I am using Jean Meeus book Astronomical Algorithms and the C software that comes with the book to calculate planetary data. I am comparing two planet's longitude to calculate the time when they are a fixed amount of longitude apart such as 45, 60, 90 degrees apart. These are the standard planetary aspects used in astrology. I can not calculate the correct time when one or both of the planets is approaching its stationary retrograde motion point. At this point the planets velocity approaches zero and the longitude does not have the decimal point accuracy to make a comparison. The time will be off by anywhere from a few minutes to eleven hours when compared to a commercial ephemeris.

Q.) Does anyone know a different method other than simple longitude comparison that can calculate the correct planetary aspect time when planets are near their retrograde motion stationary point?

-- Edit is Below --

Here is an example of my problem. My calculations below are made with Astronomical Algorithms software at 1 minute increments for August 1, 2016 at midnight. The calculations show Venus longitude which is moving Direct Motion and Uranus which is moving Retrograde Motion. The American Ephemeris at midnight lists the Venus 120(Trine) Uranus as occurring at 4:10 AM. The Astronomical Algorithms calculations below identify Venus 120 Uranus at 3:56AM which is 16 minutes early. Every time a slow outer planet like Uranus is near a station point and moving very slow my aspect time is always off.

Q) Is there a different way to calculate the aspect rather than longitude comparison? Maybe use some king of time correction function?

Geocentric Longitude

Venus Direct Motion

Uranus Retrograde Motion

Date ___ Time _______ Venus _______ Uranus

08/01/16 03:53 AM 144.5040255637 24.5061221269

08/01/16 03:54 AM 144.5048790144 24.5061207491

08/01/16 03:55 AM 144.5057324652 24.5061193708

08/01/16 03:56 AM 144.506585916 24.5061179922 Venus 120 Uranus

08/01/16 03:57 AM 144.5074393668 24.5061166132

08/01/16 03:58 AM 144.5082928175 24.5061152338

08/01/16 03:59 AM 144.5091462683 24.506113854

08/01/16 04:00 AM 144.509999719 24.5061124738

08/01/16 04:01 AM 144.5108531697 24.5061110932

08/01/16 04:02 AM 144.511706621 24.5061097123

08/01/16 04:03 AM 144.5125600718 24.5061083309

08/01/16 04:04 AM 144.5134135225 24.5061069491

08/01/16 04:05 AM 144.5142669732 24.5061055669

08/01/16 04:06 AM 144.5151204239 24.5061041844

08/01/16 04:07 AM 144.5159738746 24.5061028014

08/01/16 04:08 AM 144.5168273253 24.5061014181

08/01/16 04:09 AM 144.5176807759 24.5061000343

08/01/16 04:10 AM 144.5185342266 24.5060986502 American Ephemeris Venus 120 Uranus

08/01/16 04:11 AM 144.5193876773 24.5060972657

  • $\begingroup$ Could you give us a specific example? Meeus book is good, but you might consider using naif.jpl.nasa.gov/naif/tutorials.html which is more accurate and still free. You can even try using wgc.jpl.nasa.gov:8080/webgeocalc/#NewCalculation if you don't want to download anything. $\endgroup$
    – user21
    Nov 7, 2016 at 16:30
  • $\begingroup$ I added a sample. I do not think comparing longitude can give the correct answer. There must be another way to do this. How are other people getting the correct answer? $\endgroup$
    – homebase
    Nov 17, 2016 at 10:36
  • $\begingroup$ You could try using ssd.jpl.nasa.gov/?horizons or libnova or pyephem or skyfield. Notice that, at 04:10, the difference in longitude is 120.0124355764, which is only 45 arcseconds away from 120, so pretty close (as you point out, the time difference is larger because Uranus is moving so slowly). Even "precise" astronomical libraries and programs differ when giving results: stackoverflow.com/questions/16293146/… $\endgroup$
    – user21
    Nov 17, 2016 at 16:53
  • $\begingroup$ I believe there is a different method (other than comparing longitudes) to calculate the time of a stationary point and the aspects around the stationary points. More accurate longitudes does not seem to be the answer. I have not been able to find anyone who is calculating these values and knows for sure the best way. $\endgroup$
    – homebase
    Dec 13, 2016 at 8:16

1 Answer 1


There is software for calculating planetary aspects which is based on the JPL ephemeris -- https://ssd.jpl.nasa.gov/horizons/ It calculates geocentric planetary positions, and aspects between planets, at time intervals of 30 minutes. Geocentric longitudes are calculated to the nearest arcminute. For August 1, 2016, at 4:00 GMT, it shows that the difference from an exact trine between Venus and Uranus was 0 degrees 0 minutes. 30 minutes before 4 AM it was 0 deg 2 min, and 30 minutes after 4 AM it was 0 deg 1 min. So to within 1 arcminute the trine was exact at 4:00 AN. The program is to be seen at https://www.planetary-aspects.com/pat/pat.htm You can download a free trial version, though I don't know if it will permit this calculation of the exact trine time.


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