论文标题
通过流动媒体的时间和频率传输的相对论理论，并应用于地球的大气
Relativistic theory for time and frequency transfer through flowing media with an application to the atmosphere of Earth
论文作者
论文摘要
计划在不久的将来使用几个将在地球轨道卫星上使用原子时钟的空间任务，例如太空中的原子钟集合（ACE）或ISS上的空间光钟（I-SOC）。发达的时钟和将它们与地面站连接起来的链接的越来越多的精度对通过地球大气以及相关时间和频率传递校正的电磁信号传播理论模型施加了相应的精度要求。我们开发了一个相对论的模型和双向时间和频率传递。除了重力效应外，它还还包括相对论框架内大气折射率和大气流的影响。该模型基于空间中填充介质的光线运动方程的分析解：Gordon光学度量的无效测量方程。使用重力电势，折射率和风速，对单向和频率传递的明确公式进行校正，并考虑到非平稳性和与球形对称性的偏差。提供了数值示例，这些示例专注于双向地面到健康转移，其卫星参数类似于ISS的参数。随着卫星位置从天顶移动到地平线，大气折射率的影响增加，并且表明效果的范围从0 ps到5 ps，对于双向时间传输，从$ 10^{ - 17} $到$ 10^{ - 13} $，用于双向频率传输。对于正常大气条件的双向时间转移，风贡献的效果远低于1 ps，但是对于双向频率转移，效果可能很重要：对于水平风场的贡献是$ 10^{ - 17} $，其速度幅度约为11 m/s。
Several space missions that will use atomic clocks on board of an Earth-orbiting satellite are planned for the near future, such as the Atomic Clock Ensemble in Space (ACES) or the Space Optical Clock on the ISS (I-SOC). The increasing accuracies of the developed clocks and of the links connecting them with ground stations impose corresponding accuracy requirements for theoretical models of electromagnetic signal propagation through the atmosphere of Earth and for the related time and frequency transfer corrections. We develop a relativistic model of one- and two-way time and frequency transfer. In addition to the gravitational effects, it also includes the effects of atmospheric refractivity and atmospheric flows within the relativistic framework. The model is based on an analytical solution of the equation of motion of a light ray in spacetime filled with a medium: the null geodesic equation of Gordon's optical metric. Explicit formulas for one- and two-way time and frequency transfer corrections are given using realistic fields of the gravitational potential, the refractive index, and the wind speed, taking nonstationarity and deviations from spherical symmetry into account. Numerical examples are provided that focus on two-way ground-to-satellite transfer, with satellite parameters similar to those of the ISS. The effect of the atmospheric refractive index increases as the satellite position moves from zenith to horizon, and it is shown that the effect ranges from 0 ps to 5 ps for two-way time transfer and from $10^{-17}$ to $10^{-13}$ for two-way frequency transfer. The effect of the wind contribution is well below 1 ps for the two-way time transfer for normal atmospheric conditions, but for the two-way frequency transfer, the effect can be significant: A contribution of $10^{-17}$ is possible for a horizontal wind field with a velocity magnitude of about 11 m/s.
