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On the 14th of February 1998 Voyager 1 passed Pioneer 10 to become the most distant human-made object in space, 10.4 billion kilometres from Earth (69.4 AU from the Sun). What were the speeds of Pioneer 10 and Voyager 1 when Voyager overtook it?

I can find one source to say Voyagers speed was 17kms.

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2 Answers 2

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Horizons also gives range and range-rate data in the Observer table. I used the Sun as the observation center, rather than the Solar System barycenter.

On 1998-Feb-14 at midnight UTC, Pioneer 10 was travelling at 12.307 km/s and Voyager 1 was travelling at 17.124 km/s.

The time that Voyager 1 overtook Pioneer 10 depends on where you measure from. And it's not really possible to calculate the exact time, since the trajectory data for Pioneer 10 is of uncertain origin, as mentioned in its Horizons body data file.

Here are the approximate dates and times of overtaking.

Center Date Time
Sun 1998-Feb-17 22:00
Barycentre 1998-Feb-18 8:00
Earth 1998-Mar-05 16:00

Here's the data covering a week either side of 1998-Feb-14.

Pioneer 10

API VERSION: 1.0
API SOURCE: NASA/JPL Horizons API

*******************************************************************************
 Revised: Jul 27, 2005   Pioneer 10 Spacecraft (interplanetary) / (Sun)     -23
                       http://nssdc.gsfc.nasa.gov/nmc/tmp/1972-012A.html

 BACKGROUND
  This mission was the first to be sent to the outer solar system and the 
  first to investigate the planet Jupiter. After the encounter, it followed 
  an escape trajectory from the solar system. 

  The spacecraft achieved its closest approach to Jupiter on December 4, 1973
  (UTC), when it reached approximately 2.8 Jovian radii (about 200,000 km). 

  The last fully successful acquisition of signal was March 3, 2002. Pioneer 10
  signal at the Earth (<= 185 dBm) is now at DSN threshold limit of reception. 

          Launched            : 1972-03-03 at 01:49:00 UTC
          On-orbit dry mass   : 258 kg
          Nominal Power Output: 165 W

 SPACECRAFT TRAJECTORY: ("pfile10.nio")

  Trajectory was provided by JPL Navigation Team. The JPL Multimission NAV and 
  Solar System Dynamics Group source files merged consist of:
 
     PN10A, PN10B, PN10C, PN10D, PN10E, PN10F, PN10G, DE118
 
  The circumstances pertaining to the regeneration of the above spacecraft
  trajectory source files PN10* are not well known.
 
  DE118 was the standard JPL planet ephemeris for the P10 Jupiter flyby era.

  NOTE: This trajectory is suitable for general historical purposes, but should
  be used cautiously for high precision or tracking data applications. This is 
  due to potential dynamical mismatches between the Pioneer-10 era models 
  and the current modern solutions used by Horizons; for example, the old 
  DE-118 planetary ephemeris solution and the Lieske E3 satellite theory of
  JUP035 of that time, as compared to what is used now. 

  For example, if the Pioneer-10 solutions used here incorporate planet or 
  satellite ephemeris corrections estimated at the time, distance from the 
  satellites returned by Horizons could be slightly different relative to 
  the original solutions. However, the coordinate system transformation from 
  the original DE-118 planetary ephemeris to the modern ICRF frame IS known 
  and computed by Horizons.
*******************************************************************************


*******************************************************************************
Ephemeris / WWW_USER Wed Feb 16 15:46:44 2022 Pasadena, USA      / Horizons    
*******************************************************************************
Target body name: Pioneer 10 (spacecraft) (-23)   {source: pioneer_10}
Center body name: Sun (10)                        {source: pioneer_10}
Center-site name: BODYCENTRIC
*******************************************************************************
Start time      : A.D. 1998-Feb-07 00:00:00.0000 UT      
Stop  time      : A.D. 1998-Feb-21 00:00:00.0000 UT      
Step-size       : 1440 minutes
*******************************************************************************
Target pole/equ : No model available
Target radii    : (unavailable)                                                
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 pole/equ : IAU_SUN                         {East-longitude positive}
Center radii    : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}    
Target primary  : Earth
Vis. interferer : None
Rel. light bend : Sun                             {source: pioneer_10}
Rel. lght bnd GM: 1.3271E+11 km^3/s^2                                          
Atmos refraction: NO (AIRLESS)
RA format       : DEG
Time format     : BOTH
EOP file        : eop.220215.p220511                                           
EOP coverage    : DATA-BASED 1962-JAN-20 TO 2022-FEB-15. PREDICTS-> 2022-MAY-10
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s 
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass     n.a.    , Daylight (NO )
Table cut-offs 2: Solar elongation (  0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
Table cut-offs 3: RA/DEC angular rate (     0.0=NO )                           
Table format    : Comma Separated Values (spreadsheet)
*******************************************************************************
 Date__(UT)__HR:MN:SS, Date_________JDUT, , ,            delta,     deldot,
***************************************************************************
$$SOE
 1998-Feb-07 00:00:00, 2450851.500000000, , , 1.0372872263E+10, 12.3074289,
 1998-Feb-08 00:00:00, 2450852.500000000, , , 1.0373935578E+10, 12.3073459,
 1998-Feb-09 00:00:00, 2450853.500000000, , , 1.0374998885E+10, 12.3072631,
 1998-Feb-10 00:00:00, 2450854.500000000, , , 1.0376062185E+10, 12.3071803,
 1998-Feb-11 00:00:00, 2450855.500000000, , , 1.0377125479E+10, 12.3070975,
 1998-Feb-12 00:00:00, 2450856.500000000, , , 1.0378188765E+10, 12.3070149,
 1998-Feb-13 00:00:00, 2450857.500000000, , , 1.0379252044E+10, 12.3069323,
 1998-Feb-14 00:00:00, 2450858.500000000, , , 1.0380315315E+10, 12.3068498,
 1998-Feb-15 00:00:00, 2450859.500000000, , , 1.0381378580E+10, 12.3067673,
 1998-Feb-16 00:00:00, 2450860.500000000, , , 1.0382441838E+10, 12.3066849,
 1998-Feb-17 00:00:00, 2450861.500000000, , , 1.0383505088E+10, 12.3066026,
 1998-Feb-18 00:00:00, 2450862.500000000, , , 1.0384568331E+10, 12.3065204,
 1998-Feb-19 00:00:00, 2450863.500000000, , , 1.0385631568E+10, 12.3064382,
 1998-Feb-20 00:00:00, 2450864.500000000, , , 1.0386694797E+10, 12.3063560,
 1998-Feb-21 00:00:00, 2450865.500000000, , , 1.0387758019E+10, 12.3062739,
$$EOE
*******************************************************************************
Column meaning:
 
TIME

  Times PRIOR to 1962 are UT1, a mean-solar time closely related to the
prior but now-deprecated GMT. Times AFTER 1962 are in UTC, the current
civil or "wall-clock" time-scale. UTC is kept within 0.9 seconds of UT1
using integer leap-seconds for 1972 and later years.

  Conversion from the internal Barycentric Dynamical Time (TDB) of solar
system dynamics to the non-uniform civil UT time-scale requested for output
has not been determined for UTC times after the next July or January 1st.
Therefore, the last known leap-second is used as a constant over future
intervals.

  Time tags refer to the UT time-scale conversion from TDB on Earth
regardless of observer location within the solar system, although clock
rates may differ due to the local gravity field and no analog to "UT"
may be defined for that location.

  Any 'b' symbol in the 1st-column denotes a B.C. date. First-column blank
(" ") denotes an A.D. date. Calendar dates prior to 1582-Oct-15 are in the
Julian calendar system. Later calendar dates are in the Gregorian system.

  NOTE: "n.a." in output means quantity "not available" at the print-time.
 
 'delta,     deldot,' =
   Apparent range ("delta", light-time aberrated) and range-rate ("delta-dot")
of the target center relative to the observer. A positive "deldot" means the
target center is moving away from the observer, negative indicates movement
toward the observer.  Units: KM and KM/S

Computations by ...

    Solar System Dynamics Group, Horizons On-Line Ephemeris System
    4800 Oak Grove Drive, Jet Propulsion Laboratory
    Pasadena, CA  91109   USA

    General site: https://ssd.jpl.nasa.gov/
    Mailing list: https://ssd.jpl.nasa.gov/email_list.html
    System news : https://ssd.jpl.nasa.gov/horizons/news.html
    User Guide  : https://ssd.jpl.nasa.gov/horizons/manual.html
    Connect     : browser        https://ssd.jpl.nasa.gov/horizons/app.html#/x
                  API            https://ssd-api.jpl.nasa.gov/doc/horizons.html
                  command-line   telnet ssd.jpl.nasa.gov 6775
                  e-mail/batch   https://ssd.jpl.nasa.gov/ftp/ssd/hrzn_batch.txt
                  scripts        https://ssd.jpl.nasa.gov/ftp/ssd/SCRIPTS
    Author      : Jon.D.Giorgini@jpl.nasa.gov

*******************************************************************************

Voyager 1

API VERSION: 1.0
API SOURCE: NASA/JPL Horizons API

*******************************************************************************
 Revised: Jan 21, 2015   Voyager 1 Spacecraft (interplanetary) / (Sun)     -31
                         http://www.jpl.nasa.gov/missions/voyager-1/

 BACKGROUND
   See the web-page above for extensive information on the Voyager Mission.

 SPACECRAFT TRAJECTORY:
   This trajectory is composed of two merged sections:

     #1) 1977-Sep-5 to 1986-Jan-1:
          A patched conic mission-design type trajectory in which the conics 
          were constructed to approximately match specific events (such 
          satellite encounters), providing a rough accuracy. 

     #2) 1986-Jan-1 to 2031-Jan-1 (pfile_a54206u)
          Time-extended trajectory provided by Voyager Navigation
*******************************************************************************


*******************************************************************************
Ephemeris / WWW_USER Wed Feb 16 15:59:55 2022 Pasadena, USA      / Horizons    
*******************************************************************************
Target body name: Voyager 1 (spacecraft) (-31)    {source: Voyager_1}
Center body name: Sun (10)                        {source: Voyager_1}
Center-site name: BODYCENTRIC
*******************************************************************************
Start time      : A.D. 1998-Feb-07 00:00:00.0000 UT      
Stop  time      : A.D. 1998-Feb-21 00:00:00.0000 UT      
Step-size       : 1440 minutes
*******************************************************************************
Target pole/equ : No model available
Target radii    : (unavailable)                                                
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 pole/equ : IAU_SUN                         {East-longitude positive}
Center radii    : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}    
Target primary  : Earth
Vis. interferer : None
Rel. light bend : Sun                             {source: Voyager_1}
Rel. lght bnd GM: 1.3271E+11 km^3/s^2                                          
Atmos refraction: NO (AIRLESS)
RA format       : DEG
Time format     : BOTH
EOP file        : eop.220215.p220511                                           
EOP coverage    : DATA-BASED 1962-JAN-20 TO 2022-FEB-15. PREDICTS-> 2022-MAY-10
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s 
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass     n.a.    , Daylight (NO )
Table cut-offs 2: Solar elongation (  0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
Table cut-offs 3: RA/DEC angular rate (     0.0=NO )                           
Table format    : Comma Separated Values (spreadsheet)
*******************************************************************************
 Date__(UT)__HR:MN:SS, Date_________JDUT, , ,            delta,     deldot,
***************************************************************************
$$SOE
 1998-Feb-07 00:00:00, 2450851.500000000, , , 1.0368154427E+10, 17.1248027,
 1998-Feb-08 00:00:00, 2450852.500000000, , , 1.0369633923E+10, 17.1247593,
 1998-Feb-09 00:00:00, 2450853.500000000, , , 1.0371113416E+10, 17.1247159,
 1998-Feb-10 00:00:00, 2450854.500000000, , , 1.0372592905E+10, 17.1246724,
 1998-Feb-11 00:00:00, 2450855.500000000, , , 1.0374072390E+10, 17.1246289,
 1998-Feb-12 00:00:00, 2450856.500000000, , , 1.0375551872E+10, 17.1245854,
 1998-Feb-13 00:00:00, 2450857.500000000, , , 1.0377031349E+10, 17.1245418,
 1998-Feb-14 00:00:00, 2450858.500000000, , , 1.0378510823E+10, 17.1244982,
 1998-Feb-15 00:00:00, 2450859.500000000, , , 1.0379990294E+10, 17.1244545,
 1998-Feb-16 00:00:00, 2450860.500000000, , , 1.0381469760E+10, 17.1244108,
 1998-Feb-17 00:00:00, 2450861.500000000, , , 1.0382949223E+10, 17.1243671,
 1998-Feb-18 00:00:00, 2450862.500000000, , , 1.0384428681E+10, 17.1243233,
 1998-Feb-19 00:00:00, 2450863.500000000, , , 1.0385908137E+10, 17.1242796,
 1998-Feb-20 00:00:00, 2450864.500000000, , , 1.0387387588E+10, 17.1242357,
 1998-Feb-21 00:00:00, 2450865.500000000, , , 1.0388867035E+10, 17.1241919,
$$EOE
*******************************************************************************
Column meaning:
 
TIME

  Times PRIOR to 1962 are UT1, a mean-solar time closely related to the
prior but now-deprecated GMT. Times AFTER 1962 are in UTC, the current
civil or "wall-clock" time-scale. UTC is kept within 0.9 seconds of UT1
using integer leap-seconds for 1972 and later years.

  Conversion from the internal Barycentric Dynamical Time (TDB) of solar
system dynamics to the non-uniform civil UT time-scale requested for output
has not been determined for UTC times after the next July or January 1st.
Therefore, the last known leap-second is used as a constant over future
intervals.

  Time tags refer to the UT time-scale conversion from TDB on Earth
regardless of observer location within the solar system, although clock
rates may differ due to the local gravity field and no analog to "UT"
may be defined for that location.

  Any 'b' symbol in the 1st-column denotes a B.C. date. First-column blank
(" ") denotes an A.D. date. Calendar dates prior to 1582-Oct-15 are in the
Julian calendar system. Later calendar dates are in the Gregorian system.

  NOTE: "n.a." in output means quantity "not available" at the print-time.
 
 'delta,     deldot,' =
   Apparent range ("delta", light-time aberrated) and range-rate ("delta-dot")
of the target center relative to the observer. A positive "deldot" means the
target center is moving away from the observer, negative indicates movement
toward the observer.  Units: KM and KM/S

Computations by ...

    Solar System Dynamics Group, Horizons On-Line Ephemeris System
    4800 Oak Grove Drive, Jet Propulsion Laboratory
    Pasadena, CA  91109   USA

    General site: https://ssd.jpl.nasa.gov/
    Mailing list: https://ssd.jpl.nasa.gov/email_list.html
    System news : https://ssd.jpl.nasa.gov/horizons/news.html
    User Guide  : https://ssd.jpl.nasa.gov/horizons/manual.html
    Connect     : browser        https://ssd.jpl.nasa.gov/horizons/app.html#/x
                  API            https://ssd-api.jpl.nasa.gov/doc/horizons.html
                  command-line   telnet ssd.jpl.nasa.gov 6775
                  e-mail/batch   https://ssd.jpl.nasa.gov/ftp/ssd/hrzn_batch.txt
                  scripts        https://ssd.jpl.nasa.gov/ftp/ssd/SCRIPTS
    Author      : Jon.D.Giorgini@jpl.nasa.gov

*******************************************************************************

Here's the batch file for Pioneer 10. Change the COMMAND to -31 for Voyager 1.

!$$SOF
MAKE_EPHEM=YES
COMMAND=-23
EPHEM_TYPE=OBSERVER
CENTER='500@10'
START_TIME='1998-Feb-7'
STOP_TIME='1998-Feb-21'
STEP_SIZE='1 DAYS'
QUANTITIES='20'
REF_SYSTEM='ICRF'
CAL_FORMAT='BOTH'
TIME_DIGITS='SECONDS'
ANG_FORMAT='DEG'
APPARENT='AIRLESS'
RANGE_UNITS='KM'
SUPPRESS_RANGE_RATE='NO'
SKIP_DAYLT='NO'
SOLAR_ELONG='0,180'
EXTRA_PREC='NO'
RTS_ONLY='NO'
CSV_FORMAT='YES'
OBJ_DATA='YES'

Here's the script I used, preloaded with the batch file for Pioneer 10.


I adapted my old range script to plot the ranges of two targets. Here's a plot of the distances from the Sun to Pioneer 10 and Voyager 1. Times are in UTC. As mentioned above, JPL aren't sure of all the fine details of the trajectory data for Pioneer 10, so we should treat these results with some caution. ;)

Pioneer 10 & Voyager 1 plot

Here's a link to the script. Use @0 or @ssb as the center if you want a plot relative to the Solar System barycentre. Use @399 for Earth, or @3 for the Earth-Moon barycentre.

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note: I think that @PM2Ring's answer is far superior, more informative, and more accurate as well.


Using JPL's Horizons I got the following state vectors in solar system barycenter coordinates (most relevant for spacecraft so far away) for JD=2450858.500000000, A.D. 1998-Feb-14 00:00:00.0000:

Units are kilometers and kilometers per second.

         Voyager 1                   Pioneer 10    
X  -2.919566485636236E+09      2.447449920541947E+09
Y  -8.063430559193250E+09      1.007319426907179E+10
Z   5.846603741810939E+09      5.514966187314744E+08
R   1.037909226092241E+10      1.03809152976264E+10

Vx -2.167117050187287E+00      1.347428037636978E+00
Vy -1.396081506054589E+01      1.230541520519172E+01
Vz  1.008540978609296E+01      6.313622142272930E-01
Vr  1.735846318132446E+01      1.239505643126838E+01

So perhaps they are not exactly the same distance from the barycenter at this moment is that it wasn't exactly at midnight on February 14, or February 14 was the date they were equidistant from the Sun rather than from the center of mass of the solar system, but the difference is pretty small so we can ignore it.

What were the speeds of Pioneer 10 and Voyager 1 when Voyager overtook it in 1998?

Voyager 1: 17.36 km/sec

Pioneer 10: 12.40 km/sec

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    $\begingroup$ @AndrewMorton mea culpa xyz are copy/paste from Horizons but the final values were from Python and it likes to display digits so I scientific-notationed it by hand and made a typo. Fixed now I hope, thanks! $\endgroup$
    – uhoh
    Feb 17 at 12:15

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