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.