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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?
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
#-oc.form=dec
#-out.max=99999
#-nav=cat:I/311&tab:{I/311/

#-c.eq=J2000
#-c.r=  2
#-c.u=arcmin
#-c.geom=r
#-source=I/311/hip2
#-order=I
#-out=HIP
#-out=n_HIP
#-out=Sn
#-out=So
#-out=Plx
#-out=e_Plx
#-out=pmRA
#-out=pmDE
#-out=Hpmag
#Hpmag=<7
#-out=B-V
#-out=HIP1
#HIP1=HIP1
#Phot=Phot
#

#RESOURCE=yCat_1311
#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    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]
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:
Bellatrix
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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