My question is similar to the one posted by Abtract, whom however never got a useful answer. I am trying to calculate from scratch the exact times of sunrise and sunset anywhere on earth taking into account the 'equation of time' and other time dependent variables. This requires computing the line of sight to the rim of the sun at any universal time instant. To do this one needs an invariant as possible coordinate systems, preferably centered at the sun. I have tried using the ecliptic plane and its normal as basis, but with only moderate success (up to about a minutes difference from published values). Now many texts define the ecliptic plane as the one which contains the yearly path of the earth around the sun or, vice versa, the apparent path of the sun around the earth. However, unless stated as an "average path" over a certain (long - say 100 years) time frame, then the normal of this plane must wobble monthly due to the pertubations caused by the moon (ignoring the other planets) and the intersection between the earth's equatorial plane and the ecliptic also varies. So is the ecliptic actually the path of the earth-moon barycenter (in which case it would be more invariant) or is there another more stringent definition I can use to get accurate timings? So exactly what is the best polar coordinate system and what are it's commonly named coordinates and parameters.

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    $\begingroup$ If you want results as accurate as NASA's, use the CSPICE libraries (naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/index.html). The most basic frame, in some sense, is the ICRF: en.wikipedia.org/wiki/International_Celestial_Reference_Frame If you want accuracy to the nearest minute, you will need to take the Earth's ellipsoid shape into account, which CSPICE also does. $\endgroup$ – user21 Jun 21 '17 at 4:38
  • $\begingroup$ I consider using NASA's or other programs as sort of "cheating" since I want to test whether or not I can get ALL the equations explained and expressed in understandable mathematical terms. I might add, that my calculations include the elliptic orbits of the moon, the earth and the earth-moon barycenter as well as the time dependency of their excentricities, major axis' and inclinations. I also take in to account influences of the ellipsoid shape of the earth, the bending of rays in the earth atmosphere and time lags due to the speed of light.Despite all this I just can't get the exact answers $\endgroup$ – Jens Jun 21 '17 at 22:31
  • $\begingroup$ barrycarter: Anyway, I thank you for the reference to ICRF which seem to be just what I want. However I don't really understand their terminology and all I only need are the ICRS polar coordinates of the centers of the sun, the earth and the moon at a certain instant (vernal equinox) in J2000 as well as ICRS data that describe their orbit planes at that time in terms of the direction of the normal and the direction and length of the major axis. I don't know if the sun has an orbit around the ICRS center, but if elliptical or near-elliptical, I also need the excentricity. $\endgroup$ – Jens Jun 21 '17 at 23:24
  • $\begingroup$ While I sort of agree w/ you re "cheating", doing it yourself requires solving differential equations (astronomy.stackexchange.com/questions/13488/…), and you can at least use HORIZONS as a double check. Things like eccentricity change over time. Sun around barycenter: en.wikipedia.org/wiki/Barycenter#Inside_or_outside_the_Sun.3F $\endgroup$ – user21 Jun 22 '17 at 2:58
  • $\begingroup$ barrycarter: Maybe solving the 3-body (sun-earth-moon) differential equations numerically using RK4 is necessary to get the minutes.second right. Maybe I'm naive, but I thought that neglecting pertubation effects from other planets and thus assuming a planar elliptical paths of the earth-moon barycenter, the earth and the moon in heliocentric coordinates (and taking in to account the time dependency of the associated parameters) would yield sufficiently accurate results down to the last minute, considering the other effects I also deal with. Am I wrong? $\endgroup$ – Jens Jun 22 '17 at 12:54

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