Relativistic effects in high-accuracy dynamical modelling of asteroid orbits

该项目的目的是详细研究小行星运动中的相对论n体效应。这项研究的动机是不断提高对小行星的观测精度。在十年内，精度有望达到几毫弧秒的水平。由于来自太阳球对称引力场的轨道效应（史瓦西效应）是众所周知的，因此研究将集中在太阳和主要行星共同影响所产生的后史瓦西效应上。初步研究表明，在某些情况下，后史瓦西效应可能在设想的精度上变得重要。研究将从对后史瓦西项大小的详细数值研究开始。相关后史瓦西效应的起源将通过打开和关闭相对论力的各个部分来经验地发现。然后，我们将检验后牛顿限制三体问题作为一个相对简单的分析模型是否可以解释小行星轨道运动中最大的后史瓦西效应。该项目的第二部分致力于研究利用高精度小行星观测来检验强等效原理的可能性。Nordtvedt（1968）以现象学的方式提出的这一观点以前从未被严格地研究过。我们建议在参数为（和）的PPN形式框架下，从小行星在n个物体引力场中的后牛顿运动方程开始。从变分方程中计算轨道位置相对于Nordtvedt参数（）的偏导数，我们将模拟轨道确定的过程，并以这种方式获得（）的精度估计，例如，从盖亚观测中可以预期

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