I can compute the following data for the Moon for a given time and geographic location using the JPL Horizons system:

  • Apparent RA & DEC
  • Apparent azimuth & elevation (AZ-EL)
  • Target range & range rate (relative to observer)
  • Illuminated fraction
  • Phase angle and bisector

Is it feasible to compute the shape and orientation of the crescent from this data and if yes how is the computation procedure. I would be grateful if any one can answer this question for me.

  • $\begingroup$ For the orientation, the largest factor is the "parallactic angle". You can find many sources for info by searching for that term. $\endgroup$ Sep 21, 2022 at 15:55
  • $\begingroup$ The best source for the computation of the physical appearance of the Moon is Astronomical Algorithms, by Jean Meeus [1998]. Do you have access to it (personal copy, library copy, etc.)? $\endgroup$ Sep 22, 2022 at 2:12
  • $\begingroup$ There's also "24. Sun-Target-Observer angle", which includes stellar aberration on the down-leg from target to observer. $\endgroup$
    – PM 2Ring
    Sep 22, 2022 at 2:40
  • $\begingroup$ Thank's for the answers. I can get a copy of Astronomical Algorithms, by Jean Meeus from the Bavarian State Library in Munich. $\endgroup$
    – Klaus Rohe
    Sep 29, 2022 at 9:12

1 Answer 1


I've written a blog showing how you can do it with sample formula and python codings here: Formulas to determine, or create, the illuminated phase and orientation of the Moon (Moon tilt) at your location, as seen in your sky

  • 1
    $\begingroup$ Link only answer is likely to be removed. Please add the relevant details in the answer so that user can see without having to go to the link. $\endgroup$ Oct 18, 2022 at 10:21

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