基于广义相对论的轨道摄动卫星皮秒计时与时间比对研究

General relativistic theory for picosecond coordinate timing and time comparison of satellites under orbit perturbations

新一代空间科学任务,如空间站光学原子钟计划、广域量子通信、精细结构常数测量、引力红移测量及深空探测等,提出了皮秒量级的时间比对要求,需要基于广义相对论建立更加准确的卫星坐标时计时与时间比对模型.本文从地心非旋转坐标系(geocentric celestial reference system,GCRS)的广义相对论度规张量出发,建立了广义相对论下卫星轨道方程.在此基础上,考虑轨道摄动的影响,建立卫星坐标时计时及时间比对模型.考虑轨道摄动影响的时间比对模型,为星间长时间皮秒量级时频传递提供理论支持.首先以地球静止轨道卫星为研究对象,仿真分析了轨道方程中相对论项对卫星轨道的影响,然后仿真分析了轨道摄动引起的卫星坐标时计时误差以及星间时间比对误差.静止轨道卫星研究结果表明,轨道方程中相对论项对卫星速度的影响在μm/s量级,对位置的影响随时间累计增大,在1万秒达到3.46 mm(11.53 ps);轨道摄动引起的坐标时计时误差在1万秒达到15.36 ps;轨道摄动引起的星间时间比对时相对论项误差在1万秒达到56.69 ps.一般轨道卫星仿真结果表明,在地球主引力场范围内,轨道摄动引起的坐标时计时误差以及时间比对误差随轨道高度增加而逐渐减小.

Time comparison in picoseconds has been proposed for various space-based scientific missions,such as atomic clock ensemble in space,measurement of fine-structure constants,gravitational redshift measurement,deep space exploration,and large-scale quantum communication.It is necessary to establish more accurate coordinate-timing and time-comparison models of satellites based on general relativity.In this study,we developed an orbit dynamics model of satellites based on the metric tensor.Considering the effect of orbit perturbations,we developed coordinate-timing and time-caparison models with higher accuracy.The developed timecaparison model provides theoretical support for picosecond time comparison among satellites with longer time.Further,we simulated geostationary satellites,and the results indicate that the effect of the general relativity term on the satellite velocity is in the order ofμm/s.The effect of the general relativity term on the satellite position increases with time,reaching 3.46 mm(11.53 ps)at10000 s.The coordinate-timing and time-comparison errors resulting from the orbit perturbations reach 15.36 and 56.69 ps,respectively,at 10000 s.The simulation results of general orbits show that the coordinate-timing and time-comparison errors are lower at higher orbits in the vicinity of Earth.