Relativistic effects in high-accuracy dynamical modelling of asteroid orbits

• Applicant: Professor Dr. Sergei Klioner
• Subject Area: Astrophysics and Astronomy
• Term: from 2008 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 80749842

The aim of the project is to investigate in detail the relativistic N-body effects in the motion of asteroids. The motivation for this study is the ongoing increase of the observational accuracy for asteroids. Within a decade the accuracy is expected to attain the level of a few milliarcseconds. Since the orbital effects coming from the spherically symmetric gravitational field of the Sun (Schwarzschild effects) are well known, the investigation will be focused on the post-Schwarzschild effects resulting from the combined influence of the Sun and major planets. A preliminary study has demonstrated that the post-Schwarzschild effects may, in some circumstances, become important at the envisaged accuracy. The investigation will start with a detailed numerical investigation of the magnitude of the post-Schwarzschild terms. The origin of the relevant post-Schwarzschild effects will be found empirically by switching various parts of the relativistic force on and off. We will then check if the post-Newtonian restricted three-body problem as a relatively simple analytical model can explain the largest post-Schwarzschild effects in the orbital motion of asteroids.The second part of the project is devoted to the investigation of the possibility to test the Strong Equivalence Principle using high-accuracy observations of asteroids. This idea suggested by Nordtvedt (1968) in a phenomenological way has never been investigated before rigorously. We suggest to start from the post-Newtonian equations of motion of an asteroid in the gravitational field of N-bodies in the framework of the PPN formalism with parameters ( and (. Computing the partial derivatives of the orbital position with respect to the Nordtvedt parameter ( from the variational equations we will simulate the process of orbit determination and obtain in this way an estimate of the accuracy for ( that can be expected from, e.g., Gaia observations

• DFG Programme: Research Grants
• Participating Person: Professor Dr. Michael H. Soffel