X射线脉冲星自主导航的光子到达时间转换

Transformation of Photon Time of Arrival in XNAV

根据广义相对论的后牛顿近似时空理论,在忽略太阳系天体自转和扁率的情况下,详细推导出X射线脉冲星自主导航中,光子到达观测航天器和太阳系质心的时间差值,它是对现行公式的修正.导出了质心坐标时与航天器固有时的变换关系,根据这一关系,建议在脉冲星导航的工程设计中可以仿照GPS,将航天器携带时钟作频率调整,从而有利于工程计算.

The navigating method for XNAV （X-ray pulsar-based Navigation） is similar the one of the Differential GPS （DGPS）. In order to position and navigate the spacecraft （or satellite）, the two Time of Arrival （TOA） from one X-ray pulsar to both the spacecraft and the solar system barycenter are demanded respectively. The difference between the two TOA is generally called the transformation equation of time. But the existent transformation equation of time is not good enough. In this paper, improvements have been made on some current expressions. The time difference between photon arrival at the observation spacecraft and solar system barycenter in XNAV is presented. It is based on the post-Newtonian approximation spacetime theory in GTR and the neglection of celestial bodies spin of the solar system as well as the effect of eccentric orbit. These considerations are reasonable under the condition that the precision of measure time magnitude is in the order of the nanosecond. The transformation of the proper time from observation spacecraft to BCT （Barycentric Coordinate Time） is also obtained. Based on this relation, a proposal is presented that the frequency of clock at spacecraft can be adjusted in the same way as GPS.