GRACE后续任务的广义相对论性laser干涉观测值
General relativistic laser interferometric observables of the GRACE-Follow-On mission
摘要：
我们开发了一个高精度的激光测距干涉（LRI）观测的GRACE后续（GRACE-FO）任务的模型。为此，我们在广义相对论的后牛顿近似下，研究了电磁波在扩展体附近的引力场中的传播。我们提出了一个广义相对论模型的平面波的相位，占所有的多极的引力体，它的角动量的贡献，以及由外部源产生的潮汐场的贡献。我们开发了一种新的方法来模拟相干信号传输的引力场的太阳系，依赖于相对论处理的相位。我们使用这种方法来描述高精度的干涉测量的GRACE-FO和制定的关键LRI观测值，即相位和相位速率的相干激光链路之间的两个航天器。我们为两个GRACE-FO航天器之间的LRI启用范围开发了一个相对论模型，精确到小于1 nm，并为相应的范围速率开发了一个高精度模型，精确到优于0.1 nm/s。我们还制定了高精度的相对论模型的双单向范围（DOWR）和DOWR启用的距离率观测值最初用于GRACE和现在研究的GRACE-FO干涉测量。我们的公式证明了GRACE-FO任务设计背后的基本假设，并强调了GRACE-FO航天器实现近圆形和几乎相同轨道的重要性。
英文摘要：
We develop a high-precision model for laser ranging interferometric (LRI) observables of the GRACE Follow-On (GRACE-FO) mission. For this, we study the propagation of an electromagnetic wave in the gravitational field in the vicinity of an extended body, in the post-Newtonian approximation of the general theory of relativity. We present a general relativistic model for the phase of a plane wave that accounts for contributions of all the multipoles of the gravitating body, its angular momentum, as well as the contribution of tidal fields produced by external sources. We develop a new approach to model a coherent signal transmission in the gravitational field of the solar system that relies on a relativistic treatment of the phase. We use this approach to describe high-precision interferometric measurements on GRACE-FO and formulate the key LRI observables, namely the phase and phase rate of a coherent laser link between the two spacecraft. We develop a relativistic model for the LRI-enabled range between the two GRACE-FO spacecraft, accurate to less than 1 nm, and a high-precision model for the corresponding range rate, accurate to better than 0.1 nm/s. We also formulate high-precision relativistic models for the double one-way range (DOWR) and DOWR-enabled range rate observables originally used on GRACE and now studied for interferometric measurements on GRACE-FO. Our formulation justifies the basic assumptions behind the design of the GRACE-FO mission and highlights the importance of achieving nearly circular and nearly identical orbits for the GRACE-FO spacecraft.
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