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。这项研究的动机是小行星观测精度的不断提高。在十年内，精度有望达到几毫角秒的水平。由于来自太阳的球对称引力场的轨道效应(Schwarzschild效应)是众所周知的，因此研究的重点将是由太阳和主行星的共同影响产生的后Schwarzschild效应。一项初步研究表明，在某些情况下，后施瓦茨柴尔德效应可能会以设想的准确性变得重要。调查将首先对后施瓦茨柴尔德时代的条款的规模进行详细的数字调查。相关的后Schwarzschild效应的起源将通过切换相对论作用力的各个部分来经验地找到。然后，我们将检验后牛顿限制性三体问题作为一个相对简单的分析模型是否能够解释小行星轨道运动中最大的后Schwarzschild效应。项目的第二部分致力于利用小行星的高精度观测来检验强等价原理的可能性。诺德特维特(1968)以现象学的方式提出的这一观点以前从未被严格研究过。我们建议从小行星在N体引力场中的后牛顿运动方程出发，在带参数的PPN形式的框架内(和(.计算轨道位置相对于诺德特韦特参数的偏导数(从变分方程我们将模拟轨道确定的过程，并以这种方式获得(可以从例如Gaia观测预期的)精度的估计

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