Miriande : find approx time when this happens, and generate a series of calculation. use ecl long at 165 deg (白露) as an example from HKO, it happens on Sep 8, 05:26 UTC. the closest time is 2023-09-08T05:26:15.00 Calculate 60 steps as above figure. Reference: Type of Ephemeris, or frame of reference: use MeanOfDate , ie JNow Ap-i.net the difference between Mean J2000 and Astrometric J2000 is the first one use the proper motion for 2000.0, but the second the proper motion for the epoch of the chart. This is used for astrometry measurement when people want J2000 coordinates but also want to correct the reference star position for the date of the observation. "Mean of the date" use the mean equinox of the date, without nutation and aberration correction. Many printed almanac use this system. ...referenced to the current mean ecliptic and equinox, often called JNOW. In this context mean, includes precession but ignores the smaller oscillations due to nutation. Cloudynights ...