thus the analemma moves around the celestial sphere once per year.
A line connecting the northernmost point and the southernmost point of the analemma is meaningless. It is not perfectly vertical, nor does it divide the analemma into equal halves. If however you are talking about the y-axis of the graph, that represents when the equation of time is zero, or when the real sun would be at the same right ascension as the mean sun.
--Lasunncty (talk) 12:16, 21 May 2015 (UTC)

Parenthetical comment

I removed "(mostly in items 5 and 6 of the table of contents)" from the second paragraph of the introduction, because future edits, could change where in the table of contents those topics fall. An editor who adds a new section could easily not notice that they need to change these two numbers. And, since this comment is parenthetical, it is not essential to the meaningNick Beeson (talk) 04:46, 7 June 2015 (UTC) of the sentence.

translation from greek

seems Analemma means: “pedestal of a sundial".

Saw it in the italian wikipedia and also here, as third explanation:

http://www.yourdictionary.com/analemma Hexagone59 (talk) 00:25, 21 November 2015 (UTC)

According to the Sawyer reference used for this article, that was how the word was used in Latin. The original Greek usage was the more general meaning listed here. BTW, the link you gave uses wiktionary as its source. I would support changing all the wikis to avoid contradiction. --Lasunncty (talk) 17:34, 2 December 2015 (UTC)

Eccentricity effect on analemma

Note that the width (east-west component) of the eight-figure of analemma requires only an axial tilt. The effects of eccentricity (for the case of Earth) manifest primarily in a tilt of analemma, asymmetry of the lobes and a slight right-left assymetry. Please keep that in mind editing contributions of orbital parameters to the shape of analemma. L3erdnik (talk) 18:48, 4 July 2017 (UTC)

No, the asymmetry comes from the fact that the equinoxes are not lined up with the apsides. East-west motion could come from either eccentricity or axial tilt on their own. In the case of Earth, eccentricity is the larger contributor to the east-west motion, despite the fact that our eccentricity is less than 2%. See equation of time. --Lasunncty (talk) 20:45, 4 July 2017 (UTC)

Sorry, I apologize, I had it mixed up. The axial tilt's contribution is slightly more than the eccentricity's. I will change it back. --Lasunncty (talk) 20:55, 4 July 2017 (UTC)

I plan to edit some things not to upset those writers who have made the article what it is, but to make it more accessible to the average reader. Bear with me if I make a mistake. I am having trouble with the concept "East-west motion could come from either eccentricity or axial tilt on their own" ... after struggling with it, I can conceive how eccentricity yields the e-w effect, but not how axial tilt yields the e-w effect. There in fact seems to be an existing puzzle in the "description" section, which says "Viewed from an object with a perfectly circular orbit and no axial tilt, the Sun would always appear [to be] be a dot" ... but also says "with a circular orbit but significant axial tilt, the analemma would be a figure of eight"... and then says "with an eccentric orbit but no axial tilt, the analemma would be a straight east–west line" The problem with comprehending that is that the middle statement [circular with tilt] would be expected to say "a straight up and down line" with no east-west component. Carlw4514 —Preceding undated comment added 11:29, 13 January 2018 (UTC)

Well, yes, this is kind of a possibly counterintuitive feature of analemma's math, but it is true that only with axial tilt and no eccentricity we DO have east-west motion. I am not sure that the explanation why is it so would belong to the "description" section, but it definitely would make the article better. Maybe an extreme illustrative example would also help (say at 90 deg tilt)?.. L3erdnik (talk) 19:46, 14 January 2018 (UTC)

Carlw4514, the section you added Comprehension for the Hobbyist doesn't seem correct. Also you would need some citation for it. The comprehension of the analemma is all contained in the article Equation of time, thus I don't think we need your new section.--Gciriani (talk) 21:09, 15 January 2018 (UTC)

Thanks for the explanation. I do see where I missed the mark now. I'll look at that article carlw451413:43 Wednesday, January 17, 2018 —Preceding undated comment added 13:44, 17 January 2018 (UTC)

Asymmetry of analemma

I think the statement "The asymmetry ... arises ... from the fact that the equinoxes do not occur at the perihelion and aphelion" is incorrect. You can have an orbit in which equinoxes do not occur at the perihelion and aphelion and with a perfectly symmetric analemma. One needs only to look at the two components of the Equation of Time to grasp this concept. Just slide one of the two curves by a few days, and the equinoxes still do not occur at the perihelion/aphelion, but the resulting analemma will be perfectly symmetric.--Gciriani (talk) 14:56, 13 January 2018 (UTC)

I propose to eliminate the sentence about asymmetry in the first part of the article, since it is described in some more detail in a subsequent section. Also when describing asymmetry, we need to differentiate between N-S asymmetry and E-W asymmetry, or axis-symmetric shape.--Gciriani (talk) 23:29, 13 January 2018 (UTC)

For me it seemed pretty much appropriate in the "description", so for now I've clarified possible confusion there, however I don't see a big trouble in deleting that bit of info from the description either... L3erdnik (talk) 20:18, 14 January 2018 (UTC)

L3erdnik, I think you missed my point. You can have equinoxes occurring at perihelion-aphelion, and very large differences between lobes. I'm going to delete that sentence; that's besides the fact that there is no reference, and the reason for no reference is that it is incorrect. Actually a simulation I plotted shows no lobes when the equinoxes are aligned with aphelion-perihelion--Gciriani (talk) 18:02, 15 January 2018 (UTC)

Gciriani, ok, I would argue that for the claim in dispute one of the external links of the page (namely, Wolfram's simulation of the analemma) actually can be exploited as a source, since setting in that simulation the "spring equinox point" to 0 or 180 results in a centrally symmetric analemma, as I have claimed. I don't think it could be put as a link directly in the article since the statement it provides is not in the written form, but for purposes of validating the edit I think it is plenty (together with the reasoning I provided). I also have to say that I do not appreciate your strange attempt to impersonate me, whatever the purpose might have been. L3erdnik (talk) 07:21, 17 January 2018 (UTC)

L3erdnik, the comment in my talk page was not an impersonation but a copy and paste gone wrong. I fixed it, thanks for alerting me. That paragraph is supposed to be an explanation from me to you of why the analemma behaves in a particular way. I italicize it below.

Did you look at the equation of time link I gave you? It shows that the contribution of eccentricity is close to a sine function of period Y, where Y is one year, and the contribution of tilt is close to a sine function of period Y/2. The phase difference between the two sine functions is the difference between the winter solstice and the the perihelion. Thus in the case in which the equinox coincides with the perihelion, the phase difference is 90 degrees, and you can easily see how the analemma shape turns out. You can also convince yourself easily that a perfectly symmetrical eight shape is possible only when there is not eccentricity. That explains the whole thing.

I looked at the Wolfram's simulation, but it doesn't seem correct; I have found in Wolfram in the past other wrong simulations on other subjects; most simulations in Wolfram are submitted by volunteers and are not rigorously checked for correctness. In particular the screen shots I see do not show the units, so it's difficult to say what eccentricity, tilt, and equinox point they are supposed to show. Regarding your demonstration that if the equinox happened at the apsis, the shape of the analemma would be central symmetric, that is different than from symmetry with respect to one or both axis. The earth's analemma would be a slanted-eight shape with central symmetricity.--Gciriani (talk) 16:20, 17 January 2018 (UTC)

It seems we are closing in on something. The last couple of sentences you wrote is exactly the point I tried to make. And exactly for the reasons you mentioned (the confusion between different types of symmetry) I've made an edit in the very beginning of our conversation that clarifies that. The current version says the following:

The difference in size of the lobes of the figure-eight form arises mainly from the fact that the perihelion and aphelion occur far from equinoxes. They also occur a mere couple of weeks after solstices, and this discrepancy in turn causes slight tilt of the figure eight and its minor lateral asymmetry.

To me that seems to be in agreement with both yours and mine points and also fairly unambiguous. So, is there still an issue then?

PS. The Wolfram simulation looks indeed quite suspicious, after I've explored it some more... — Preceding unsigned comment added by L3erdnik (talk • contribs) 21:15, 17 January 2018 (UTC)

I'm including for reference links with simulations for equinox at 90 degrees and equinox at 0 degrees. The relative contributions of tilt and eccentricity are approximately in the same proportion as for the earth, where the effect of eccentricity is about 80% of the effect caused by tilt.--Gciriani (talk) 05:07, 18 January 2018 (UTC)

Updated with simulation for earth's analemma.--Gciriani (talk) 17:07, 18 January 2018 (UTC)

Solar analemmas seen from other planets

I removed these sentences from the other planets section, but was then reverted:

• If either of these variables (like eccentricity) always dominates the other (as is the case on Mars), the analemma will resemble a teardrop. If either of the variables (like eccentricity) is significant, and the other is practically zero (as is the case on Jupiter, with only a 3° tilt), the figure will be something much closer to an ellipse. If both are important enough, that sometimes eccentricity or axial tilt dominates, a figure-eight results.

The source used to support these sentences was already in question, and plus there is already discussion about the shape of the analemma earlier in the article. What I can tell from simulations is that a loop occurs only when obliquity is low and the angle between apsides and equinoxes is high. Eccentricity only has a minor effect. The teardrop is a transitional state between the elliptical loop and the figure-eight. --Lasunncty (talk) 17:05, 25 January 2018 (UTC)

It's a fallacy, because for Jupiter, just changing the equinox angle, one can obtain either an ellipse or a figure 8. Just thinking about what determines a figure 8, one realizes that a figure 8 happens when the maximum and minimum happen alternatively before and after the solstices. I think the Wolfram page could be used as reference, but it would be better to find a reliable source. I partly agree with your teardrop being a transitional state, but not always, as you can conclude by playing with the parameters for Mars first and then for Jupiter.--Gciriani (talk) 21:27, 25 January 2018 (UTC)

The example you give supports my assertion. I looked at the code for the Wolfram module and they use a very complicated formula for EOT, but it doesn't seem to be correct when obliquity > 90°. Also, it doesn't have the correct equinox angles for the planets other than earth. --Lasunncty (talk) 15:46, 27 January 2018 (UTC)