arXiv:0906.0399v1 [gr-qc] 2 Jun 2009
Space Science Reviews manuscript No.
(will be inserted by the editor)
The Pioneer Anomaly in the Light of New Data
Slava G. Turyshev · Viktor T. Toth
Received: date / Accepted: date
Abstract The radio-metric tracking data received from the Pioneer 10 and 11 spacecraft
from the distances between 20–70 astronomical units from the Sun has consistently indi-
cated the presence of a small, anomalous, blue-shifted Doppler frequency drift that limited
the accuracy ofthe orbit reconstruction for these vehicles.This drift wasinterpreted asa sun-
ward acceleration of aP= (8.74±1.33)×10−10m/s2for each particular spacecraft. This
signal has become known as the Pioneer anomaly; the nature of this anomaly is still being
Recently new Pioneer 10 and 11 radio-metric Doppler and flight telemetry data be-
came available. The newly available Doppler data set is much larger when compared to the
data used in previous investigations and is the primary source for new investigation of the
anomaly. In addition, the flight telemetry files, original project documentation, and newly
developed software tools are now used to reconstruct the engineering history of spacecraft.
With the help of this information, a thermal model of the Pioneers was developed to study
possible contribution of thermal recoil force acting on the spacecraft. The goal of the ongo-
ing efforts is to evaluate the effect of on-board systems on the spacecrafts’ trajectories and
possibly identify the nature of this anomaly.
Techniques developed for the investigation of the Pioneer anomaly are applicable to the
New Horizons mission. Analysis shows that anisotropic thermal radiation from on-board
sources will accelerate this spacecraft by ∼41×10−10m/s2. We discuss the lessons learned
from the study of the Pioneer anomaly for the New Horizons spacecraft.
Keywords Pioneer anomaly · gravitational experiments · deep-space navigation · thermal
Slava G. Turyshev
Jet Propulsion Laboratory, California Institute of Technology,
4800 Oak Grove Drive, Pasadena, CA 91109 USA
Viktor T. Toth
Ottawa, ON K1N 9H5, Canada
The first spacecraft to leave the inner solar system (Anderson et al. 1998; Turyshev et al.
1999; Anderson et al. 2002; Turyshev et al. 2005), Pioneer 10 and 11 were designed to con-
duct an exploration of the interplanetary medium beyond the orbit of Mars and perform
close-up observations of Jupiter during the 1972-73 Jovian opportunities.
The spacecraft were launched in March 1972 (Pioneer 10) and April 1973 (Pioneer
11) on top of identical three-stage Atlas-Centaur launch vehicles. After passing through the
asteroid belt, Pioneer 10 reached Jupiter in December 1973. The trajectory of its sister craft,
Pioneer 11, in addition to visiting Jupiter in 1974, also included an encounter with Saturn in
1979 (Anderson et al. 2002; Turyshev et al. 2006a).
Afterthe planetary encounters andsuccessful completion oftheirprimary missions, both
Pioneers continued to explore the outer solar system. Due to their excellent health and nav-
igational capabilities,the Pioneers were used tosearch fortrans-Neptunian objects and toes-
tablishlimitsonthepresence oflow-frequency gravitational radiation(NASA Ames Research Center
Eventually, Pioneer 10 became the first man-made object to leave the solar system, with
its official mission ending in March 1997. Since then, NASA’s Deep Space Network (DSN)
made occasional contact with the spacecraft. The last successful communication from Pio-
neer 10 was received by the DSN on 27 April 2002. Pioneer 11 sent its last coherent Doppler
data inOctober 1990; the last scientific observations were returned by Pioneer 11 in Septem-
The orbits ofPioneer10and 11were reconstructed primarily onthe basisofradio-metric
Doppler tracking data. The reconstruction between heliocentric distances of 20–70 AU
yieldedapersistentsmalldiscrepancy betweenobservedandcomputed values (Anderson et al.
1998, 2002; Turyshev et al. 1999, 2005). After accounting for known systematic effects, the
unmodeled change in the Doppler residual for Pioneer 10 and 11 is equivalent to an approx-
imately sunward constant acceleration of
The magnitude of this effect, measured between heliocentric distances of 40–70 AU, re-
mains approximately constant within the 3 dB gain bandwidth of the high-gain antenna
(Turyshev et al. 2005, 2006a). The nature of this anomalous acceleration remains unex-
plained; this signal has become known as the Pioneer anomaly.
There were numerous attempts in recent years to provide an explanation for the anoma-
lous acceleration of Pioneer 10 and 11. These can be broadly categorized as either invoking
conventional mechanisms or utilizing principles of “new physics”.
Initial efforts to explain the Pioneer anomaly focused on the possibility of on-board sys-
tematicforces. Whilethesecannot beconclusively excluded(Anderson et al.2002;Turyshev et al.
2005), the evidence to date did not support these mechanisms: it was found that the magni-
tude of the anomaly exceeds the acceleration that these mechanisms would likely produce,
and the temporal evolution of the anomaly differs from that which one would expect, for
instance, if the anomaly were due to thermal radiation of a decaying nuclear power source.
Conventional mechanisms external to the spacecraft were also considered. First among
these was the possibility that the anomaly may be due to perturbations of the spacecrafts’ or-
bits by as yet unknown mass distributions in the Kuiper belt. Another possibility is that dust
in the solar system may exert a drag force, or it may cause a frequency shift, proportional to
distance, in the radio signal. These proposals could not produce a model that is consistent
with the known properties of the Pioneer anomaly, and may also be in contradiction with the
known properties of planetary orbits.
The value of the Pioneer anomaly happens tobe approximately cH0,where c is the speed
of light and H0is the Hubble constant at the present epoch. Attempts were made to exploit
this numerical coincidence to provide a cosmological explanation for the anomaly, but it has
been demonstrated that this approach would likely produce an effect with the opposite sign
(Anderson et al. 2002; Turyshev et al. 2006a).
As the search for a conventional explanation for the anomaly appeared unsuccessful,
this provided a motivation to seek an explanation in “new physics”. No such attempt to date
produced a clearly viable mechanism for the anomaly (Turyshev et al. 2006a).
Here we report on the status of the recovery of the Pioneers’ radiometric Doppler data
and flight telemetry and their usefulness for the analysis of the Pioneer anomaly.
2 New Doppler data and their preliminary analysis
The inability to explain the anomalous behavior of the Pioneers with conventional physics
has resulted in a growing discussion about the origin of the detected signal. The limited size
of the previously analyzed data set also limits our current knowledge of the anomaly. To
determine the origin of aPand especially before any serious discussion of new physics can
take place, one must analyze the entire set of radio-metric Doppler data received from the
Since 2002, multiple on-going efforts have contributed significantly to our ability to ex-
plore and comprehend the nature of the Pioneer anomaly (Turyshev et al. 2005, 2006a,b;
Toth & Turyshev 2006, 2008). Most notable among these are: (i) the availability of an ex-
tended Doppler data set; (ii) the recovery of spacecraft telemetry; (iii) the recovery of Pio-
neer project documentation; (iv) the development of a comprehensive thermal model of the
spacecraft; (v) the development of new methods to incorporate thermal telemetry into orbit
determination; and (vi) several independent confirmations of the Pioneer anomaly. These
developments led to the formulation of a comprehensive strategy to establish reliably the
temporal dependence and direction of the anomalous acceleration, and correlate it with re-
vised estimates of the thermal recoil force.
2.1 The extended Pioneer Doppler data set
Immediately afterthe resultsofthefirstmajorstudyoftheanomaly wereannounced (Anderson et al.
2002), a focused effort began at JPL to recover as much Doppler data as possible. Initially, it
was hoped that nearly all the Doppler record of the Pioneer 10 and 11 spacecraft from 1972
until the end of their respective missions can be recovered. Unfortunately, this proved much
more difficult than anyone anticipated at the time.
Recovery of radio-metric data for a mission operating for more then 30 years is an effort
that was never attempted before. Indeed, 30 years is a long time, presenting many unique
challenges, including changes in the data formats, navigational software, as well as sup-
porting hardware (Turyshev et al. 2006a). Even the DSN configuration had changes – new
stations were built, and some stations were moved, upgraded and reassigned. By 2005 all
the DSN data formats, navigational software used to support Pioneers, all the hardware used
to read, write and maintain the data have become obsolete and are no longer operationally
supported by existing NASA protocols. The main asset of the entire mission support – its
people – changed the most, as personnel with the necessary expertise to answer questions or
shed light on obscure details are either retired or no longer with us.
Despitethese multiplecomplexities (Turyshev et al.2006a;Toth & Turyshev 2006,2008),
the transfer of the available Pioneer Doppler data to modern media formats has been com-
pleted. However, as a result of these issues, less data is available for analysis than what was
initially hoped. Nonetheless, we now have a significantly expanded data set that is available
For Pioneer 10, good quality Doppler data are available covering the period between
1980 and 1995. Some additional data from the year 2000 also appear usable. Yet more data
files, from 1996-97, may be usable if absent ramp information can be recovered from the
transmitting DSN stations.
For Pioneer 11, good quality Doppler data are available from the periods 1983-85, and
1987-90. Data from 1980-82 and from 1986, while recovered, appear unusable.
Additional data covering the Jupiter encounter of Pioneer 10, and the Saturn encounter
of Pioneer 11, are also available and appear to be of good quality. Modeling encounters with
gas giants is fraught with additional difficulties, as both gravitational and nongravitational
effects of the complex planetary environment must be modeled with precision. On the other
hand, the rapid changes in the spacecrafts’ velocities can help uncover small systematic
effects that are otherwise difficult to observe.
2.2 A strategy to find the origin of the Pioneer anomaly
The primary objective of the new investigation is to determine the origin of the Pioneer
anomaly. Specifically, the investigation intends to accomplish the following three major ob-
I. By using the early mission Doppler data we aim: (i) to determine the true direction
of anomalous acceleration by discriminating between the four possible directions: sun-
ward, Earth-pointing, along the velocity vector, or along the spin-axis, and (ii) to study
the physics of the planetary encounters and to learn more about the onset of the anomaly
(see Figs. 6-7 in (Anderson et al. 2002));
II. Analysis of the entire set of Doppler data: (iii) to study the temporal behavior of the sig-
nal,and (iv) toperform a comparative analysis of the individual anomalous accelerations
of the two Pioneers with data taken from similar heliocentric distances; and finally
III. The newly recovered telemetry information from the spacecrafts’ thermal, electrical,
power, propulsion, and communication subsystems will be used (v) to investigate con-
tributions of known sources of on-board systematics and study their effects on aP. This
investigation of the on-board small forces will be done in conjunction with the analysis
of the Doppler data, thereby strengthening the ultimate outcome.
The new extended data set enables us to investigate the Pioneer anomaly with the entire
available Pioneer10and11radiometric Doppler data(Turyshev et al.2006a;Toth & Turyshev
2008). In particular, it is used to build a thermal/electrical/dynamical model of the Pioneer
vehicles and verify it with the actual data from the telemetry; the goal here is the devel-
opment of a model that can be used to calibrate the Doppler anomaly with respect to the
on-board sources of dynamical noise.
2.2.1 Direction of the Pioneer anomaly
Analysis of the earlier data is critical in establishing a precise time history of the effect.
With the radiation pattern of the Pioneer antennae and the lack of precise navigation in the
plane of the sky, the determination of the exact direction of the anomaly was a difficult
task (Anderson et al. 2002). While in deep space, for standard antennae without good 3-D
navigation, the directions: (i) towards the Sun, (ii) towards the Earth, (iii) along the direc-
tion of motion of the craft, or (iv) along the spin axis, are all observationally synonymous
(Nieto & Turyshev 2004).
The four possible directions for the anomaly all indicate a different physical mecha-
nism. Specifically, if the anomaly is: (i) in the direction towards the Sun, this would indicate
a force originating from the Sun, likely signifying a need for gravity modification; (ii) in the
direction towards the Earth, this would indicate an effect on signal propagation or a time
signal anomaly impacting the design of the DSN hardware and space flight-control meth-
ods; (iii) in the direction of the velocity vector, this would indicate an inertial force or a
drag force providing support for a media-dependent origin; or, finally, (iv) in the spin-axis
direction, this would indicate an on-board systematic, which is the most plausible expla-
nation for the effect. The corresponding directional signatures of these four directions are
distinct and could be extracted from the data (Nieto & Turyshev 2004; Turyshev et al. 2005;
Toth & Turyshev 2006).
The increased data span, and especially the earlier data segment, is crucial in our ability
to determine the direction of the signal and its true nature. If the anomaly is due to on-
board effects, direct along the spin axis, the solution for the anomaly will be different after
each re-pointing of the spacecraft, namely, every re-pointing will produce a step-function
discontinuity in the solution for the aP. Earlier in the mission, there were many of these re-
pointing maneuvers; understanding their impact on the anomaly would be a very important
activity of the proposed analysis of the earlier data (Turyshev et al. 2005).
Withthe early data, we expect to improve the sensitivity of the solutions inthe directions
perpendicular to the line-of-sight by at least an order of magnitude. We started to analyze
the early parts of the trajectories of the Pioneers with the goal of determining the true direc-
tion of the Pioneer anomaly and possibly its origin (Nieto & Turyshev 2004; Turyshev et al.
2005, 2006b); results will be reported elsewhere.
2.2.2 Study of the planetary encounters
It is alarming is that the early Pioneer 10 and 11 data (before 1987) was never analyzed
in detail, especially in regards to the effect of on-board systematics. For instance, a nearly
constant anomalous acceleration seems to exist in the data of Pioneer 10 as close as 27
AU from the Sun (Anderson et al. 2002; Turyshev et al. 2005). Pioneer 11, beginning just
after Jupiter flyby, shows a small value for the anomaly during the Jupiter-Saturn cruise
phase in the interior of the solar system. However, right at Saturn encounter, when the craft
passed into a hyperbolic escape orbit, analysis of early navigation results tentatively shows a
fast increase in the anomaly to its canonical value (Nieto & Turyshev 2004; Turyshev et al.
We first study the Saturn encounter for Pioneer 11. We will use the data for nearly two
years surrounding this event. If successful, we should be able to learn the mechanism that
led to the onset of the anomaly during the flyby. The Jovian encounters are also of interest;
however, they were in the region much too close to the Sun. One expects large contributions
from the standard sources of acceleration noise that exist at heliocentric distances ∼ 5 AU.
We use a similar strategy as with the Saturn encounter and will attempt to make full use of
the data available.
2.2.3 Study of the temporal evolution of the anomaly
The same investigation as above is used to revisit the question of collimated thermal emis-
sionby studying the temporal evolution ofthe anomaly. Ifthe anomaly is due tothe on-board
nuclear fuel inventory (238Pu) present on the vehicles and the related heat recoil force, one
expects that a decrease in the anomaly’s magnitude will be correlated with238Pu decay with
a half-life of 87.74 years. The previous analysis of 11.5 years of data (Anderson et al. 2002)
found no support for a thermal mechanism. However, Markwardt (2002) and Toth (2009)
did not rule out this possibility finding an appropriate trend in the solution for aP. The now
available 30-year interval of data (20 years for Pioneer 11) may demonstrate the effect of
a ∼ 21 % reduction in the heat contribution to the anomaly. This behavior would strongly
support a thermal origin of the effect (Toth & Turyshev 2008).
Asymmetrically radiated heat due to available on-board thermal inventory, if appropri-
ately directed, may result in a recoil force with properties similar to those of the Pioneer
anomaly. This is the “primary suspect” for the origin of the effect. Therefore, an investi-
gation of heat exchange mechanisms that may lead to a thermal thrust on the craft is an
important part our effort. This investigation is done in two ways: (i) to use the longest pos-
sible set of Doppler data to study the temporal evolution of aPand (ii) to build a model of
thermal thrust of the Pioneer craft and use available telemetry data to derive the resulted
acceleration. If the anomaly is due to a thermal mechanism, the two methods should agree.
The much extended data span, augmented by all the ancillary spacecraft information,
willhelptostudyasignature oftheexponential decayofthe on-board power source(Markwardt
2002; Toth 2009). The wealth of the recently acquired data presents an exciting opportunity
to learn more about the anomaly in various regimes and will help to determine the nature of
this anomalous signal.
2.2.4 Analysis of the individual trajectories for both Pioneers
The much largernewlyrecovered setsofthe Pioneer10 and11Doppler data make itpossible
to study the properties of the individual acceleration solutions for both Pioneers obtained
with the data collected from similar heliocentric distances. The limited data set used in the
previous analysis (Anderson et al. 1998, 2002) precluded such a comparison; however, the
now available data allows such an investigation.
Previously, even though we had individual solutions from the two craft, the fact re-
mained that aP10and aP11were obtained from data segments that not only were very dif-
ferent in length (11.5 and 3.75 years), but they were also taken from different heliocentric
distances. We anticipate that analysis of their data from similar heliocentric regions will help
us better understand the properties of the anomaly, especially if it were to be attributed to
an on-board systematic source. Analysis of the individual data would also help to calibrate
the final solution for the anomaly by properly accounting for the individual properties of the
2.2.5 Investigation of on-board systematics
The availability of telemetry information makes it possible to conduct a detailed investiga-
tion of the on-board systematic forces as a source of the anomalous acceleration. Here we
Fig. 1 A drawing of the Pioneer spacecraft.
consider forces that are generated by on-board spacecraft systems and that are thought to
contribute to the constant acceleration seen in the analysis of the Pioneer Doppler data (see
Section 3 for discussion).
3 Using flight telemetry to study the spacecrafts’ behavior
AlltransmissionsofbothPioneerspacecraft,including allengineering telemetry,werearchived
(Turyshev et al. 2006a) in the form of files containing Master Data Records (MDRs). Origi-
nally,MDRswerescheduledforlimitedretention. Fortunately, thePioneers’missionrecords
avoided this fate: with the exception of a few gaps in the data (Turyshev et al. 2006a) the en-
tire mission record has been saved. These recently recovered telemetry readings are impor-
tant in reconstructing a complete history of the thermal, electrical, and propulsion systems
for both spacecraft. This, may data lead to a better determination of the crafts’ acceleration
due to on-board systematic effects.
3.1 The Pioneer spacecraft
As evident from Fig. 1, the appearance of the Pioneer spacecraft is dominated by the 2.74 m
diameter high gain antenna (HGA). The spacecraft body, located behind the HGA, consists
of a larger, regular hexagonal compartment housing the propellant tank and spacecraft elec-
tronics; an adjacent, smaller compartment housed science instruments. The spacecraft body
is covered by multilayer thermal insulating blankets, except for a louver system located on
the side opposite the HGA, which was activated by bimetallic springs to expel excess heat
from the spacecraft.
Each spacecraft was powered by four radioisotope thermoelectric generators (RTGs)
mounted in pairs at the end of two booms, approximately three meters in length, extended
from two sides of the spacecraft body at an angle of 120◦. A third boom, approximately 6 m
long, held a magnetometer.
The total (design) mass of the spacecraft was ∼250 kg at launch, of which 27 kg was
propellant (NASA Ames Research Center 1971).
For the purposes of attitude control, the spacecraft were designed to spin at the nominal
rate of 4.8 rpm. Six small monopropellant (hydrazine) thrusters, mounted in three thruster
cluster assemblies, were used for spin correction, attitude control, and trajectory correction
maneuvers (see Fig. 3).
3.2 Compartment temperatures and thermal radiation
IfthePioneeranomaly isdue toanisotropically emittedthermal radiation, one expects tofind
a near constant supply of heat radiated off the back of the spacecraft that would produce a
thermal recoil force with the well established properties (Turyshev et al. 2005). The lack of
constancy of heat dissipated during the longest Doppler segment analyses (i.e. 11.5 years of
the Pioneer 10 data (Anderson et al. 2002)) appears to have invalidated the hypothesis.
The newly acquired data (both Doppler and telemetry) is very valuable for the investi-
gation as it contributes to addressing this possibility. We also have a much larger segment of
Doppler data that will be used to analyze these heat dissipation processes on the vehicles.
In addition, we now have the actual design, fabrication, testing, pre- and in-flight calibra-
tion data that characterize the Pioneer craft performance for the duration of their missions.
Finally, we have all the detailed information on properties of the spacecraft and the data
needed to reconstruct the behavior of its major components, including electrical power and
This data tells precisely at what time the louvers were open and closed, when a certain
instrument was powered “on” and “off”, what was the performance of the battery, shunt
current and all electric parts of the spacecraft. This information is being used in the devel-
opment of a model of the Pioneers that is needed to establish the true thermal and electrical
power dissipation history of the vehicles and also to correlate major events on the Pioneers
(such as powering “on” or “off” certain instruments or performing a maneuver) with the
anaysis of the available Doppler data.
3.3 Telemetry overview
Telemetry formats can be broadly categorized as science formats versus engineering for-
mats. Telemetry words included both analog and digital values. Digital values were used
to represent sensor states, switch states, counters, timers, and logic states. Analog readings,
from sensors measuring temperatures, voltages, currents andmore, were encoded using 6-bit
words. This necessarily limited the sensor resolution and introduced a significant amount of
quantization noise. Furthermore, the analog-to-digital conversion was not necessarily linear;
prior to launch, analog sensors were calibrated using a fifth-order polynomial. Calibration
ranges were also established; outside these ranges, the calibration polynomials are known to
yield nonsensical results.
With the help of the information contained in these words, it is possible to reconstruct
the history of RTG temperatures and power, radio beam power, electrically generated heat
inside the spacecraft, spacecraft temperatures, and propulsion system history.
Relevant on-board telemetry falls into two categories: temperature and electrical mea-
surements. In the first category, we have data from several temperature sensors on-board,
most notably the fin root temperature readings for all four RTGs. Figure 5 shows the location
of most temperature sensors on board for which readings are available. Other temperature
sensors are located at the RTGs and inside the propellant tank.
The electrical power profile of the spacecraft can be reconstructed toa reasonable degree
of accuracy using electrical telemetry measurements. Available are the individual voltage
and current readings for the RTGs, the readings on the main bus voltage and current, as well
as the shunt current; known are the power on/off state of most spacecraft subsystems. From
these and other readings, one can calculate the complete electrical profile of the spacecraft.
3.4 RTG temperatures and anisotropic heat reflection
It hasbeen arguedthat the anomalous acceleration maybe due toanisotropic reflectionofthe
heat coming from the RTGs off the back of the spacecraft high gain antennae. Note that only
∼65 W of directed constant heat is required to explain the anomaly, which certainly is not a
great deal of power when the craft has heat sources capable of producing almost 2.5 kW of
heat at the beginning ofthe missions. However, using available information onthe spacecraft
and RTG designs, Anderson et al. (2002) estimated that only 4W of directed power could
be produced by this mechanism. Adding an uncertainty of the same size, they estimated a
contribution to the anomalous acceleration from heat reflection to be ahr=(−0.55±0.55)×
10−10m/s2. Furthermore, if this mechanism were the cause of the anomaly, ultimately an
unambiguous decrease inthe sizeof aPshould be observed, because the RTGs’radioactively
produced radiant heat is decreasing. In fact, one would expect a decrease of about 0.75×
10−10m/s2in aPover the 11.5 year Pioneer 10 data interval if this mechanism were the
origin of aP.
Alternative estimates presented put the magnitude of this effect at ∼24W or the corre-
sponding value for ahrat the level of ahr∼ −3.3×10−10m/s2(see discussion in (Scheffer
2003)). We comment on the fact that both groups acknowledged that a thermal model for
the Pioneer spacecraft is hard to build. However, this seems to be exactly what one would
have to do in order to reconcile the differences in analyzing the role of the thermal heat in
the formation of the Pioneer anomaly.
It is clear that any thermal explanation should clarify why either the radioactive decay
(if the heat is directly from the RTGs (Katz 1999)) or electrical power decay (if the heat
is from the instrument compartment (Murphy 1999)) is not seen. One reason could be that
previous analyses used only a limited data set of only 11.5 years when the thermal signature
was hard to disentangle from the Doppler residuals or the fact that the actual data on the
performance of the thermal and electrical systems was not complete or unavailable at the
time the analyses were performed.
The present situation is very different. Not only do we have a much longer Doppler
data segment for both spacecraft, we also have the actual telemetry data on the thermal and
electric power subsystems for both Pioneers for the entire lengths of their missions. The
electrical power profile of the spacecraft can be reconstructed to a reasonable degree of
accuracy using electrical telemetry measurements. We have individual voltage and current
readings for the RTGs; we have readings on the main bus voltage and current, as well as the
1970197319761979 19821985 19881991 19941997 20002003
Pioneer 10 RTG1 Fin Root Temperature (degF)
Fig. 2 RTG 1 fin root temperatures (telemetry word C201; in◦F) for Pioneer 10.
shunt current; we know the power on/off state of most spacecraft subsystems. From these
and other readings, the complete electrical profile of the spacecraft can be calculated, as
discussed in (Turyshev et al. 2006a).
To utilize this data for the upcoming investigation, it is possible to reconstruct the di-
rection of heat flow (with the help of a thermal model built for this purpose) and study the
absorption and re-emission by, and reflection off the craft surfaces (Turyshev et al. 2006a;
Toth & Turyshev 2008).
In the following discussion, telemetry words are labeled using identifiers in the form of
Cn, where n is a number indicating the word position in the fixed format telemetry frames.
The exterior temperatures of the RTGs were measured by one sensor on each of the
four RTGs: the so-called “fin root temperature” sensor. Telemetry words C201through C204
contain the fin root temperature sensor readings for RTGs 1 through 4, respectively. Figure 2
depicts the evolution of the RTG 1 fin root temperature for Pioneer 10 (other fin root sensors
exhibited similar behavior (Turyshev et al. 2006a)).
A best fit analysis confirms that the RTG temperature indeed evolves in a manner con-
sistent with the radioactive decay of the nuclear fuel on board. The results for all the other
RTGs on both spacecraft are similar, confirming that the RTGs were performing thermally
in accordance with design expectations.
3.5 RTG power electrically generated heat
RTG electrical power can be estimated using two sensor readings per RTG, measuring RTG
current and voltage. Currents for RTGs 1 through 4 appear as telemetry words C127, C105,
C114, and C123, respectively; voltages are in telemetry words C110, C125, C131, and C113.
Combined, these words yield the total amount of electrical power available on board:
All this electrical power is eventually converted to waste heat by the spacecrafts’ instru-
ments, with the exception of power radiated away by transmitters.
Pioneer 10 RTG electrical power (W)
Fig. 3 Changes in total RTG electrical output (in W) on board Pioneer, as computed using the mission’s
Whatever remains of electrical energy (Fig. 3) after accounting for the power of the
transmitted radio beam is converted to heat on-board. Some of it is converted to heat outside
the spacecraft body by externally mounted components.
The Pioneer electrical system is designed to maximize the lifetime of the RTG thermo-
couples by ensuring that the current draw from the RTGs is always optimal. This means
that power supplied by the RTGs may be more than that required for spacecraft operations.
Excess electrical energy is absorbed by a shunt circuit that includes an externally mounted
radiator plate. Especially early in the mission, when plenty of RTG power was still available,
this radiator plate was the most significant component external to the spacecraft body that
radiated heat. Telemetry wordC122tells us the shunt circuit current, from which the amount
of power dissipated by the external radiator can be computed using the known ohmic resis-
tance (∼5.25 Ω) of the radiator plate.
Other externally mounted components that consume electrical power are the Plasma
Analyzer (PPA= 4.2 W, telemetry word C108bit 2), the Cosmic Ray Telescope (PCRT=
2.2 W, telemetry word C108, bit 6), and the Asteroid/Meteoroid Detector (PAMD= 2 W,
telemetry word C124, bit 5). Though these instruments’ exact power consumption is not
telemetered, we know their average power consumption from design documentation, and
the telemetry bits tell us when these instruments were powered.
Twoadditional external loads are the batteryheaterandthe propellant line heaters. These
represent a load of PLH= PBH= 2 W (nominal) each. The power state of these loads is not
telemetered. According to mission logs, the battery heater was commanded off on both
spacecraft on 12 May 1993.
Yet a further external load is the set of cables connecting the RTGs to the inverters. The
resistance of these cables is known: it is 0.017 Ω for the inner RTGs (RTG 3 and 4), and
0.021 Ω for the outer RTGs (RTG 1 and 2). Using the RTG current readings it is possible to
accurately determine the amount of power dissipated by these cables in the form of heat:
After accounting for all these external loads, whatever remains of the available electri-
cal power on board is converted to heat inside the spacecraft. So long as the body of the
Fig. 4 Bottom view of the Pioneer 10 and 11 vehicle, showing the louver system. A set of 12 2-blade louver
assemblies cover the main compartment in a circular pattern; an additional two 3-blade assemblies cover the
compartment with science instruments.
spacecraft is in equilibrium with its surroundings, heat dissipated through its walls has to be
equal to the heat generated inside:
with all the terms defined above.
3.6 The thermal control subsystem
The passive thermal control system consisted of a series of spring-activated louvers (see
Fig. 4). The springs were bimetallic, and thermally (radiatively) coupled to the electronics
platform beneath the louvers. The louver blades were highly reflective in the infrared. The
assembly was designed so that the louvers fully open when temperatures reach 30◦C, and
fully close when temperatures drop below 5◦C.
The effective emissivity of the thermal blankets used on the Pioneers is εsides= 0.085
(Toth & Turyshev 2006). The total exterior area of the spacecraft body is Awalls= 4.92 m2.
The front side of the spacecraft body that faces the HGA has an area of Afront=1.53 m2, and
its effective emissivity, accounting for the fact that most thermal radiation this side emits is
reflected by the back of the HGA, can be computed as εfront= 0.0013. The area covered by
louver blades is Alouv= 0.29 m2; the effective emissivity of closed louvers is εlouv= 0.04
(NASA Ames Research Center 1971). The area that remains, consisting of the sides of the
spacecraft and the portion of the rear not covered by louvers is Asides=Awalls−Afront−Alouv.
Using these numbers, we can estimate the amount of electrically generated heat radiated
through the (closed) louver system as a ratio of total electrical heat generated inside the
Fig. 5 Location
(NASA Ames Research Center 1971). Temperature sensors are mounted at locations 1 to 6.
of thermal sensors inthe instrumentcompartmentof Pioneer10 and 11
spacecraft body. If we assume that the exterior of the spacecraft isapproximately isothermal,
This result is a function of the electrical power generated inside the spacecraft body.
However, we also have in our possession thermal vacuum chamber test results of the Pio-
neer louver system. These results characterize louver thermal emissions as a function of the
temperature of the electronics platform beneath the louvers, with separate tests performed
for the 2-blade and 3-blade louver assemblies. To utilize these results, we turn our attention
to telemetry words representing electronics platform temperatures.
There are 6 platform temperature sensors (Fig. 5) inside the spacecraft body: 4 are lo-
cated inside the main compartment, 2 sensors are in the science instrument compartment.
The main compartment has a total of 12 2-blade louver blade assemblies; the science com-
partment has 2 3-blade assemblies.
The thermal vacuum chamber tests provide values for emitted thermal power per louver
assembly as a function of the temperature of the electronics platform behind the louver. This
allows us to estimate the amount of thermal power leaving the spacecraft body through the
louvers, as a function of platform temperatures (Toth & Turyshev 2006), providing means
to estimate the amount of heat radiated by the louver system.
The study of the thermal hypothesis as the likely cause of the Pioneer anomaly is still
on-going. Our preliminary thermal modeling indicates that anisotropic thermal radiation
may account for some, but not necessarily for all of the anomalous acceleration of the Pi-
oneers. Rather than treating this result as the “smoking gun”, we realized that the study of
the anomaly requires a thorough and complete understanding and characterization of this
thermal recoil force. This means that the most difficult part of our work only just began.
Initial results are very intriguing, leading us to believe that we will be able to address all the
main objectives of the study of the Pioneer anomaly (see discussion in Sec. 2.2). We will
report the results of this investigation elsewhere.
Although significant speculation in the investigation of the Pioneer anomaly has arisen
over “new physics,” it is likely that the anomaly is systematic in nature. Still, further high
precision tests of this effect might confirm or refute the Pioneer results. We suggest that the
New Horizons spacecraft would provide an opportunity for a test.
4 Studying the Pioneer anomaly with New Horizons
Computation of recoil forces due to thermal momentum transfer is rarely needed in ground-
based applications, as the resulting forces are exceedingly small for any practical purpose
(Toth & Turyshev 2009). However, corresponding effects become important for precision
navigated spacecraft such as Pioneer 10 and 11 where, in order to find the origin of the
Pioneer anomaly, one needs to account for all minuscule dynamical disturbances of the
spacecraft trajectory and its attitude at the level of ∼ 10−10m/s2(Anderson et al. 2002;
Turyshev et al. 2005). Reaching this level of accuracy depends on i) thermal spacecraft de-
sign that is free from introducing parasitic sources of non-gravitational noise and ii) an abil-
ity to compensate for unwanted forces during orbit determination process. One particular
example to apply our methods is the New Horizons mission to Pluto and beyond.
New Horizons began its decade long journey to Pluto and beyond on January 19, 2006.
The spacecraft and its mission bear many similarities to the Pioneer 10 and 11 spacecraft
and missions. Both types of spacecraft are spin-stabilized. They are powered by RTGs. Both
spacecraft utilize a louver systemto vent excess heat from the spacecraft body. Their appear-
ance is dominated by a large HGA with the spacecraft body located behind it. They all fol-
low hyperbolic escape trajectories. Due to these similarities, the possibility exists that New
Horizons might provide a means to further investigate the Pioneer anomaly (Anderson et al.
There are some differences between the two spacecraft. New Horizons uses X-band
frequencies forcommunication, whichallow forbetterqualityradiometric data. Also,during
the New Horizons cruise phase to Pluto, the spacecraft is in “hibernation” mode, with low
operational activity and minimal tracking.
Thestudyoftheanomalous accelerationofthePioneer10and11spacecraft (Anderson et al.
2002;Toth & Turyshev 2006)demonstrates the importance of taking intoaccount very small
forces that might affect the accuracy of spacecraft navigation. We developed an approach to
investigate this claim, thereby establishing a foundation for the study ofthe Pioneer anomaly
using recently recovered extended set of radio-metric Doppler and flight telemetry data
(Toth & Turyshev 2006, 2008).
During the course of our work, we learned some lessons that are directly applicable to
New Horizons. Specifically, we found that the two main sources of thermal acceleration
are asymmetrically reflected heat from the RTGs, and electrical heat generated inside the
Based solely on publicly available information sources, we can develop a preliminary
estimate of these heat sources on the trajectory of New Horizons. We start with electrically
4.1 Electrically generated heat
The New Horizons power source is a GPHS-RTG fueled with 61 fuel elements. The nominal
electrical power of a GPHS-RTG fueled with the maximum of 72 fuel elements is 285 W,
and its total power is ∼4.3 kW. Thus, we calculate the electrical power of the New Horizons
RTG at the time of launch as PE= 240 W, and its total power, 3.36 kW. These values agree
with values published in (New Horizons Launch Press Kit 2006).
To maximize the lifetime of the thermocouple elements inside the RTG, the spacecraft
is designed to always draw the optimal amount of current from the RTG; excess electrical
power is directed to a shunt circuit. Shunted power may be dissipated in the form of heat
either inside the spacecraft body or outside, depending on thermal conditions. This design
suggests that the amount of electrical power converted to heat inside the craft body remains
approximately constant throughout the mission, at least after it leaves the inner solar system
and is no longer significantly heated by the Sun.
Accordingly, we assume that the amount of electrically generated heat inside the space-
craft body will be the nominal figure of 150 W, constant throughout the mission except for
the very early phases, when solar heating is significant, and the very late phases, when RTG
power drops to a low level.
Heat will leave the interior of the spacecraft body through its walls. The walls are gen-
erally covered with multilayer insulation, whose typical effective emissivity is on the order
of εw= 0.01 (Stimpson and Jaworski 1972). One exception is the area covered by the lou-
vers of the thermal control system. On Pioneer 10 and 11, the effective emissivity of the
closed louvers is approximately εl= 0.04 (NASA Ames Research Center 1971). As we do
not have a separate value for New Horizons, we shall use the Pioneer figure. The emissivity
changes as the louvers open partially, but the system also becomes highly non-Lambertian,
as the angled louvers preferentially reflect internal heat in one particular direction. Due to
the complexities of this scenario, we ignore the case when louvers are partially open, i.e.,
when the spacecraft is still near the Sun.
We assume that the spacecraft walls and the louver blades are Lambertian emitters. The
side walls will not contribute to acceleration; heat radiated by these walls will, on average,
be emitted in a direction perpendicular to the spin axis. Similarly, the wall facing the back
of the HGA will not contribute to acceleration either; as it is facing the highly (∼99%) re-
flective backside of the HGA, very little heat will leave the spacecraft body in this direction.
Therefore, the amount of heat contributing to acceleration can be calculated as the ratio of
heat leaving through the bottom of the spacecraft (which is partially covered by louvers) to
the total heat leaving through the bottom and sides:
where PE is the total electrically generated heat inside the spacecraft body, PEaccelis the
amount of electrically generated heat contributing to acceleration, ε is the emissivity, and A
is the area of a surface (b: bottom, s: sides). The factor of 2/3 is due to the assumption that
the surfaces are Lambertian emitters.
No published data appears to exist on the actual size of the New Horizons louvers,
but published “artist’s renderings” appear to depict at least four louver assemblies with ten
louver blades each. On Pioneer 10 and 11, a set of 30 louver blades covered an area of
∼ 0.3m2; therefore, we shall assume that the area of the louver system on New Horizons
is Al≃ 0.4m2. The surface area of the rest of the craft body can be calculated using low-
resolution, but dimensionally correct drawings, leading to the estimate
PEaccel= 0.46PE= 68.4W.
4.2 Heat from the RTG
Most of the power from the RTG is not converted to electricity but radiated away into space
in the form of heat. The radiation pattern of the RTG is fore-aft symmetric, resulting in
no net (average) acceleration force on a spinning spacecraft. Some of the heat, however, is
reflected by the back of the HGA, resulting in an acceleration force.
A quick look at published drawings of the New Horizons spacecraft makes it clear that
no parts of the spacecraft body stand in the way of thermal radiation emitted from the RTG
in the direction of the back of the HGA. However, an approximately circular heat shield at
the base of the RTG blocks some thermal radiation.
Any radiation that impacts the back of the HGA will transfer momentum to the space-
craft. Additionally, radiation that is reflected by the HGA transfers further momentum. To
estimate the total amount of momentum transferred to the spacecraft this way, one needs to
enumerate the following:
i) Pincident, the spin-axis component of thermal radiation incident on the back of the HGA,
as a function of the angle between the ray of radiation and the spin axis;
ii) Pspecular, the spin-axis component of thermal radiation specularly reflected by the back
of the HGA, as a function of the angle of incidence at the HGA and the angle of the
HGA surface normal at the point of incidence relative to the spin axis;
iii) Pdiffuse, the spin-axis component of thermal radiation diffusely reflected by the back of
the HGA, as a function of the angle between the HGA surface normal at the point of
incidence relative to the spin axis.
To compute these quantities, we begin with the equation of heat transfer between two
Lambertian surfaces (Toth & Turyshev 2009):
where A1and A2represent the surface of the emitting and the absorbing body, respectively; r
is the distance between the surface elements dA1and dA2; θ1and θ2are the angles between
the line connecting the two surface elements and their respective normals; and P1is the
emitted power density (power per unit area) at the surface A1.
We can eliminate one of the double integrals by noting that the RTG is approximately
isothermal along its length, and it is approximately cylindrically symmetrical (indeed, the
hexagonal fin arrangement means that one can substitute a cylindrical body of a diameter
that is the mean of unity and cos30◦=√3/2, introducing an error no larger than ∼ 7%;
in actuality, as the fins are likely colder than the core of the RTG, the error will be even
smaller.) Put together, these considerations help us reduce Eq. (8) to
? ?sinβ cosθ
where L represents the length ofthe RTG and A represents the portion ofthe backof the RTG
illuminated bythatpoint oftheRTG.Asthe RTGisassumedtobe lengthwise isothermal, we
could also move PRTG, denoting the RTG thermal power (total power minus power removed
by the thermocouples in the form of electricity; ∼3360 W at the beginning of mission),
outside the integration sign. β now denotes the angle between the ray of radiation and the
lengthwise RTG axis, and θ is the angle of incidence relative to the RTG surface normal.
To obtain the spin-axis component of this incident ray of radiation, we need to further
multiply by sinβ:
? ?sin2β cosθ
For diffusely reflected radiation, we note that for a Lambertian reflector, momentum
transferred will be in a direction perpendicular to the surface element, and it will be propor-
tional to the incident radiation times 2ρ/3, where ρ denotes the reflectance. To calculate the
spin-axis component of diffusely reflected radiation, we need to therefore compute
? ?sinβ cosγcosθ
where γ is the angle between the normal of the surface element dA and the spin axis, and σ
is the ratio of specular vs. total reflected radiation.
Radiation that is specularly reflected will be emitted in accordance with the laws of
geometric optics. Denoting the angle of specularly reflected radiation at surface element dA
by δ, we can compute the spin axis component of specularly reflected radiation as
? ?sinβ cosδ cosθ
Thevalues ofβ,γ,δ,andθ,aswellasthe integrationlimitsforthe surface integrals (i.e.,
the boundaries of the HGA area illuminated by the RTG) can be computed using geometric
considerations. An examination of the geometry also tells us that approximately 20% of
reflected radiation will be intercepted by the spacecraft body, and thus not contribute to
thrust. The total amount of radiation that contributes to thrust in the direction of the spin
axis can be summed as:
Numerical evaluation of these integrals yields
as the amount of thermal power, as a function of total RTG power PRTG, that will contribute
to acceleration along the spin axis. At the beginning of mission, this translates into approxi-
mately 500 W of power contributing to acceleration.
While the approximations used in this section are clearly no substitute for the evaluation
of a detailed finite element model of the spacecraft, the result indicates that anisotropic
thermal radiation is a potentially significant source of acceleration for New Horizons during
its long interplanetary cruise.
4.3 Acceleration due to emitted heat
The relationship between the momentum and energy of electromagnetic radiation is well
known: p = E/c. To calculate the acceleration due to collimated electromagnetic radiation
of power P emitted by a body of mass m, one can use the formula a =P/(mc). The nominal
mass at launch of the New Horizons spacecraft is about 465 kg (NHF 2005). Thus, we
can calculate an anomalous acceleration for the New Horizons spacecraft due to thermal
radiation from the RTG and electrical equipment as
aNH= 41×10−10m/s2≃ 4.7aP.
When the spacecraft’s 15 W transmitter is operating, the power of the radio beam (emit-
ted in the direction opposite to the direction of thermal effects), which translates into an
acceleration of 1×10−10m/s2, would have to be subtracted from our result.
The availability of the entire history of the Pioneer spacecraft makes it possible for us
to calculate acceleration due to on-board forces to a significantly greater precision, and as a
function of spacecraft parameters that evolve with time. The contribution of on-board forces
to acceleration can be significant. Therefore, preserving and making available raw (engi-
neering) telemetry of New Horizons to researchers is of great importance if accurate orbit
determination is desired, and especially if conclusions are to be derived from any discrep-
ancies between computed and observed orbits.
By 2009, the existence of the Pioneer anomaly is no longer in doubt. Our continuing effort
to process and analyze Pioneer radio-metric and telemetry data is part of a broader strategy
(Turyshev et al. 2005, 2006a).
Based on the information provided by the telemetry, we were able to develop a high
accuracy thermal, electrical, and dynamical model of the Pioneer spacecraft. This model is
used to investigate the anomalous acceleration and especially to study the contribution from
the on-board thermal environment to the anomaly.
The available thermal model for the Pioneer spacecraft accounts for all heat radiation
produced by the spacecraft. In fact, we use telemetry information to accurately estimate the
amount of heat produced by the spacecrafts’ major components. We are in the process of
evaluating the amount of heat radiated in various directions.
This entails, on the one hand, an analysis of all available radio-metric data, to character-
ize the anomalous acceleration beyond the periods that were examined in previous studies.
Telemetry, on the other hand, enables us to reconstruct a thermal, electrical, and propulsion
system profile of the spacecraft. Soon, we should be able to estimate effects on the motion
of the spacecraft due to on-board systematic acceleration sources, expressed as a function
of telemetry readings. This provides a new and unique way to refine orbital predictions and
may also lead to an unambiguous determination of the origin of the Pioneer anomaly.
Concluding, we mention that before Pioneer 10 and 11, Newtonian gravity had never
been measured—and was therefore never confirmed—with great precision over great dis-
tances. The unique “built-in” navigation capabilities of Pioneer 10 and 11 allowed them to
reach the levels of ∼ 10−10m/s2in acceleration sensitivity. Such an exceptional sensitivity
means that Pioneer 10 and 11 represent the largest-scale experiment to test the gravitational
inverse square law ever conducted. However, the experiment failed to confirm the valid-
ity of this fundamental law of Newtonian gravity in the outer regions of the solar system.
19 Download full-text
One can demonstrate, beyond 15 AU the difference between the predictions of Newton and
Einstein are negligible. So, at the moment, two forces seem to be at play in deep space:
Newton’s laws of gravity and the mysterious Pioneer anomaly. Until the anomaly is thor-
oughly accounted for by natural causes, and can therefore be eliminated from consideration,
the validity of Newton’s laws in the outer solar system will remain unconfirmed. This fact
justifies the importance of the investigation of the nature of the Pioneer anomaly.
Acknowledgements This work was partially performed at the International Space Science Institute (ISSI),
Bern, Switzerland, when both of us visited ISSI as part of an International Team program. In this respect we
thank Roger M. Bonnet, Vittorio Manno, Brigitte Schutte and Saliba F. Saliba of ISSI for their hospitality
and support. We especially thank The Planetary Society for support and, in particular, Louis D. Freidman,
Charlene M. Anderson, and Bruce Betts for their interest, stimulating conversations and encouragement.
The work of SGT was carried out at the Jet Propulsion Laboratory, California Institute of Technology,
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