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.
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
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.
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
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. ;)
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.
