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Re: Jupiter and Mars
From: Paul Hirose
Date: 2024 Aug 7, 15:52 -0700
From: Paul Hirose
Date: 2024 Aug 7, 15:52 -0700
> *From: *Robert H. van Gent > *Date: *2024 Aug 7, 10:15 +0000 > > https://www.imcce.fr/lettre-information/archives/214#current-article4 > > Aldo Vitagliano’s SOLEX software gives 0.30645° at 14:54:18 TT. The IMCCE newsletter says separation is 18′23.2″ at 2024-08-14 14:53:09 UTC [= 14:54:18 TT]. SOLEX gives the same time, and minimum separation 18′23.22″. I agree exactly with SOLEX. My method was described in these pages some time ago. The first step is to compute geocentric apparent coordinates of both bodies at equally spaced times t0, t1, t2. The coordinates can be in any system. Let's say it's the ICRS. The estimated time of minimum separation is t1. At each time, compute the separation and position angles from one body (body0) to the other (body1). Those values can be considered spherical coordinates (north polar distance and RA) of body1, in a system where body0 is the north pole and the ICRS pole is on the zero meridian. (The latter is true because position angles were calculated from ICRS coords.) Call the points p0, p1, p2. Now transform the coordinates to a new frame where the points have the same relative positions but p0 and p2 are on the equator and p0 is on the prime meridian. Coordinates of body0 are also transformed from the "north pole" to the new system. Now p0, p1, p2 represent the relative motion of body1. If it's practically linear, p1 "declination" in this new system is very near zero (p0 and p2 are on the equator by definition). Also, the points should have almost equal differences in "RA". Failure to attain this condition is a warning the algorithm won't work well. Remember, body0 was also transformed to the new system. If t1 is truly the time of minimum distance, body0 and p1 have identical RA. If not, adjust t1 and recompute. After the solution converges, body0 "declination" is the minimum separation. In this case, linearity was virtually perfect, the initial time (intentionally a minute in error) needed only one adjustment, and the solution was sharply defined. But in other cases, where the separation was larger and the bodies slower, my algorithm didn't work very well. -- Paul Hirose sofajpl.com
