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Observer Table
The image above is a screenshot from Horizons Web Application with the Ephemeris type: Observer Table.
It shows the distance (delta) from the geocentric observer location to target Moon on April 15, 1970 at 00:34 min., being 404460 km.

Vector Table
This image is a screenshot from Horizons Web Application with Ephemeris type: Vector Table.
It shows the distance (RG) from the geocentric coordinate center to the Moon on April 15, 1970 at 00:34 min., being 404421.4 km.

Is there a credible explanation for the 38.6 km difference beween the "Observer Table" and "Vector Table" type ?

Here are the Earth-Moon distance differences between Observer table and Vector table on 31 successive days at the same daytime from April 15 to May 15, 1970 in km:
38.6 35.3 30.7 24.9 18.2 10.8 2.9 -5.0 -12.8 -19.9 -26.2 -31.2 -34.8 -36.6 -36.6 -34.7 -30.9 -25.5 -18.8 -11.0 -2.7 5.7 13.8 21.3 27.7 32.9 36.7 38.9 39.6 38.8 36.4

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  • 1
    $\begingroup$ I had thought the problem was a difference in time scales. The Observer Table time is expressed as UT (i.e. UTC), while the Vector Table time is TDB. There is a difference of 69.184 seconds between the two (UTC + 69.184 seconds = TDB). However, when I attempt to compensate, the range problem that you highlight does not disappear. $\endgroup$
    – Bob Werner
    Commented Dec 4, 2022 at 19:44
  • $\begingroup$ @BobWerner It's a mystery! BTW, Delta T at that time was only ~40.455 s. I rediscovered that since Oct 2021 Horizons allows you to specify UT or TT (not just TDB) for vector tables, elements tables must use TDB. $\endgroup$
    – PM 2Ring
    Commented Dec 5, 2022 at 9:22
  • 1
    $\begingroup$ One possible source of the difference is the observer tables are "apparent" coordinates, where the vector table are geometric coordinates (e.g. not adjusted for light time, annual aberration, etc). I also noticed the vector table lists the "Center-site name" as "Body Center" for the vector table and "GEOCENTRIC" for the observer table. Since the Earth's center vs center of mass is about 40Km, that would align with different centers being used. $\endgroup$ Commented Dec 6, 2022 at 13:35
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    $\begingroup$ However, there is another difference between the two table types. By default, Observer tables use UTC, but Vector tables use TDB. But it's possible to explicitly state which time scale you want to use. So the numbers you appended to the end of your question have an extra difference caused by that time scale difference of ~40.455 seconds. $\endgroup$
    – PM 2Ring
    Commented Dec 6, 2022 at 15:19
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    $\begingroup$ Maybe give it a few more days. You never know, someone might have a perfectly logical explanation. $\endgroup$
    – PM 2Ring
    Commented Dec 6, 2022 at 17:16

2 Answers 2

2
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If you change the vector table settings to be "apparent states", the error goes to the millimeter range. Not sure why it isn't exact, but still a lot more accurate than the error margin of the ephemieris.

enter image description here

Vector table:

2440691.522916667 = A.D. 1970-Apr-15 00:33:00.0000 UTC 
X =-2.592670760523030E+05 Y = 3.098416379718271E+05 Z = 1.914428047852615E+04
VX=-7.436303188457583E-01 VY=-6.130967807986689E-01 VZ=-7.420234845227733E-02
LT= 1.349132800160780E+00 RG= 4.044598383286231E+05 RR= 3.499474924335833E-03

Observer table:

$$SOE
1970-Apr-15 00:33     08 52 33.51 +20 22 27.6  -10.525   4.952  4.0445983833E+05   0.0034739  106.523 277.760        n.a.       n.a.   29.577389   110.09186   0.2074268         n.a.     n.a.

Difference:

1.3769022189080715e-06

Also, as I pointed out in my comment, the Center-Site name changes to GEOCENTRIC when you select the apparent states option, so it is likely using a different origin for the different types.

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1
  • $\begingroup$ Good to have an answer with other explanations, but I asked for the distance difference between Observer table and Vector table at April 15, 00:34 min. not 00:33. Also, only the Observer table has the GEOCENTRIC Center-site name, all the different Vector tables have the Center-site name BODY CENTER, also the apparent states option. (see the other answer) $\endgroup$
    – Cornelis
    Commented Dec 7, 2022 at 13:40
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+100
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This doesn't answer your question, but hopefully it sheds some light on it.

As I said in this comment the difference in distances isn't caused by the table type, it's caused by the light-time correction. However, I don't understand why that leads to such a large discrepancy.

The Horizons Observer table allows you to choose between astrometric and apparent values for RA & declination (Quantities 1 & 2), but it gives you no options for the range.

20. Target range & range rate (relative to observer)

Target apparent range ("delta", light-time aberrated) and range-rate ("delta-dot") relative to the observer.

The vector table gives you the options of plain geometric values (the default), astrometric (light-time corrected), or apparent (light-time and aberration corrected).

Aberration corrections:

  • NONE (geometric state vectors)
  • LT (light-time)
  • LT+S (light-time & stellar aberration)

Here's a comparison. Each table lists the calendar date / time and Julian day in UTC, Delta T (= TDB - UTC) (in seconds), the light-time from the centre of the Moon to the centre of the Earth, the range (in km), and the range-rate (in km/s). Note that the observer table reports light travel time in minutes, but the vector tables report it in seconds. Each heading is a link to the full Horizons output.

Vector table, GEOMETRIC cartesian states

*******************************************************************************
            JDUT ,            Calendar Date (UT ),        delta-T,                     LT,                     RG,                     RR,
******************************************************************************************************************************************
$$SOE
2440691.522222222, A.D. 1970-Apr-15 00:32:00.0000,      40.455330,  1.349003752066716E+00,  4.044211506833034E+05,  3.507416288023241E-03,
2440691.522916667, A.D. 1970-Apr-15 00:33:00.0000,      40.455332,  1.349004453018408E+00,  4.044213608233342E+05,  3.497251234683748E-03,
2440691.523611111, A.D. 1970-Apr-15 00:34:00.0000,      40.455334,  1.349005151935714E+00,  4.044215703534710E+05,  3.487086509335641E-03,
2440691.524305556, A.D. 1970-Apr-15 00:35:00.0000,      40.455336,  1.349005848818700E+00,  4.044217792737343E+05,  3.476922112318192E-03,
2440691.525000000, A.D. 1970-Apr-15 00:36:00.0000,      40.455337,  1.349006543667431E+00,  4.044219875841435E+05,  3.466758043990613E-03,
$$EOE
******************************************************************************************************************************************

Vector table, LT CORRECTED

*******************************************************************************
            JDUT ,            Calendar Date (UT ),        delta-T,                     LT,                     RG,                     RR,
******************************************************************************************************************************************
$$SOE
2440691.522222222, A.D. 1970-Apr-15 00:32:00.0000,      40.455330,  1.349132103821229E+00,  4.044596295712772E+05,  3.484037521090640E-03,
2440691.522916667, A.D. 1970-Apr-15 00:33:00.0000,      40.455332,  1.349132800160780E+00,  4.044598383286230E+05,  3.473861373118514E-03,
2440691.523611111, A.D. 1970-Apr-15 00:34:00.0000,      40.455334,  1.349133494463880E+00,  4.044600464754561E+05,  3.463685553580587E-03,
2440691.524305556, A.D. 1970-Apr-15 00:35:00.0000,      40.455336,  1.349134186730390E+00,  4.044602540117345E+05,  3.453510062668777E-03,
2440691.525000000, A.D. 1970-Apr-15 00:36:00.0000,      40.455337,  1.349134876960339E+00,  4.044604609374676E+05,  3.443334900674379E-03,
$$EOE
******************************************************************************************************************************************

Vector table, LT+S CORRECTED

*******************************************************************************
            JDUT ,            Calendar Date (UT ),        delta-T,                     LT,                     RG,                     RR,
******************************************************************************************************************************************
$$SOE
2440691.522222222, A.D. 1970-Apr-15 00:32:00.0000,      40.455330,  1.349132103821229E+00,  4.044596295712773E+05,  3.509638977137701E-03,
2440691.522916667, A.D. 1970-Apr-15 00:33:00.0000,      40.455332,  1.349132800160780E+00,  4.044598383286231E+05,  3.499474924335833E-03,
2440691.523611111, A.D. 1970-Apr-15 00:34:00.0000,      40.455334,  1.349133494463880E+00,  4.044600464754561E+05,  3.489311199569758E-03,
2440691.524305556, A.D. 1970-Apr-15 00:35:00.0000,      40.455336,  1.349134186730390E+00,  4.044602540117345E+05,  3.479147803031668E-03,
2440691.525000000, A.D. 1970-Apr-15 00:36:00.0000,      40.455337,  1.349134876960339E+00,  4.044604609374675E+05,  3.468984735012534E-03,
$$EOE
******************************************************************************************************************************************

Observer table

*******************************************************************************************************
 Date__(UT)__HR:MN, Date_________JDUT, , ,       TDB-UT,  1-way_down_LT,             delta,     deldot,
*******************************************************************************************************
$$SOE
 1970-Apr-15 00:32, 2440691.522222222, , ,    40.455330,     0.02248554,  4.0445962957E+05,  0.0034840,
 1970-Apr-15 00:33, 2440691.522916667, , ,    40.455332,     0.02248555,  4.0445983833E+05,  0.0034739,
 1970-Apr-15 00:34, 2440691.523611111, , ,    40.455334,     0.02248556,  4.0446004648E+05,  0.0034637,
 1970-Apr-15 00:35, 2440691.524305556, , ,    40.455336,     0.02248557,  4.0446025401E+05,  0.0034535,
 1970-Apr-15 00:36, 2440691.525000000, , ,    40.455337,     0.02248558,  4.0446046094E+05,  0.0034433,
$$EOE
*******************************************************************************************************

The range and range-rate reported in the second vector table is the same as in the observer table.

The light-time and range-rate are both quite small, so it's certainly a puzzle where that ~38 km range difference is coming from. Surely, it's not a bug...

The JPL DE stores major body positions using its nominal Solar System barycentre as the origin. Perhaps that makes a difference between the geometric and light-time corrected values.


Here's a plot of the Light-time Corrected vector range minus the Geometric vector range over a few months, for 0:00 TDB, with a 1 day timestep. I've checked 5 decades of the 20th century, at various times of year, and it's always quite close to the Moon phases.

Moon position delta plot

Here's the plotting script, which can be used to explore this discrepancy for other pairs of bodies. Select the verbose checkbox to get a printed list of the differences.


Here's a small Sage / Python script which processes Horizons batch command lists and displays the output in a format that's easy to copy and paste. The Horizons Web GUI app can print such lists, but it doesn't accept them as input. You may find this script convenient for experimenting with those lists. I find it easier than tweaking parameters in the Horizons GUI. The command list must start with the line!$$SOF. You can use an exclamation mark ! to create a comment (which extends to the end of the line). Here's a typical example:

!$$SOF
MAKE_EPHEM='YES'
!REF_PLANE='FRAME'
EPHEM_TYPE='VECTORS'
VEC_TABLE='6'
VEC_CORR='LT'
VEC_DELTA_T='YES'
CSV_FORMAT='YES'
OBJ_DATA='NO'
COMMAND=301
CENTER=@399
START_TIME='1970-Apr-15 0:32'
STOP_TIME='1970-Apr-15 0:36'
STEP_SIZE='1m'

There are a few other versions of this script on Github

For further information, please see the Horizon API docs and the the Horizons batch example/instructions document.

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  • $\begingroup$ That 's a clear comparison between the different tables. It's also clear for me now that the time difference of about 40 sec, cannot be the problem since 1 min. after pericynthion the distance has only become a few hundred m. larger. I'm interested if you can explain why the Solar System barycentre could make a difference. $\endgroup$
    – Cornelis
    Commented Dec 5, 2022 at 10:47
  • 1
    $\begingroup$ @Cornelis Sorry, I just mentioned it as a vague possibility. My motivation is that the distance from the SSB to the Earth-Moon system is ~500 light-seconds. Maybe the difference in Earth & Moon positions between geometric & light-corrected versions is somehow affected by that 500 light-seconds, not just the few light-seconds between the Earth & Moon. $\endgroup$
    – PM 2Ring
    Commented Dec 5, 2022 at 11:08
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    $\begingroup$ @Cornelis Just put UT after the Start time. See ssd.jpl.nasa.gov/horizons/manual.html#time $\endgroup$
    – PM 2Ring
    Commented Dec 7, 2022 at 15:21

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