Celestial reference frames and the gauge freedom in the post-Newtonian mechanics of the Earth–Moon system
Celestial reference frames and the gauge freedom in the post-Newtonian mechanics of the Earth–Moon system
复制标题
DOI：
10.1007/s10569-010-9303-5
复制
发表时间：
2010-09
影响因子：
1.6
通讯作者：
Sergei M Kopeikin;Yi Xie
中科院分区：
文献类型：
--
作者：
Sergei M Kopeikin;Yi Xie
我们介绍了地月系统相对论天体力学高级理论分析所采用的雅可比坐标。理论推导采用了国际天文学联合会（IAU）于2000年通过的相对论参考系分辨率。该分辨率假设太阳系是孤立的，时空在无穷远处渐近平坦，并且主参考系覆盖整个时空，其原点位于太阳系质心（SSB），空间轴延伸至无穷远。 SSB 参考系不相对于一组遥远的类星体旋转，这些类星体被假定静止在天空上，形成国际天体参考系 (ICRF)。第二个参考系的原点位于地月质心（EMB）。 EMB 框架是局部惯性的，并且在相对于 EMB 框架移动的测试粒子的运动方程不包含科里奥利力和向心力的意义上来说不是动态旋转。另外两个局部坐标系——地心坐标系和硒心坐标系——分别起源于地球和月球的质心，并且不动态旋转。每个局部坐标系由于彼此之间的相对运动而受到相对于其他局部坐标系和 ICRF 的大地进动的影响。动态非旋转局部框架的理论优势在于对月球相对于地球的度量张量和相对运动方程的更简单的数学描述。通过应用 IAU 决议建议的相对论进动矩阵，每个局部坐标系在与 ICRF 轴对齐后都可以转换为运动学非旋转坐标系。引入一组由一个全局框架和三个局部框架组成的集合，以便将重力的物理效应与月球相对于地球的相对运动方程中的规范相关效应分离。
We introduce the Jacobi coordinates adopted to the advanced theoretical analysis of the relativistic Celestial Mechanics of the Earth–Moon system. Theoretical derivation utilizes the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. The resolutions assume that the Solar System is isolated and space-time is asymptotically flat at infinity and the primary reference frame covers the entire space-time, has its origin at the Solar System barycenter (SSB) with spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are assumed to be at rest on the sky forming the International Celestial Reference Frame (ICRF). The second reference frame has its origin at the Earth–Moon barycenter (EMB). The EMB frame is locally inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames—geocentric and selenocentric—have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description of the metric tensor and relative equations of motion of the Moon with respect to Earth. Each local frame can be converted to kinematically non-rotating one after alignment with the axes of ICRF by applying the matrix of the relativistic precession as recommended by the IAU resolutions. The set of one global and three local frames is introduced in order to decouple physical effects of gravity from the gauge-dependent effects in the equations of relative motion of the Moon with respect to Earth.