Other
Scientific paper
Apr 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008acasn..49..198s&link_type=abstract
Acta Astronomica Sinica, vol. 49, no. 2, p. 198-206
Other
3
Celestial Mechanics: Relativity
Scientific paper
X-ray signals from celestial sources, such as stars and pulsars, may be used as navigation beacons for satellites and deep space probes. XNAV is the abbreviation of the X-ray Source-based Navigation for Autonomous Position Determination. The basic measurement principle in XNAV is based on the distance between the observer and the X-ray pulsar. Theoretically, if an observer receives simultaneously the X-ray pulse signals from three pulsars and computes the propagation time intervals of their X-ray pulses, then the spatial position of the observer can be determined. The general relativistic effects existing in XNAV are resulted from the bending of light and gravitational delay. Because the magnitude of GMs / c3~10- 5s is larger than that of the measurement error in XNAV, so the high order effects due to the bending of light and gravitation delay must be considered. The general relativistic effects in XNAV are discussed in detail by using the Post-Newtonian approximate method of the DSX scheme in the paper. First, the bending of light and the gravitational time delay, which is mainly due to the action of the Solar gravitational field, are discussed under the 1PN metric. The discussion is limited in plane motion. The standard differential equation of the light curve path is obtained. Although the equation is different slightly from the rigid solution under Schwarzschild metric,both the deflected angles of light solved under the two different metrics are the same. It is also obtained that the gravitational time delay due to the bending of light and its coordinate speed smaller than light speed under the 1PN metric. Second, the gravitational time delay under the 2PN metrics of the DSX scheme are calculated, and a quadratic equation about dt is considered. Only the term of O(c- 5) is remained. The many factors are considered, which includes not only the Newtonian gravitational action of the Sun and Earth as well as other celestial bodies, but also the quadrupole moment (shape factor) effect of the Sun and Earth and correction due to the Solar spin (angular moment) as well as the contribution of the mass square of the Sunand Earth. Lastly, the high accuracy time equation of light propagation in XNAV is obtained. In fact, the measurement equation of XNAV we obtained is basically same as that of the millisecond pulsar timing measurement, and also same as Ref.[12]. The methods of the post-Newtonian approximate metric in this paper and the parameter-post-Newtonian approximate metric in the Ref.[12] are different.
Fei Bao-Jun
Ji Cheng-Xiang
Sun Wei-Jin
Xiao Yong
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