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I have obtained the hindcast position of Mercury relative to the Sun for the epoch 2000-Jan-01 12:00:00 using two methods: PlanEph ver 4.2 (Dos-based) and JPL Horizons DE431 (online).

The two methods give positions which are over 2000 Km apart.

Details are presented in the following figure:-

enter image description here

I presume that such a large discrepancy is due to some error of specification or understanding on my part. I wonder if anyone can suggest or help me find out what that error might be?

(EDIT)

APPENDIX 1 JPL HORIZONS QUERY SETTINGS

Ephemeris Type:VECTORS    
Target Body: Mercury(199)    
Coordinate Origin: Sun (body center) [500@10]    
Time Span: Start=2000-01-01 11:59, Stop=2000-01-02 12:03,Step=1m    
Table Settings: output units=KM-S; CSVformat=YES    
Display/Output:download/save(plain text file).

APPENDIX 2 Full listing of the JPL Horizons Output File

(CSV format)

*******************************************************************************
 Revised: Jul 31, 2013              Mercury                             199 / 1

 GEOPHYSICAL DATA (updated 2008-Feb-07):
  Mean radius (km)      =  2440(+-1)     Density (g cm^-3)     =  5.427
  Mass (10^23 kg )      =     3.302      Flattening, f         =  
  Volume (x10^10 km^3)  =     6.085      Semi-major axis       = 
  Sidereal rot. period  =    58.6462 d   Rot. Rate (x10^5 s)   =  0.124001
  Mean solar day        =   175.9421 d   Polar gravity ms^-2   =
  Mom. of Inertia       =     0.33       Equ. gravity  ms^-2   =  3.701     
  Core radius (km)      = ~1600          Potential Love # k2   =

  GM (km^3 s^-2)        = 22032.09       Equatorial Radius, Re =    2440 km
  GM 1-sigma (km^3 s^-2)=   +-0.91       Mass ratio (sun/plnt) = 6023600

  Atmos. pressure (bar) =                Max. angular diam.    = 11.0"   
  Mean Temperature (K)  =                Visual mag. V(1,0)    = -0.42 
  Geometric albedo      =   0.106        Obliquity to orbit[1] = 2.11' +/- 0.1'  
  Sidereal orb. per.    =   0.2408467 y  Mean Orbit vel.  km/s = 47.362 
  Sidereal orb. per.    =  87.969257  d  Escape vel. km/s      =  4.435
  Hill's sphere rad. Rp =  94.4          Planetary Solar Const = 9936.9 (Wm^2)

[1] Margot et al., Science 316, 2007
*******************************************************************************




*******************************************************************************
Ephemeris / WWW_USER Thu Jan  4 09:47:08 2018 Pasadena, USA      / Horizons    
*******************************************************************************
Target body name: Mercury (199)                   {source: DE431mx}
Center body name: Sun (10)                        {source: DE431mx}
Center-site name: BODY CENTER
*******************************************************************************
Start time      : A.D. 2000-Jan-01 11:59:00.0000 TDB
Stop  time      : A.D. 2000-Jan-01 12:03:00.0000 TDB
Step-size       : 1 minutes
*******************************************************************************
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center radii    : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}    
Output units    : KM-S                                                         
Output type     : GEOMETRIC cartesian states
Output format   : 3 (position, velocity, LT, range, range-rate)
Reference frame : ICRF/J2000.0                                                 
Coordinate systm: Ecliptic and Mean Equinox of Reference Epoch                 
*******************************************************************************

                JDTDB,            Calendar Date (TDB),                      X,                      Y,                      Z,                     VX,                     VY,                     VZ,                     LT,                     RG,                     RR,
    **************************************************************************************************************************************************************************************************************************************************************************
    $$SOE
    2451544.999305556, A.D. 2000-Jan-01 11:59:00.0000, -1.946394607859077E+07, -6.691260531388976E+07, -3.679595954330999E+06,  3.699453582609515E+01, -1.116598386942620E+01, -4.307714204076275E+00,  2.327713739463555E+02,  6.978310234741506E+07,  6.152788768051691E-01,
    2451545.000000000, A.D. 2000-Jan-01 12:00:00.0000, -1.946172639275932E+07, -6.691327522588462E+07, -3.679854414596554E+06,  3.699499188030234E+01, -1.116441595690670E+01, -4.307627980092747E+00,  2.327714970537363E+02,  6.978313925407939E+07,  6.149432668355465E-01,
    2451545.000694444, A.D. 2000-Jan-01 12:01:00.0000, -1.945950667956619E+07, -6.691394504380433E+07, -3.680112869688489E+06,  3.699544788177393E+01, -1.116284803117785E+01, -4.307541750189781E+00,  2.327716200939488E+02,  6.978317614060709E+07,  6.146076565335312E-01,
    2451545.001388889, A.D. 2000-Jan-01 12:02:00.0000, -1.945728693901455E+07, -6.691461476764810E+07, -3.680371319606457E+06,  3.699590383050987E+01, -1.116128009224054E+01, -4.307455514367438E+00,  2.327717430669925E+02,  6.978321300699817E+07,  6.142720458993068E-01,
    2451545.002083333, A.D. 2000-Jan-01 12:03:00.0000, -1.945506717110758E+07, -6.691528439741514E+07, -3.680629764350098E+06,  3.699635972651007E+01, -1.115971214009566E+01, -4.307369272625786E+00,  2.327718659728678E+02,  6.978324985325259E+07,  6.139364349330478E-01,
    $$EOE
    **************************************************************************************************************************************************************************************************************************************************************************

Coordinate system description:

  Ecliptic and Mean Equinox of Reference Epoch

    Reference epoch: J2000.0
    XY-plane: plane of the Earth's orbit at the reference epoch
              Note: obliquity of 84381.448 arcseconds wrt ICRF equator (IAU76)
    X-axis  : out along ascending node of instantaneous plane of the Earth's
              orbit and the Earth's mean equator at the reference epoch
    Z-axis  : perpendicular to the xy-plane in the directional (+ or -) sense
              of Earth's north pole at the reference epoch.

  Symbol meaning:

    JDTDB    Julian Day Number, Barycentric Dynamical Time
      X      X-component of position vector (km)                               
      Y      Y-component of position vector (km)                               
      Z      Z-component of position vector (km)                               
      VX     X-component of velocity vector (km/sec)                           
      VY     Y-component of velocity vector (km/sec)                           
      VZ     Z-component of velocity vector (km/sec)                           
      LT     One-way down-leg Newtonian light-time (sec)                       
      RG     Range; distance from coordinate center (km)                       
      RR     Range-rate; radial velocity wrt coord. center (km/sec)            

    Geometric states/elements have no aberrations applied.

     Computations by ...
         Solar System Dynamics Group, Horizons On-Line Ephemeris System
         4800 Oak Grove Drive, Jet Propulsion Laboratory
         Pasadena, CA  91109   USA
         Information: http://ssd.jpl.nasa.gov/
         Connect    : telnet://ssd.jpl.nasa.gov:6775  (via browser)
                      http://ssd.jpl.nasa.gov/?horizons
                      telnet ssd.jpl.nasa.gov 6775    (via command-line)
         Author     : [email protected]
    *******************************************************************************
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    $\begingroup$ I cannot replicate your results with Horizons, where I get a J2000.0 ecliptic and mean equinox of reference epoch position vector of Mercury with respect to the Sun of $[19,461,726; -66,913,275; -3,679,854] \text{ km}$ at 2000-Jan-01 12:00:00 TDB. I tried many different variations and cannot reproduce your results. Please explain how you used Horizons to obtain those results. $\endgroup$
    – David Hammen
    Jan 4, 2018 at 9:28
  • $\begingroup$ @David Hammen. I have added appendices to my question:- (1) JPL Horizons Settings, (2) Output File. $\endgroup$
    – steveOw
    Jan 4, 2018 at 13:18
  • 1
    $\begingroup$ @David Hammen. I just figured out that I had not specified the centre of the Sun appropriately i.e. "Coordinate Origin" should be "Sun (body center) [500@10]". Now I get same position as you posted. Which is about 2,200 to 2,500 Km distant from the two PlanEph positions and different in Range by about 40Km. Are those discrepancies reasonable? $\endgroup$
    – steveOw
    Jan 4, 2018 at 16:31
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    $\begingroup$ You should incorporate your newfound results into the question. Note my edit to your question. I simply added four spaces to the start of each nonempty line in your appendix 2, making that part a so-called code block. I also suggest just making your request be a few minutes around noon, 1 Jan 2000 rather than a whole days worth of data. (e.g., from 11:59 to 12:03 in steps of one minute). I will answer the question as if it used the corrected request from HORIZONS. $\endgroup$
    – David Hammen
    Jan 4, 2018 at 17:14
  • $\begingroup$ @David Hammen I revised the question as suggested. Many thanks :). $\endgroup$
    – steveOw
    Jan 4, 2018 at 18:04

1 Answer 1

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The key difference between the two (VSOP87 from PlanEph versus DE431 from the JPL HORIZONS web site) is the time reference. PlanEph uses UT (Universal Time) while JPL uses TDB (Barycentric Dynamic Time; the acronym is from the French equivalent). On 1 Jan 2000, TDB was ahead of UT by 64.183927 seconds. This means that 12:01:04.183927 TDB on 1 Jan 2000 is the same as 12:00 UT on 1 Jan 2000. The values from JPL HORIZONS at this time are an X,Y,Z position of $X = -19459352\ \text{km}$, $Y=-66913992\ \text{km}$, $Z = -3680131\ \text{km}$ - a mere 30.5 kilometer root sum square difference compared to the VSOP87 vector.


For completeness, here is my request to and response from the HORIZONS web site:

The request:

Current Settings

Ephemeris Type : VECTORS
Target Body : Mercury [199]
Coordinate Origin : Sun (body center) [500@10]
Time Span : Start=2000-01-01 12:01:04.183927, Stop=2000-01-01 12:01:05.183927, Step=1 m
Table Settings : output units=KM-S; delta-T (TDB-UT)=YES
Display/Output : default (formatted HTML)

The response, sans verbiage:

$$SOE
2451545.000742869 = A.D. 2000-Jan-01 12:01:04.1839 TDB [del_T=     64.183927 s]
 X =-1.945935189324640E+07 Y =-6.691399174811687E+07 Z =-3.680130892116148E+06
 VX= 3.699547967775486E+01 VY=-1.116273869590535E+01 VZ=-4.307535736975350E+00
 LT= 2.327716286712980E+02 RG= 6.978317871203169E+07 RR= 6.145842537044049E-01
$$EOE
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