* Astronomy

In April 2008, Slava Turyshev used tracking and telemetry data from one hundred different measurements on the Pioneer 11 spacecraft, including the varied temperatures within the spacecraft caused by the different metals and materials used to build the spacecraft.
The spacecraft is made with such materials as Teflon, aluminium, Mylar, aluminium-based paints, Kapton. The plutonium, which provides power for the spacecraft, also generates heat.
The team found that Pioneer 11 gives off more heat in certain directions than it does in other directions. The varied rates of heat emissions on the spacecraft are large enough to force the spacecraft off of its nominal trajectory.

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Anomalies spotted in spacecraft flight
Could a mystery force be altering their course?
The speed and direction of some spacecraft are being mysteriously altered as they pass near the Earth. This unexplained velocity shift hints that there is either something missing from current models used for space navigation, or, possibly, something missing from our understanding of physics.
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The Pioneer anomaly or Pioneer effect is the observed deviation from expectations of the trajectories of various unmanned spacecraft visiting the outer solar system, notably Pioneer 10 and Pioneer 11.

Source

Title: Jupiter, Saturn and the Pioneer anomaly: a planetary-based independent test
Authors: Lorenzo Iorio

In this paper we use the ratio of the corrections to the standard Newtonian/Einsteinian secular precessions of the longitudes of perihelia of Jupiter and Saturn, recently estimated by the Russian astronomer E.V. Pitjeva by fitting almost one century of data with the EPM ephemerides, to make an independent, planetary-based test of the hypothesis that the Pioneer anomaly (PA), as it is presently known in the 5-10 AU region, is of gravitational origin. Accounting for the errors in the determined apsidal extra-rates and in the values of the PA acceleration at the orbits of Jupiter and Saturn the answer is negative. If and when the re-analysis of the entire Pioneer 10/11 will be completed more firm conclusions could be reached. Moreover, it would also be important that other teams of astronomers estimate independently their own corrections to the perihelion precessions.

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Ed ~ It should be said that current MOND theories are now considered unlikely by most scientists.

Title: Pioneer anomaly: the velocity vector orientation and a drift in the proper time
Authors: Vikram H. Zaveri
(Version v2)

A relativistic theory is proposed to explain the anomalous accelerations of Pioneer 10/11, Galileo and Ulysses spacecrafts. The theory points out at the limitations of the weak field approximation and proposes a drift in the proper time of the spacecraft outside the framework of general relativity. In this theory the proper time of a body is associated with the gravitational frequency shift of the constituent fundamental particles of the body. The frequency shift changes the energy level of the body which gets reflected in its motion. This change in energy level causes the time like geodesics to deviate from that of the standard theoretical models. We introduce proper time in the line element of a metric theory according to a fixed set of rules laid down by general relativity for introducing deviation in the flat Minkowski metric. The frequency shift for bodies of different composition traversing different trajectories however, is not the same and this gets reflected in its motion as an unmodelled anomalous effect. This association of proper time with the gravitational frequency shift of the body requires the flat Minkowski metric to deviate in different ways for different two body systems. This solves the problem of anomalous acceleration in a very simple way. Gravitational redshift of light, bending of light and perihelic precession of planets are within the permissible limits. Another independent proposal involving angle between the heliocentric radial vector and the tangential velocity vector is discussed. This yields a component of acceleration which is of the same order of magnitude as that of the Pioneer anomaly but has a large variation over distances.

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