A new correction method for quasi-Keplerian orbits  

作　　者：Yue Chen Da-Zhu Ma Fang Xia 

机构地区：[1]Purple Mountain Observatory,Chinese Academy of Sciences,Nanjing 210033,China [2]School of Astronomy and Space Science,University of Science and Technology of China,Hefei 230026,China [3]School of Information and Engineering,Hubei Minzu University,Enshi 445000,China

出　　处：《Research in Astronomy and Astrophysics》2020年第11期191-204,共14页天文和天体物理学研究（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.11703005,11533004,11178006,11673071,11263003 , 11273066).

摘　　要：A pure two-body problem has seven integrals including the Kepler energy,the Laplace vector and the angular momentum vector.However,only five of them are independent.When the five independent integrals are preserved,the two other dependent integrals are naturally preserved from a theoretical viewpoint;but they may not necessarily be from a numerical computational viewpoint.Because of this,we use seven scale factors to adjust the integrated positions and velocities so that the adjusted solutions strictly satisfy the seven constraints.Noticing the existence of the two dependent integrals,we adopt the Newton iterative method combined with singular value decomposition to calculate these factors.This correction scheme can be applied to perturbed two-body and N-body problems in the solar system.In this case,the seven quantities associated with each planet slowly vary with time.More accurate values can be given to the seven slowly-varying quantities by integrating the integral invariant relations of these quantities and the equations of motion.They should be satisfied with the adjusted solutions.Numerical tests show that the new method can significantly reduce the rapid growth of numerical errors for all orbital elements.

关 键 词：Computational methods Computational astronomy planets and satellites DYNAMICAL 

分 类 号：P135[天文地球—天体力学]