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The Pioneer anomaly, or Pioneer effect, was the observed deviation from predicted accelerations of the ''
Pioneer 10 ''Pioneer 10'' (originally designated Pioneer F) is an American space probe, launched in 1972 and weighing , that completed the first mission to the planet Jupiter. Thereafter, ''Pioneer 10'' became the first of five artificial objects to ac ...
'' and ''
Pioneer 11 ''Pioneer 11'' (also known as ''Pioneer G'') is a robotic space probe launched by NASA on April 5, 1973, to study the asteroid belt, the environment around Jupiter and Saturn, solar winds, and cosmic rays. It was the first probe to encoun ...
'' spacecraft after they passed about on their trajectories out of the
Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
. The apparent anomaly was a matter of much interest for many years but has been subsequently explained by
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
radiation pressure Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is a ...
caused by the spacecraft's heat loss. Both ''Pioneer'' spacecraft are escaping the Solar System but are slowing under the influence of the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
's gravity. Upon very close examination of navigational data, the spacecraft were found to be slowing slightly more than expected. The effect is an extremely small acceleration towards the Sun, of , which is equivalent to a reduction of the outbound velocity by 1 km/h over a period of ten years. The two spacecraft were launched in 1972 and 1973. The anomalous acceleration was first noticed as early as 1980 but not seriously investigated until 1994. The last communication with either spacecraft was in 2003, but analysis of recorded data continues. Various explanations, both of spacecraft behavior and of gravitation itself, were proposed to explain the anomaly. Over the period from 1998 to 2012, one particular explanation became accepted. The spacecraft, which are surrounded by an
ultra-high vacuum Ultra-high vacuum (UHV) is the vacuum regime characterised by pressures lower than about . UHV conditions are created by pumping the gas out of a UHV chamber. At these low pressures the mean free path of a gas molecule is greater than approximatel ...
and are each powered by a
radioisotope thermoelectric generator A radioisotope thermoelectric generator (RTG, RITEG), sometimes referred to as a radioisotope power system (RPS), is a type of nuclear battery that uses an array of thermocouples to convert the heat released by the decay of a suitable radioa ...
(RTG), can shed heat only via
thermal radiation Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) i ...
. If, due to the design of the spacecraft, more heat is emitted in a particular direction by what is known as a radiative
anisotropy Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
, then the spacecraft would accelerate slightly in the direction opposite of the excess emitted radiation due to the
recoil Recoil (often called knockback, kickback or simply kick) is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, as according to Newton's third law the force r ...
of thermal
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
s. If the excess radiation and attendant radiation pressure were pointed in a general direction opposite the Sun, the spacecraft's velocity away from the Sun would be decreasing at a rate greater than could be explained by previously recognized forces, such as gravity and trace friction due to the
interplanetary medium The interplanetary medium (IPM) or interplanetary space consists of the mass and energy which fills the Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding ...
(imperfect vacuum). By 2012, several papers by different groups, all reanalyzing the thermal radiation pressure forces inherent in the spacecraft, showed that a careful accounting of this explains the entire anomaly; thus the cause is mundane and does not point to any new phenomenon or need for a different physical paradigm. The most detailed analysis to date, by some of the original investigators, explicitly looks at two methods of estimating thermal forces, concluding that there is "no statistically significant difference between the two estimates and ..that once the thermal
recoil Recoil (often called knockback, kickback or simply kick) is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, as according to Newton's third law the force r ...
force is properly accounted for, no anomalous acceleration remains."


Description

''Pioneer 10'' and ''11'' were sent on missions to
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...
and Jupiter/Saturn respectively. Both spacecraft were spin-stabilised in order to keep their high-gain antennas pointed towards
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
using gyroscopic forces. Although the spacecraft included thrusters, after the planetary encounters they were used only for semiannual
conical scanning Conical scanning is a system used in early radar units to improve their accuracy, as well as making it easier to steer the antenna properly to point at a target. Conical scanning is similar in concept to the earlier lobe switching concept used ...
maneuvers to track Earth in its orbit, leaving them on a long "cruise" phase through the outer Solar System. During this period, both spacecraft were repeatedly contacted to obtain various measurements on their
physical environment A biophysical environment is a biotic and abiotic surrounding of an organism or population, and consequently includes the factors that have an influence in their survival, development, and evolution. A biophysical environment can vary in scale ...
, providing valuable information long after their initial missions were complete. Because the spacecraft were flying with almost no additional stabilization thrusts during their "cruise", it is possible to characterize the
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
of the solar medium by its effect on the spacecraft's motion. In the outer Solar System this effect would be easily calculable, based on ground-based measurements of the deep space environment. When these effects were taken into account, along with all other known effects, the calculated position of the Pioneers did not agree with measurements based on timing the return of the radio signals being sent back from the spacecraft. These consistently showed that both spacecraft were closer to the inner Solar System than they should be, by thousands of
kilometre The kilometre ( SI symbol: km; or ), spelt kilometer in American English, is a unit of length in the International System of Units (SI), equal to one thousand metres (kilo- being the SI prefix for ). It is now the measurement unit used for ...
s—small compared to their distance from the Sun, but still statistically significant. This apparent discrepancy grew over time as the measurements were repeated, suggesting that whatever was causing the anomaly was still acting on the spacecraft. As the anomaly was growing, it appeared that the spacecraft were moving more slowly than expected. Measurements of the spacecraft's speed using the
Doppler effect The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who ...
demonstrated the same thing: the observed
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in fr ...
was less than expected, which meant that the Pioneers had slowed down more than expected. When all known forces acting on the spacecraft were taken into consideration, a very small but unexplained force remained. It appeared to cause an approximately constant
sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
ward acceleration of for both spacecraft. If the positions of the spacecraft were predicted one year in advance based on measured velocity and known forces (mostly gravity), they were actually found to be some 400 km closer to the sun at the end of the year. This anomaly is now believed to be accounted for by thermal recoil forces.


Explanation: thermal recoil force

Starting in 1998, there were suggestions that the thermal recoil force was underestimated, and perhaps could account for the entire anomaly. However, accurately accounting for thermal forces was hard, because it needed telemetry records of the spacecraft temperatures and a detailed thermal model, neither of which was available at the time. Furthermore, all thermal models predicted a decrease in the effect with time, which did not appear in the initial analysis. One by one these objections were addressed. Many of the old telemetry records were found, and converted to modern formats.See pp. 10–15 in This gave power consumption figures and some temperatures for parts of the spacecraft. Several groups built detailed thermal models, which could be checked against the known temperatures and powers, and allowed a quantitative calculation of the recoil force. The longer span of navigational records showed the acceleration was in fact decreasing. In July 2012,
Slava Turyshev Slava G. Turyshev (russian: Слава Турышев) is a Russian physicist now working in the US at the NASA Jet Propulsion Laboratory (JPL). He is known for his investigations of the Pioneer anomaly, affecting Pioneer 10 and Pioneer 11 spac ...
''et al.'' published a paper in ''
Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journa ...
'' that explained the anomaly. The work explored the effect of the thermal recoil force on Pioneer 10, and concluded that "once the thermal recoil force is properly accounted for, no anomalous acceleration remains." Although the paper by Turyshev ''et al.'' has the most detailed analysis to date, the explanation based on thermal recoil force has the support of other independent research groups, using a variety of computational techniques. Examples include "thermal recoil pressure is not the cause of the
Rosetta Rosetta or Rashid (; ar, رشيد ' ; french: Rosette  ; cop, ϯⲣⲁϣⲓⲧ ''ti-Rashit'', Ancient Greek: Βολβιτίνη ''Bolbitinē'') is a port city of the Nile Delta, east of Alexandria, in Egypt's Beheira governorate. The R ...
flyby anomaly The flyby anomaly is a discrepancy between current scientific models and the actual increase in speed (i.e. increase in ''kinetic energy'') observed during a planetary flyby (usually of Earth) by a spacecraft. In multiple cases, spacecraft have b ...
but likely resolves the anomalous acceleration observed for ''Pioneer 10''." and "It is shown that the whole anomalous acceleration can be explained by thermal effects".


Indications from other missions

The Pioneers were uniquely suited to discover the effect because they have been flying for long periods of time without additional course corrections. Most deep-space probes launched after the Pioneers either stopped at one of the planets, or used thrusting throughout their mission. The Voyagers flew a mission profile similar to the Pioneers, but were not spin stabilized. Instead, they required frequent firings of their thrusters for
attitude control Attitude control is the process of controlling the orientation of an aerospace vehicle with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, etc. Controlling vehicle ...
to stay aligned with Earth. Spacecraft like the Voyagers acquire small and unpredictable changes in speed as a side effect of the frequent attitude control firings. This 'noise' makes it impractical to measure small accelerations such as the Pioneer effect; accelerations as large as 10−9 m/s2 would be undetectable. Newer spacecraft have used spin stabilization for some or all of their mission, including both ''
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
'' and '' Ulysses''. These spacecraft indicate a similar effect, although for various reasons (such as their relative proximity to the Sun) firm conclusions cannot be drawn from these sources. The '' Cassini'' mission has
reaction wheel A reaction wheel (RW) is used primarily by spacecraft for three-axis attitude control, and does not require rockets or external applicators of torque. They provide a high pointing accuracy, and are particularly useful when the spacecraft must be ...
s as well as thrusters for attitude control, and during cruise could rely for long periods on the reaction wheels alone, thus enabling precision measurements. It also had
radioisotope thermoelectric generators A radioisotope thermoelectric generator (RTG, RITEG), sometimes referred to as a radioisotope power system (RPS), is a type of nuclear battery that uses an array of thermocouples to convert the heat released by the decay of a suitable radioact ...
(RTGs) mounted close to the spacecraft body, radiating kilowatts of heat in hard-to-predict directions. After ''Cassini'' arrived at Saturn, it shed a large fraction of its mass from the fuel used in the insertion burn and the release of the ''Huygens'' probe. This increases the acceleration caused by the radiation forces because they are acting on less mass. This change in acceleration allows the radiation forces to be measured independently of any gravitational acceleration. Comparing cruise and Saturn-orbit results shows that for ''Cassini'', almost all the unmodelled acceleration was due to radiation forces, with only a small residual acceleration, much smaller than the Pioneer acceleration, and with opposite sign.


Potential issues with the thermal solution

There are two features of the anomaly, as originally reported, that are not addressed by the thermal solution: periodic variations in the anomaly, and the onset of the anomaly near the orbit of Saturn. First, the anomaly has an apparent annual periodicity and an apparent Earth sidereal daily periodicity with amplitudes that are formally greater than the error budget. However, the same paper also states this problem is most likely not related to the anomaly: "The annual and diurnal terms are very likely different manifestations of the same modeling problem. ..Such a modeling problem arises when there are errors in any of the parameters of the spacecraft orientation with respect to the chosen reference frame." Second, the value of the anomaly measured over a period during and after the Pioneer 11 Saturn encounter had a relatively high uncertainty and a significantly lower value. The Turyshev, et al. 2012 paper compared the thermal analysis to the ''Pioneer 10'' only. The Pioneer anomaly was unnoticed until after ''Pioneer 10'' passed its Saturn encounter. However, the most recent analysis states: "Figure 2 is strongly suggestive that the previously reported "onset" of the Pioneer anomaly may in fact be a simple result of mis-modeling of the solar thermal contribution; this question may be resolved with further analysis of early trajectory data".


Previously proposed explanations

Before the thermal recoil explanation became accepted, other proposed explanations fell into two classes — "mundane causes" or "new physics". Mundane causes include conventional effects that were overlooked or mis-modeled in the initial analysis, such as measurement error, thrust from gas leakage, or uneven heat radiation. The "new physics" explanations proposed revision of our understanding of
gravitational physics In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
. If the Pioneer anomaly had been a gravitational effect due to some long-range modifications of the known laws of gravity, it did not affect the orbital motions of the major natural bodies in the same way (in particular those moving in the regions in which the Pioneer anomaly manifested itself in its presently known form). Hence a gravitational explanation would need to violate the
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (su ...
, which states that all objects are affected the same way by gravity. It was therefore argued that increasingly accurate measurements and modelling of the motions of the outer planets and their satellites undermined the possibility that the Pioneer anomaly is a phenomenon of gravitational origin. However, others believed that our knowledge of the motions of the outer planets and dwarf planet
Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...
was still insufficient to disprove the gravitational nature of the Pioneer anomaly. The same authors ruled out the existence of a gravitational Pioneer-type extra-acceleration in the outskirts of the
Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
by using a sample of
Trans-Neptunian object A trans-Neptunian object (TNO), also written transneptunian object, is any minor planet in the Solar System that orbits the Sun at a greater average distance than Neptune, which has a semi-major axis of 30.1 astronomical units (au). Typically ...
s. The magnitude of the Pioneer effect a_p () is numerically quite close to the product () of the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
c and the
Hubble constant Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
H_0, hinting at a
cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
connection, but this is now believed to be of no particular significance. In fact the latest
Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a Federally funded research and development centers, federally funded research and development center and NASA field center in the City of La Cañada Flintridge, California, La Cañada Flintridge, California ...
review (2010) undertaken by Turyshev and Toth claims to rule out the cosmological connection by considering rather conventional sources whereas other scientists provided a disproof based on the physical implications of cosmological models themselves. Gravitationally bound objects such as the Solar System, or even the Milky Way, are not supposed to partake of the
expansion of the universe The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not ex ...
—this is known both from conventional theory and by direct measurement. This does not necessarily interfere with paths new physics can take with drag effects from planetary secular accelerations of possible cosmological origin.


Deceleration model

It has been viewed as possible that a real
deceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
is not accounted for in the current model for several reasons.


Gravity

It is possible that deceleration is caused by
gravitational In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
forces from unidentified sources such as the
Kuiper belt The Kuiper belt () is a circumstellar disc in the outer Solar System, extending from the orbit of Neptune at 30 astronomical units (AU) to approximately 50 AU from the Sun. It is similar to the asteroid belt, but is far larger—20 tim ...
or
dark matter Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ...
. However, this acceleration does not show up in the orbits of the outer planets, so any generic gravitational answer would need to violate the
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (su ...
(see modified inertia below). Likewise, the anomaly does not appear in the orbits of Neptune's moons, challenging the possibility that the Pioneer anomaly may be an unconventional gravitational phenomenon based on range from the Sun.


Drag

The cause could be drag from the
interplanetary medium The interplanetary medium (IPM) or interplanetary space consists of the mass and energy which fills the Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding ...
, including
dust Dust is made of fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian process), volcanic eruptions, and pollution. Dust in ...
,
solar wind The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sol ...
and
cosmic rays Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our ...
. However, the measured densities are too small to cause the effect.


Gas leaks

Gas leaks, including
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
from the spacecraft's
radioisotope thermoelectric generator A radioisotope thermoelectric generator (RTG, RITEG), sometimes referred to as a radioisotope power system (RPS), is a type of nuclear battery that uses an array of thermocouples to convert the heat released by the decay of a suitable radioa ...
s (RTGs) have been thought as possible cause.


Observational or recording errors

The possibility of observational errors, which include measurement and computational errors, has been advanced as a reason for interpreting the data as an anomaly. Hence, this would result in approximation and statistical errors. However, further analysis has determined that significant errors are not likely because seven independent analyses have shown the existence of the Pioneer anomaly as of March 2010. The effect is so small that it could be a statistical anomaly caused by differences in the way data were collected over the lifetime of the probes. Numerous changes were made over this period, including changes in the receiving instruments, reception sites, data recording systems and recording formats.


New physics

Because the "Pioneer anomaly" does not show up as an effect on the planets, Anderson ''et al.'' speculated that this would be interesting if this was ''new physics''. Later, with the Doppler shifted signal confirmed, the team again speculated that one explanation may lie with new physics, if not some unknown systemic explanation.


Clock acceleration

Clock acceleration was an alternate explanation to anomalous acceleration of the spacecraft towards the Sun. This theory took notice of an
expanding universe The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
, which was thought to create an ''increasing'' background 'gravitational potential'. The increased gravitational potential would then accelerate cosmological time. It was proposed that this particular effect causes the observed deviation from predicted trajectories and velocities of
Pioneer 10 ''Pioneer 10'' (originally designated Pioneer F) is an American space probe, launched in 1972 and weighing , that completed the first mission to the planet Jupiter. Thereafter, ''Pioneer 10'' became the first of five artificial objects to ac ...
and
Pioneer 11 ''Pioneer 11'' (also known as ''Pioneer G'') is a robotic space probe launched by NASA on April 5, 1973, to study the asteroid belt, the environment around Jupiter and Saturn, solar winds, and cosmic rays. It was the first probe to encoun ...
. From their data, Anderson's team deduced a steady frequency drift of 1.5 Hz over eight years. This could be mapped on to a clock acceleration theory, which meant all clocks would be changing in relation to a constant acceleration: in other words, that there would be a non-uniformity of time. Moreover, for such a distortion related to time, Anderson's team reviewed several models in which time distortion as a phenomenon is considered. They arrived at the "clock acceleration" model after completion of the review. Although the best model adds a quadratic term to defined
International Atomic Time International Atomic Time (abbreviated TAI, from its French name ) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 ato ...
, the team encountered problems with this theory. This then led to ''non-uniform time in relation to a constant acceleration'' as the most likely theory.''non-uniform time in relation to a constant acceleration'' is a summarized term derived from the source or sources used for this sub-section.


Definition of gravity modified

The
Modified Newtonian dynamics Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaini ...
or MOND
hypothesis A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obse ...
proposed that the force of gravity deviates from the traditional Newtonian value to a very different force law at very low accelerations on the order of 10−10 m/s2. Given the low accelerations placed on the spacecraft while in the outer Solar System, MOND may be in effect, modifying the normal gravitational equations. The Lunar Laser Ranging experiment combined with data of
LAGEOS LAGEOS, Laser Geodynamics Satellite or Laser Geometric Environmental Observation Survey, are a series of two scientific research satellites designed to provide an orbiting laser ranging benchmark for geodynamical studies of the Earth. Each satel ...
satellites refutes that simple gravity modification is the cause of the Pioneer anomaly. The precession of the longitudes of perihelia of the solar planets or the trajectories of long-period comets have not been reported to experience an anomalous gravitational field toward the Sun of the magnitude capable of describing the Pioneer anomaly.


Definition of inertia modified

MOND Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining ...
can also be interpreted as a modification of inertia, perhaps due to an interaction with
vacuum energy Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum. The effects of vacuum energy can be experimental ...
, and such a trajectory-dependent theory could account for the different accelerations apparently acting on the orbiting planets and the Pioneer craft on their escape trajectories. A possible terrestrial test for evidence of a different model of modified inertia has also been proposed.


Parametric time

Another theoretical explanation was based on a possible non-equivalence of the atomic time and the astronomical time, which could give the same observational fingerprint as the anomaly.


Celestial ephemerides in an expanding universe

A rather straightforward explanation of Pioneer anomaly can be achieved if one takes into account that the background spacetime is described by cosmological
Friedmann–Lemaître–Robertson–Walker metric The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
that is not Minkowski flat. In this model of spacetime manifold, light moves uniformly with respect to the conformal cosmological time whereas physical measurements are performed with the help of atomic clocks that count the
proper time In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval ...
of observer coinciding with the
cosmic time Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at ...
. The difference between the conformal and cosmic times yields exactly the same numerical value and signature of the anomalous, blue Doppler shift effect that was measured in the Pioneer experiment. A small discrepancy between this theoretical prediction and the measured value of the Pioneer effect is a clear evidence of the presence of the thermal recoil that accounts up only to 10–20 percent of the overall effect. If the origin of the Pioneer effect is cosmological, it gives a direct access to measuring the numerical value of the
Hubble constant Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
independently of observations of the
cosmic microwave background radiation In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space ...
or supernova explosions in distant galaxies ( Supernova Cosmology Project).


Further research avenues

It is possible, but not proven, that this anomaly is linked to the
flyby anomaly The flyby anomaly is a discrepancy between current scientific models and the actual increase in speed (i.e. increase in ''kinetic energy'') observed during a planetary flyby (usually of Earth) by a spacecraft. In multiple cases, spacecraft have b ...
, which has been observed in other spacecraft. Although the circumstances are very different (planet flyby vs. deep space cruise), the overall effect is similar—a small but unexplained velocity change is observed on top of a much larger conventional gravitational acceleration. The Pioneer spacecraft are no longer providing new data (the last contact was on 23 January 2003) and ''
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
'' and '' Cassini'' were deliberately disposed of in the atmospheres of Jupiter and Saturn respectively at the ends of their missions. So far, attempts to use data from current missions have not yielded any conclusive results. There are several remaining options for further research: * Further analysis of the retrieved Pioneer data. This includes not only the data that was first used to detect the anomaly, but additional data that until recently was saved only in older, inaccessible computer formats and media. This data was recovered in 2006, converted to more modern formats, and is now available for analysis. * The ''
New Horizons ''New Horizons'' is an interplanetary space probe that was launched as a part of NASA's New Frontiers program. Engineered by the Johns Hopkins University Applied Physics Laboratory (APL) and the Southwest Research Institute (SwRI), with a ...
'' spacecraft to Pluto is spin-stabilised for much of its cruise, and there is a possibility that it can be used to investigate the anomaly. ''New Horizons'' may have the same problem that precluded good data from the ''Cassini'' mission—its RTG is mounted close to the spacecraft body, so thermal radiation from it, bouncing off the spacecraft, may produce a systematic thrust of a not-easily predicted magnitude, several times as large as the Pioneer effect. Nevertheless, efforts are underway to study the non-gravimetric accelerations on the spacecraft, in the hopes of having them well modeled for the long cruise to Pluto after the Jupiter fly-by that occurred in February 2007. In particular, despite any large systematic bias from the RTG, the 'onset' of the anomaly at or near the orbit of Saturn might be observed. * A dedicated mission has also been proposed. Such a mission would probably need to surpass 200  AU from the Sun in a hyperbolic escape orbit. * Observations of
asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...
s around 20 AU may provide insights if the anomaly's cause is gravitational.


Meetings and conferences about the anomaly

A meeting was held at the
University of Bremen The University of Bremen (German: ''Universität Bremen'') is a public university in Bremen, Germany, with approximately 23,500 people from 115 countries. It is one of 11 institutions which were successful in the category "Institutional Strategi ...
in 2004 to discuss the Pioneer anomaly. The Pioneer Explorer Collaboration was formed to study the Pioneer Anomaly and has hosted three meetings (2005, 2007, and 2008) at International Space Science Institute in
Bern german: Berner(in)french: Bernois(e) it, bernese , neighboring_municipalities = Bremgarten bei Bern, Frauenkappelen, Ittigen, Kirchlindach, Köniz, Mühleberg, Muri bei Bern, Neuenegg, Ostermundigen, Wohlen bei Bern, Zollikofen , website ...
, Switzerland, to discuss the anomaly, and discuss possible means for resolving the source.


Notes


See also

*
Flyby anomaly The flyby anomaly is a discrepancy between current scientific models and the actual increase in speed (i.e. increase in ''kinetic energy'') observed during a planetary flyby (usually of Earth) by a spacecraft. In multiple cases, spacecraft have b ...


References


Further reading

* : The original paper describing the anomaly * :A lengthy survey of several years of debate by the authors of the original 1998 paper documenting the anomaly. The authors conclude, "Until more is known, we must admit that the most likely cause of this effect is an unknown systematic. (We ourselves are divided as to whether 'gas leaks' or 'heat' is this 'most likely cause.')" The ISSI meeting above has an excellen
reference list
divided into sections such as primary references, attempts at explanation, proposals for new physics, possible new missions, popular press, and so on. A sampling of these are shown here: * Theory establishes a gravitational connection between the unexplained periastron advance observed in two binary star systems and the Pioneer anomaly. * * * : Further elaboration on a dedicated mission plan (restricted access) * * * ;Popular press * * * * * – STVG ( Scalar-tensor-vector gravity) theory claims to predict Pioneer anomaly * * *


External links


Shows number of publications about the Pioneer anomaly on arXiv.org, by year.
* * {{DEFAULTSORT:Pioneer Anomaly Pioneer program Astrodynamics