Talk:Mean longitude

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The lead defines the concept in terms of a counterfactual. The problem with doing so is that counterfactuals admit multiple interpretations depending on how they're reconciled with reality. How about defining it instead as 360 degrees times the fraction of a year elapsed since the last periapsis? The current opening sentence is fine as a second sentence as long as it isn't taken as the definition. If no one objects I'll do it myself. Vaughan Pratt (talk) 00:54, 23 December 2013 (UTC)Reply

No objections from me. However, your description here describes the mean anomaly rather than the mean longitude. But if you can come up with a good definition, go for it. --Lasunncty (talk) 06:45, 1 January 2014 (UTC)Reply

A very wordy article for a simple concept. Mean longitude is just the angular distance from a reference direction which a body would have if it moved at a uniform angular rate, rather than the non-uniform rate which occurs because of an elliptical orbit. That's it. The second paragraph is discussing, in a convoluted, repetitive fashion, so-called mean elements, which have nothing to do with mean longitude. Mean elements are a sort of average over a long time period. Yes, you can have a mean longitude as part of a set of mean elements, but this "mean mean longitude" thing is a little contrived. I had to search for it to find out what it was supposed to be, and only came up with a couple of hits. Tfr000 (talk) 01:05, 28 October 2015 (UTC)Reply

The lead also mentions "if its inclination were zero". Mean longitude is typically measured from a reference direction, along a reference plane to an ascending node, then along the orbital plane to the mean position of the object. Good luck reducing all of that to zero inclination - and in practice, this isn't done. Tfr000 (talk) 02:09, 29 October 2015 (UTC)Reply

Mean longitude and ascending node longitude are found in ephemeris tables. The mean longitude, as defined in this article, is the sum of the ascending node longitude, measured in the ecliptic plane, and the perihelion argument, measured in the orbital plane. Such a quantity can't be used as the argument of a trigonometric function. Instead, the (published) ascending node longitude is subtracted from the (published) mean longitude to give the perihelion argument, an angle entirely in the orbital plane. Likewise, the (published) perihelion longitude is another sum of angles in two different planes, the perihelion argument (orbital) and the ascending node longitude (ecliptic). The mean anomaly, an angle entirely in the orbital plane, may then be calculated by subtracting the (published) perihelion longitude from the (published) mean longitude. Mean anomaly is then used, with orbital eccentricity, in Kepler's equation to give eccentric anomaly, which, along with orbital eccentricity and semimajor axis distance, are used to calculate orbital plane planetary coordinates, which are then used along with perihelion argument, ascending node longitude, and orbital inclination, in standard Eulerian angle rotations, to give heliocentric ecliptic coordinates. I am sure this discussion is correct because I have used this method, as described in the reference, to reproduce, to about the accuracy also described in the reference, the positions of planets as may be calculated from the JPL HORIZONS web page.

Reference: Urban S, Seidelmann P (eds). Explanatory Supplement to the Astronomical Almanac, 3rd ed. 2013: Mill Valley, CA. University Science Books. pp 338-341, 347-348 — Preceding unsigned comment added by 172.56.40.177 (talk) 17:09, 14 February 2018 (UTC)Reply