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    Re: Short Term Proper Motion
    From: Bill Bertrand
    Date: 2019 Mar 11, 08:54 -0700

    Thanks Paul.  I negelected to include the Hipparcos fragments at the bottom of my firs post.  I am including the complete post to avoid neeing to jump between them.  In answer to your comments

    • The header notes indicate that the j2000 values are extrapolated.  (In BOLD)
    • The j1991.25 Dec value is listed (it differs ~3x10^-5) degrees for the 9 year difference
    • I used BOLD font for important parts
    • I assumed that I could multiply mas/year * years to get the delta declination (mas) for this simple short term declination change.  (Is that incorrect?)
    • As you noted, I fear I am using the catalog data incorrectly.

    I am having a problem calculating simple short term proper motion.  Since I am off by orders of magnitude, it's certain I missed a point obvious to others.

    To use the simplest case, I am confining my example on proper motion in declination, to avoid RA's need to be a function of the cos(declination).
    The example:  Bellatrix on Date: 2016/12/28 T 23:14:15 UTC
    • (Stellarium output for the date is listed below and the Bellatrix fragment of Hipparcos below that)
    • Dec J2000            (Stellarium &  Hipparcos): 6°20'58.7" or 6°20.98'
    • Declination on that date (USNO, Stellarium): 6°21'41.0" or 6°21.68'
    • The Declination on the 2 dates differ by 0.7 minutes of arc!
    • I calculate 16.99 Julian years between J2000 and the date above at 365.25 JDays/JYear
    • Stellarium pmDec =-13.6 (mas/yr), Hipparcos pmDec = -12.88 (mas/yr) milliarcseconds/year
    • {at}-12.88 mas/yr  I get -218.86 mas in 16.99 years or -0.218 arcseconds
    Where did I go wrong?
    Thank you in advance,
    Bill Bertrand

    What follows is the Hipparcos catalog fragment (supplied by VizieR) for Belletrix that I used:

    #   VizieR Astronomical Server vizier.u-strasbg.fr
    #    Date: 2018-07-31T21:42:33 [V1.99+ (14-Oct-2013)]
    #   In case of problem, please report to:    cds-question{at}unistra.fr
    #Coosys    J2000:    eq_FK5 J2000
    #INFO    votable-version=1.99+ (14-Oct-2013)   
    #INFO    -ref=VIZ5b60d1c7543c   
    #INFO    -out.max=99999   
    #INFO    queryParameters=26   

    hip2}&key:source=I/311/hip2&HTTPPRM:&&-ref=VIZ5b60d1c7543c&-out.src=I/311/hip2&Clear= Clear&-c.r=  2&-out=HIP&-out=n_HIP&-out=Sn&-out=So&-out=RArad&-out=DErad&-out=Plx&-out=e_Plx&-out=pmRA&-out=pmDE&-out=Hpmag&Hpmag=<2.0&-out=B-V&-out=HIP1&-meta.ucd=2&-meta=1&-meta.foot=1&-usenav=1&-bmark=POST&-out.add=_RAJ,_DEJ&-order=I&-oc.form=dec&-c.geom=r&-out.max=10&-out.form=| -Separated-Values&undefined=CDS, France&-c.eq=J2000&-c.u=arcmin&
    #-c.r=  2

    #Name: I/311
    #Title: Hipparcos, the New Reduction (van Leeuwen, 2007)
    #Coosys    J2000_1991.250:    eq_FK5 J2000
    #Table    I_311_hip2:
    #Name: I/311/hip2
    #Title: The Astrometric Catalogue
    #Column    _RAJ2000    (F14.10)    Right ascension (FK5, Equinox=J2000.0) at Epoch=J2000, proper motions taken into account     [ucd=pos.eq.ra]
    #Column    _DEJ2000    (F14.10)    Declination (FK5, Equinox=J2000.0) at Epoch=J2000, proper motions taken into account     [ucd=pos.eq.dec]

    #Column    HIP    (I6)    Hipparcos identifier    [ucd=meta.id;meta.main]
    #Column    n_HIP    (A1)    Simbad column added by the CDS    [ucd=meta.note]
    #Column    Sn    (I3)    [0,159] Solution type new reduction (1)    [ucd=meta.id;stat.fit]
    #Column    So    (I1)    [0,5] Solution type old reduction (2)    [ucd=meta.id;stat.fit]
    #Column    RArad    (F12.8)    Right Ascension in ICRS, Ep=1991.25    [ucd=pos.eq.ra;meta.main]
    #Column    DErad    (F12.8)    Declination in ICRS, Ep=1991.25    [ucd=pos.eq.dec;meta.main]
    #Column    Plx    (F7.2)    Parallax    [ucd=pos.parallax]
    #Column    e_Plx    (F6.2)    Formal error on Plx    [ucd=stat.error;pos.parallax]
    #Column    pmRA    (F8.2)    Proper motion in Right Ascension    [ucd=pos.pm;pos.eq.ra]
    #Column    pmDE    (F8.2)    Proper motion in Declination    [ucd=pos.pm;pos.eq.dec]
    #Column    Hpmag    (F7.4)    Hipparcos magnitude    [ucd=phot.mag;em.opt.V]
    #Column    B-V    (F6.3)    Colour index    [ucd=phot.color;em.opt.B;em.opt.V]
    #Column    HIP1    (A4)    Data from the first edition of the Hipparcos Catalog (1997, Cat. I/239)    [ucd=meta.ref.url]
    _RAJ2000         |_DEJ2000           |HIP    |n_HIP|Sn|So|RArad             |DErad              |Plx      |e_Plx |pmRA |pmDE  |Hpmag|B-V   |HIP1
    deg                    |deg                     |      | |   |                   |deg                 |deg                  |mas    |mas   |mas/yr|mas/yr |mag     |mag   |
    ----------------------|-----------------------|------|-|---|-                |-------------------|--------------------|---------|--------|---------|----------|----------|--------|----
    081.2827635599|+06.3497032659| 25336| |  7|0           |081.28278339|+06.34973457|  12.92|  0.52|   -8.11|  -12.88| 1.5493|-0.224|HIP1

    #Table: IV/27A/catalog.dat (cdsarc.u-strasbg.fr)
          |            |     |    |      | R  R         D  D     |     |   |     |
        HD|DM          |   GC|  HR|   HIP|Ah Am   RAs  Ed Em  DEs| Vmag| Fl|Bayer|Cst
     35468|BD+06   919 | 6668|1790| 25336|05 25 07.87 +06 20 59.0| 1.64| 24|gam  |Ori
     #Table: IV/27A/table3.dat (cdsarc.u-strasbg.fr)
        HD|BFD          |Name                                                   |r_
     35468| 24 gam   Ori|Bellatrix                                              | 2,15,17,19,22
    Stellarium Output Bellatrix 2016/12/28 T 23:14:15 UTC:
    γ Ori - 24 Ori - HIP 25336 - SAO 112740 - HD 35468 - HR 1790 - WDS J05251+0621AB
    Type: double star
    Magnitude: 1.60 (extincted to: 2.06)
    Absolute Magnitude: -2.84
    Color Index (B-V): -0.22
    RA/Dec (J2000.0): 5h25m07.86s/+6°20'58.7"
    RA/Dec (on date): 5h26m03.06s/+6°21'41.0"

    HA/Dec: 18h59m30.86s/+6°23'10.8" (apparent)
    Az./Alt.: +90°59'13.0"/+16°08'00.3" (apparent)
    Gal. long./lat.: -163°04'19.7"/-15°57'11.8"
    Supergal. long./lat.: -20°28'43.1"/-58°39'59.6"
    Ecl. long./lat. (J2000.0): +80°56'47.1"/-16°48'57.9"
    Ecl. long./lat. (on date): +81°11'08.7"/-16°48'50.0"
    Ecliptic obliquity (on date): +23°26'04.3"
    Mean Sidereal Time: 0h25m22.1s
    Apparent Sidereal Time: 0h25m21.7s
    IAU Constellation: Ori
    Distance: 252.44 ly
    Spectral Type: B2III
    Parallax: 0.01292"
    Position angle (2009): 144.00°
    Separation (2009): 178.000" (+0°02'58")
    Proper motions by axes: -9.1 -13.6 (mas/yr)
    Position angle of the proper motion: 213.8°
    Angular speed of the proper motion: 16.4 (mas/yr)
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