Se p 20 09 A possible scenario of the Pioneer anomaly in the framework of Finsler geometry

The weak field approximation of geodesics in Randers-Finsler space is investigated. We show that a Finsler structure of Randers space corresponds to the constant and sunward anomalous acceleration demonstrated by the Pioneer 10 and 11 data. The additional term in the geodesic equation acts as “electric force”, which provides the anomalous acceleration. PACS numbers: 02.40.-k, 04.50.Kd, 95.10.Ce [email protected] [email protected] 1 Newton’s theory of gravitation was proposed almost three hundred and fifty years ago. Einstein’s general relativity reveals the intrinsic geometric property of gravity. Newton’s theory of gravitation is the main guideline of the celestial mechanics, especially for the solar system. General relativity provides small corrections. It is wellknown that the Newton and Einstein’s theory of gravitation still faces problems. One of them is that the flat rotation curves of spiral galaxies violate the prediction of Newton and Einstein’s gravity. Another is related with recent astronomical observations[1]. Our universe is acceleratedly expanding. This result can not be obtained directly from Einstein’s gravity and his cosmological principle. In fact, new puzzle has also arisen in the solar system. That is the Pioneer anomaly. The Pioneer spacecrafts are excellent tools for dynamical astronomy studies in the solar system. The radio metric data from the Pioneer 10/11 spacecraft indicate the presence of a small, anomalous, Doppler frequency drift over the range of 20–70 astronomical units[2]. The drift is blue-shift, uniformly changing with a rate of 6 × 10Hz/s[3]. It has revealed an anomalous constant sunward acceleration, aP = (8.74± 1.33)× 10 m/s. The Pioneer data have been studied in three different navigational computer programs. Namely: the JPL’s Orbit Determination Program (ODP), the Aerospace Corporation’s CHASPM code extended for deep space navigation[2], and a code written in the Goddard Space Flight Center[4]. These data analysis all confirm the existence of anomalous acceleration with the following basic properties: the direction of the anomalous acceleration of the spacecraft towards the Sun, the anomalous acceleration