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Analytical solution of the geodesic equation in Kerr--de Sitter space--times

Generalizing our results of the complete analytic solutions of the geodesic equation in Schwarzschild--de Sitter space--time (Phys. Rev. Lett. 100, 171101 (2008) and Phys. Rev. D 78, 024035 (2008)) we here present the complete analytical solution of the geodesic equation in Kerr--de Sitter space--times. Starting with the Hamilton-Jacobi equations we separate the equations of motion. We disuss the effective potential for the $r$-- and the $\theta$--motion which characterizes the shape of the orbits. Using the method of hyperelliptic integrals restricted to the theta--divisor and employing hyperelliptic integrals of first and third kind we can represent the complete set of solutions in terms of Kleinian sigma and related functions.

Thermal rediation and the Pioneer anomaly

The disturbance acceleration resulting from thermal recoil forces for the Pioneer 11 spacecraft is presented. An analytical test case including the main power sources (RTGs) and the main reflective surface (high gain antenna) is formulated and processed. The results show that for a precise computation of the effect the reflecting and absorbing surface geometries have to be modeled in detail and that the effect of thermal recoil forces cannot be neglected on the level of the Pioneer anomaly (PA). The limitations of the method are discussed and the need for new improved modeling techniques for a complete assessment of the problem is underlined.

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