火星任务中星上原时τ与TCG的相对论变换

Relativistic Transformation between the Proper Time τ and TCG for Mars Missions

爱因斯坦的广义相对论已成为当今深空探测任务中一部分,为此将在研究环火星探测器星载钟原时τ与地球质心坐标时(TCG)的变换中应用相对论变换关系,将τ与地球相关联的局部时间尺度联系起来,从而扩展了之前关于τ与太阳系质心坐标时(TCB)相对论变换的工作(TCB是应用于整个太阳系的全局坐标时)。研究发现τ和TCG的差在经历一年的时间后可达到0.2s量级。为了区分相对论变换中各种效应的贡献,用数值方法计算了太阳、八大行星、三个大质量小行星以及探测器的贡献。发现在精确到1μs量级下,相对论变换必须包括太阳、金星、月球、火星、木星、土星的引力影响以及探测器和地球的速度影响。

Considering the fact that the general theory of relativity has become a part of deep space missions,we investigate the relativistic transformation between the proper time of an onboard clockτand the geocentric coordinate time（TCG）for Mars missions.By connectingτ with this local timescale associated with the Earth,we extend previous works which focus on the transformation betweenτand the barycentric coordinate time（TCB）.（TCB is the global coordinate time for the whole solar system.）For practical convenience,the relation betweenτand TCG is recast to directly depend on quantities which can be read from ephemerides.We find that the difference betweenτand TCG can reach the level of about 0∶2seconds in a year.To distinguish various sources in the transformation,we numerically calculate the contributions caused by the Sun,eight planets,three large asteroids and the spacecraft.It is found that if the threshold of 1microsecond is adopted,this transformation must include effects due to the Sun,Venus,the Moon,Mars,Jupiter,Saturn and the velocities of the spacecraft and Earth.