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火星任务中星上原时τ与TCG的相对论变换
潘军洋1, 谢懿1,2,3
1.南京大学天文与空间科学学院, 南京 210093;2.上海市空间导航与定位技术重点实验室, 上海 200030;3.南京大学现代天文与天体物理教育部重点实验室, 南京 210093
摘要:
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0.2 s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1 μs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。
关键词:  参考系;时间;数值方法;空间探测器
DOI:10.15982/j.issn.2095-7777.2015.01.010
分类号:
基金项目:国家自然科学基金资助项目(J1210039);上海市空间导航与定位技术重点实验室基金(14DZ2276100)
Relativistic Transformation between the Proper Time τ and TCG for Mars Missions
PAN Junyang1, XIE Yi1,2,3
1.Department of Astronomy, Nanjing University, Nanjing 210093, China;2.Shanghai Key Laboratory of Space Navigation and Position Techniques, Shanghai 200030, China;3.Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education, Nanjing 210093, China
Abstract:
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 clock τ and the geocentric coordinate time (TCG) for Mars missions. By connecting τ with this local timescale associated with the Earth, we extend previous works which focus on the transformation between τ and the barycentric coordinate time (TCB). (TCB is the global coordinate time for the whole solar system.) For practical convenience, the relation between τ and TCG is recast to directly depend on quantities which can be read from ephemerides. We find that the difference between τ and TCG can reach the level of about 0:2 seconds 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 1 microsecond 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.
Key words:  reference systems;time;numerical method;space vehicles