利用重力卫星任务检验相对论性引力理论初步研究

Relativistic experiments played an important part in the developments of relativistic gravitational theories. Through the measurements of inter-satellite ranges or relative accelerations between free falling proof masses or spacecrafts, satellite gravity missions are able to recover in details the Earth gravity field.Today,the well-test measurement principles are satellite-to-satellite trackings whose resolutions or accuracies in the measurements of Earth geopotentials had already reached or even above the level of post-Newtonian fields, therefore in this project we suggest that high precision satellite gravity missions (including the future planned ones) can be employed to test modern relativistic gravitational theories and be established as the new platform for relativistic gravitational experiments in space. In this project, we plan to derive, within the parameterized post-Newtonian framework, the relativistic equation describing the relative motions between orbiting satellites or adjacent test masses, which can be viewed as a relativistic extension of the classic Clohessy-Wiltshire equations. Since it has already been noticed that the relativistic gravitational effects in missions like GRACE and LAGEOS can not be ignored, our extended equations will contribute to the theoretical foundations of the future planned high precision gravity missions, relativistic geodesy and.related relativistic experiments in space. Through analytic and numerical method, the characteristic signal in the modern and active alternative theories of gravitation will be studied. New tests and constraints on such theories based on the real data from the GRACE and GOCE missions will be obtained. For the future planned GRACE Follow On and GRACE II missions, the related pre-studies on their abilities in testing relativistic gravitational theories will also be carried out.

相对论性实验检验在引力理论的发展过程中起着关键作用。当前重力卫星的测量精度已经达到甚至超越后牛顿相对论性效应的量级，因此高精度重力卫星任务除了可以反演地球重力场之外，还可以应用于相对论性实验检验。本项目研究内容包括：（1）在参数化后牛顿的框架下，推导航天器编队飞行的中Clohessy-Wiltshire（CW）方程的广义相对论性推广。该方程可用于未来精密空间基础科学实验、相对论性大地测量和高精度重力卫星任务。（2）针对相对论性引力理论,推导卫卫跟踪和梯度测量两种测量方式下的相对论性特征信号，并给出利用重力卫星任务的测量数据检验相对论性引力理论的具体方案。

相对论实验在相对论引力理论的发展中发挥了重要作用。通过测量卫星间的距离或自由落体质量或航天器之间的相对加速度，卫星重力任务能够反演地球重力场。目前基于卫星跟踪卫星测量技术的的重力卫星任务，对地球重力场的测量精度已经达到甚至超过了后牛顿场的水平，因此本项目尝试采用高精度的卫星引力任务来检验相对论性参数，建立空间相对论引力实验的新平台。在参数化的后牛顿框架内，推导出了描述轨道卫星或相邻测试质量之间相对运动的相对论方程，并给出该方程的解析解。该方程可视为航天器编队飞行的中Clohessy-Wiltshire（CW）方程的广义相对论性推广，可用于未来精密空间基础科学实验、相对论性大地测量和高精度重力卫星任务。此外，通过分析和数值方法，本项目研究了星间测距信号中的广义相对论特征信号，完成了广义相对论在卫卫跟踪任务中的相对论性特征信号分析，基于能量法实现了的相对论性重力场和相对论参数联合反演。针对仿真数据给出相对论参数Gamma的反演值为0.99999821，相对误差为10^-6，相对论性参数beta的反演值为1.00001653，相对误差为10^-5。项目完成了利用GRACE实际数据反演分析。此外，本项目还将数据预处理、单星能量法反演地球重力场程序包应用到空间Taiji-1任务中，完成Taiji-1卫星载荷数据预处理、重力场反演工作，获得首个国内自主的重力场模型。