# Talk:Ecliptic coordinate system

## Celestial latitude and longitude

I thought this was the place to explain a series of related changes I've made. I restored the Ecliptic latitude and Ecliptic longitude articles, because the orphan Celestial latitude and Celestial longitude articles had become redirects to Declination and Right ascension, which are quite wrong. They needed something to point to and they now redirect to the restored Ecliptic latitude and Ecliptic longitude articles. SteveMcCluskey 05:22, 20 February 2007 (UTC)

A question: the stars on the ecliptic are steady, so is more or less the ecliptic pole, the pole around which the north or south pole turn in about 25000 years (I mean here the ecliptic pole and the ecliptic are steady in millions of years, that have to do with the movement of the stars and the galaxy and not the precession). I have the impression that this is not so clear in the article (of course it can be, that i havn't understand it well)Yormomo (talk) 00:23, 23 February 2012 (UTC)

## conversion algorithm

I've been trying to implement functions based on the text provided in this section and I must confess to being totally confused. If we consider the first cas eof converting from ecliptic (RA,Dec) to equatorial (lat,lon) then to state the obvious we know (RA,Dec) but we do not know (lat,lon), but the article reads as if we know all 4 variables. For instance, the first line of the algorithm states "Calculate the terms right of the = sign of the 3 equations given above", but how is it possible to do this if we don't yet know (lat,lon)?

If you know (RA,Dec), you compute the right sides of the second set of equations. If you know (lat,lon), you compute the right sides of the first set of equations. —Tamfang (talk) 07:39, 4 April 2008 (UTC)

The second line of the algorithm states "taking the cos α cos δ as the X value". Are we to interpret this x=cos α cos δ or x=cos λ cos β because if it's the 2nd version, again we don't know lambda and beta.

I would suggest interpreting "α" as α and "δ" as δ, but that's just me, you may find some other approach more useful. —Tamfang (talk) 07:39, 4 April 2008 (UTC)

The closing line of the algorithm section states "Similarly for the equatorial to ecliptic transformation". After coding what I thought was the algorithm was, doing the inverse calculation I don't get back the original (RA,Dec) values from the (lat,lon) computer values. What's really needed for this page is an example. gmseed 28/03/2008

If I understand it well, the conversion algorithms don't take the precession in considerationYormomo (talk) 00:17, 23 February 2012 (UTC) But I see now that precession is included in the equatorial coordinates, so they are ok 93.82.149.44 (talk) 17:41, 23 February 2012 (UTC)

## Rectangular coordinate system (ecliptic)

The article seems to be exclusively about spherical ecliptic coordinates and says nothing about the 3D (x,y,z) rectangular coordinate system that is used extensively in orbital and positional computations. Perhaps the article could be better titled "Spherical ecliptic coordinate system"? Pomona17 (talk) 13:11, 8 November 2008 (UTC)

The wording of the paragraph on xyz coords is confusin'. I'm a-changin' it, and you can see if that's better or worse. Friendly Person (talk) 16:50, 30 August 2015 (UTC)

Nope, doesn't work.
the x axis toward the vernal equinox, that is, the place in the earth's orbit where the earth passes from winter into summer. (At this point in the orbit, observers on earth see the Sun cross the celestial equator in a northward direction.)
These are two opposite sides of Earth's orbit. Look at the diagram. The x-axis extends out from the place where the Sun is seen (from the Earth) at the June equinox, not where the Earth is at the time. Yes, the Earth is on the negative side of the x-axis, but that's not where the origin is. Tfr000 (talk) 17:38, 30 August 2015 (UTC)
I agree with Friendly person's change. I couldn't understand Tfr000's comment; there is no June equinox, but there is a June solstice, which has nothing to do with this discussion. Jc3s5h (talk) 18:18, 30 August 2015 (UTC)
Now that I look it, I'm thinking my change, while simpler English perhaps, did have that one thing incorrect. One could define a coordinate system any way that's handy, but we're trying to get at the one that corresponds to the standard polar coordinates. It seems that, at spring equinox, the sun is at 0 degrees celestial longitude, ie. the earth is indeed on the negative part of the x axis. Since this is an article that someone might rely on for something important, like programming a nav system, I will fix it forthwith. Friendly Person (talk) 00:56, 31 August 2015 (UTC)

The edit to the article by Friendly person at 17:14, 30 August 2015‎ is correct. The statement immediately above, "at spring equinox, the sun is at 0 degrees celestial longitude" is wrong because the Sun (or the barycenter if you prefer) is at the origin and the celestial longitude is undefined. Here is output from the Multiyear Interactive Computer Almanac (created by the US Naval Observatory) to show the situation at the March equinox:

                                   Earth

Heliocentric Ecliptic Positions
Mean Ecliptic and Equinox of J2000.0

Date        Time          Longitude         Latitude         Distance
(TT)
h  m   s           °                 °                AU
2015 Mar 20 22:46:00.0       179.79203        +  0.00017      0.995946417


We see the Earth is in the negative x direction from the Sun (that is, close to 180°). Thus, if we began at Earth, which had coordinates approximately (-1 AU, 0 AU, 0 AU), and proceeded in a straight line we would pass through the Sun, which is at (0, 0, 0) and continue on to the constellation Pisces. Several thousand years ago it would have been the nearby constellation of Aires, which is why this direction is still known as the first point of Aires. Jc3s5h (talk) 02:12, 31 August 2015 (UTC)

Oops...
there is no June equinox, but there is a June solstice
...March equinox...
So now with that out of the way,
the vernal equinox, that is, the place in the earth's orbit where the earth passes from winter into summer.
still doesn't work. The vernal equinox on the celestial sphere is not at the place where, from the Sun, the Earth would appear to be when the Northern hemisphere passes from winter to summer. It is where the Sun, seen from the Earth would be at that time - exactly opposite.
at spring equinox, the sun is at 0 degrees celestial longitude
is just imprecisely worded. It should be something like "at the spring equinox, the sun appears to be at 0 degrees celestial longitude from Earth." Bit of a pain, this stuff. Tfr000 (talk) 02:49, 31 August 2015 (UTC)
True, the equinox is not located at the Earth; it isn't a place at all, it's a direction. I deleted the offending passage. We shouldn't define the same direction in several places. It's defined in the lead; if that definition isn't good enough, that's where it should be fixed. Jc3s5h (talk) 03:22, 31 August 2015 (UTC)
Thank you all for helping me. There are two ways to get information: 1) go find it 2) put out some wrong information, and people will correct you. (2) can be unintentional as in my case here (and I humbly apologize) or intentional, which I have seen done. Friendly Person (talk) 13:59, 3 October 2015 (UTC)

## Diagram is needed

Per the guidance of the header [The article may be too technical for most readers to understand], this topic needs a diagram to explain the topic. Bcwilmot (talk) 20:53, 25 July 2010 (UTC)

## Spherical Trigonometry

This article should make some reference to the fact that the formulas shown were derived using Spherical Trigonometry. This would address most of the concerns expressed above, including the need for a diagram. — Preceding unsigned comment added by Alexselkirk1704 (talkcontribs) 16:13, 8 January 2011 (UTC)

## Units of measurement

Should astrological signs be mentioned? Sometimes astrological signs are used as the units of measurement for ecliptic longitude, just as hours can be used as the units of measurement for right ascension. (Astrological signs are also a unit of angular measurement (used only for ecliptic longitude), although some people do not know this.) --Zzo38 (talk) 05:44, 18 June 2012 (UTC)

Outlines of Astronomy by John Herschel, 7th ed. in 1864, makes no mention of zodiac signs as a measure of ecliptic longitude. I've seen this work described as highly influential. I have not come across any work on astronomy that actually uses zodiac signs for longitude, although I think I've seen this mentioned as a historical practice. I think the thing to do is leave it out until some editor with access to sources on the history of mathematical, scientific, or astronomical terminology is able to look up when this terminology faded out. Jc3s5h (talk) 11:44, 18 June 2012 (UTC)
Yes, astrological signs were used (360°/12 = 30° each), maybe back around Kepler's time and before, but this was dropped pretty quickly once measuring devices were developed. I don't think there will be much mention of them in any English references... it was far back enough that they will mostly be in Latin. Might be worth a sentence or two if we can find a reference. Tfr000 (talk) 13:23, 18 June 2012 (UTC)
I found a reference. Tfr000 (talk) 15:00, 21 June 2012 (UTC)
It is not true that they are not used any more today; perhaps they are not used as often today, though, and usually astrologers use it, astronomers rarely use it today (in the past, before science was invented, it was the same thing). Astronomers more commonly using equatorial coordinates today, anyways (since equatorial coordinates is more useful for observation of stars by telescopes, than ecliptic coordinates are). (I still use both ecliptic and equatorial coordinates, and will use different units too depend what is being done. Notice also that, you need to have some zero longitude reference, and whatever zero of ecliptic longitude is will be called 0 Aries, even if it is not near that constellation (signs and constellation are two different things; tropics of Cancer/Capricorn correspond to astrological signs not to constellations).) --Zzo38 (talk) 23:41, 2 November 2012 (UTC)

## This was "dumped" in the article. I relocated it here.

### Ecliptic latitude and longitude

Ecliptic latitude and longitude are defined for the planets, stars, and other celestial bodies in a broadly similar way to that in which terrestrial latitude and longitude are defined, but there is a special difference.

The plane of zero latitude for celestial objects is the plane of the ecliptic. This plane is not parallel to the plane of the celestial equator, but rather is inclined to it by the obliquity of the ecliptic, which currently has a value of about 23° 26′. The closest celestial counterpart to terrestrial latitude is declination, and the closest celestial counterpart to terrestrial longitude is right ascension. These celestial coordinates bear the same relationship to the celestial equator as terrestrial latitude and longitude do to the terrestrial equator, and they are also more frequently used in astronomy than celestial longitude and latitude.

The polar axis (relative to the celestial equator) is perpendicular to the plane of the Equator, and parallel to the terrestrial polar axis. But the (north) pole of the ecliptic, relevant to the definition of ecliptic latitude, is the normal to the ecliptic plane nearest to the direction of the celestial north pole of the Equator, i.e. 23° 26′ away from it.

Ecliptic latitude is measured from 0° to 90° north (+) or south (−) of the ecliptic. Ecliptic longitude is measured from 0° to 360° eastward (the direction that the Sun appears to move relative to the stars), along the ecliptic from the vernal equinox. The equinox at a specific date and time is a fixed equinox, such as that in the J2000 reference frame.

However, the equinox moves because it is the intersection of two planes, both of which move. The ecliptic is relatively stationary, wobbling within a 4° diameter circle relative to the fixed stars over millions of years under the gravitational influence of the other planets. The greatest movement is a relatively rapid gyration of Earth's equatorial plane whose pole traces a 47° diameter circle caused by the Moon. This causes the equinox to precess westward along the ecliptic about 50″ per year. This moving equinox is called the equinox of date. Ecliptic longitude relative to a moving equinox is used whenever the positions of the Sun, Moon, planets, or stars at dates other than that of a fixed equinox is important, as in calendars, astrology, or celestial mechanics. The 'error' of the Julian or Gregorian calendar is always relative to a moving equinox. The years, months, and days of the Chinese calendar all depend on the ecliptic longitudes of date of the Sun and Moon. The 30° zodiacal segments used in astrology are also relative to a moving equinox. Celestial mechanics (here restricted to the motion of solar system bodies) uses both a fixed and moving equinox. Sometimes in the study of Milankovitch cycles, the invariable plane of the solar system is substituted for the moving ecliptic. Longitude may be denominated from 0 to ${\displaystyle {\begin{matrix}2\pi \end{matrix}}}$ radians in either case.

Tfr000 (talk) 15:24, 28 February 2015 (UTC)

I removed the following incorrect addition:

Because of axial precession, ecliptic longitude of "fixed stars" (referred to the equinox of date) increases by about 50.3 arcseconds per year, or 83.8 arcminutes per century.[1]

References

1. ^ J.H. Lieske et al. (1977), "Expressions for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants". Astronomy & Astrophysics 58, pp. 1-16. See p. 15 where the value 5029.0966 arcseconds per century is given.

The problem is that the cited source is giving p = 5029.0966 arcseconds per Julian century. The variable p is used for precession in right ascension, that is, measured along the celestial equator. But the phrasing of the addition indicated it was measured along the ecliptic; the variable for that would be ζ. Jc3s5h (talk) 19:57, 28 February 2016 (UTC)

@Jc3s5h: I think you have misunderstood what ζ is. (It is the negation of the right ascension, in coordinates of a certain fixed epoch, of the new north pole at some other date.) But I agree that my statement was not quite correct. It's not quite correct because the ecliptic pole moves slightly. So the ecliptic longitude of a fixed star near the ecliptic pole can change at an unbounded rate! Since the ecliptic moves much less than the equator, what I wrote is approximately true for most stars. I will rephrase it. Eric Kvaalen (talk) 09:57, 29 February 2016 (UTC)

I see that the source says 5029.0966" is the "speed of general precession in longitude" so, for the variable definitions used in that paper, your figures are valid. Jc3s5h (talk) 16:39, 29 February 2016 (UTC)