超90%的近地空间目标在近圆轨道上,其余为椭圆轨道。近圆轨道的初轨确定已有许多针对性方法,这些方法在应用于大偏心率光学短弧初轨确定时,往往出现无解或错误解的问题。而无论近圆或椭圆轨道,距离搜索法和Gooding方法都可以产生一个待选解集合。分析表明,对于近圆和椭圆轨道,待选解的半长轴和偏心率的二维分布显著不同。根据这一特征,本文提出了一种针对光学短弧初轨确定的初始轨道偏心率判定方法。实验结果表明,该方法可以准确判定轨道类型为近圆或椭圆,并能估计较精确的偏心率范围,可基本解决了距离搜索法和Gooding方法等在应用于大偏心率轨道无解或错解问题,显著增加了距离搜索法和Gooding方法等初轨确定方法的轨道普适性。
Over 90% of near-Earth resident space objects are on near-circular orbits,others are on elliptical orbits.There are a number of initial orbit determination(IOD)methods designed for near-circular orbits.However,when these methods are applied to high eccentricity orbits,the problem of no solution or inaccurate solution will occur often.On the other hand,applying the range search method or the Gooding method to short-arc angular data will yield a set of IOD solutions.Notably,the semi-major axis(SMA)and eccentricity distributions of such IOD solutions are significantly different for the near-circular and elliptical orbits.Thus,we propose a novel method for determining the orbital eccentricity estimated from short-arc angular data.Experimental results demonstrate that the proposed method can accurately discern whether the orbit is a near-circular or an elliptical one,while also provides a more precise estimate of the eccentricity.Importantly,this method effectively addresses the issue of no solution or inaccurate solution encountered by the range search method and the Gooding method when applied to high elliptical orbits.Consequently,it enhances the applicability of these IOD methods.
[1] LAPLACE P S.Memoires de l'Academie royale des sciences de paris[M].Collected Works,1780.
[2] GAUSS C F.Theory of the motion of the heavenly bodies moving about the sun in conic sections:A translation of gauss's“ Theoria Motus.”with an appendix[M].Little,Brown,1857.
[3] ESCOBAL P.Methods of orbit determination[M].Methods of orbit determination,1970.
[4] GOODING R H.A procedure for the solution of Lambert's orbital boundary-value problem[J].Celestial Mechanics and Dynamical Astronomy,1990,48(2):145-165.
[5] GOODING R H.A new procedure for orbit determination based on three lines of sight(angles only)[R].DEFENCE RESEARCH AGENCY FARNBOROUGH(UNITED KINGDOM),1993.
[6] GOODING R H.A new procedure for the solution of the classical problem of minimal orbit determination from three lines of sight[J].Celestial Mechanics and Dynamical Astronomy,1996,66(4):387-423.
[7] VALLADO D A.Evaluating Gooding angles-only orbit determination of space based space surveillance measurements[J].Paper Usr,2010,10:1-21.
[8] 张郑元.Gooding甚短弧初轨确定方法的改进技术研究[D].武汉大学,2021.
[9] HENDERSON T A,MORTARI D,DAVIS J.Modifi-cations to the Gooding algorithm for angles-only initial orbit determination[C].AAS/AIAA Space Flight Mechanics Meeting.2010.
[10] 章品,桑吉章,潘腾,等.应用距离搜索的低轨空间碎片初始轨道确定方法[J].航天器工程,2017a,26(2):22-28.
[11] 张郑元,桑吉章,陈俊宇.神经网络在甚短弧初轨确定问题中的应用[J].测绘地理信息,2022,47(6):16-19.