ORBITAL PERTURBATION DIFFERENTIAL EQUATIONS WITH NON‐LINEAR CORRECTIONS FOR CHAMP‐LIKE SATELLITE

IF 1.6 4区 地球科学 Q3 GEOCHEMISTRY & GEOPHYSICS
Yuan Jin-hai, Zhu Yong-chao, Meng Xiang-chao
{"title":"ORBITAL PERTURBATION DIFFERENTIAL EQUATIONS WITH NON‐LINEAR CORRECTIONS FOR CHAMP‐LIKE SATELLITE","authors":"Yuan Jin-hai, Zhu Yong-chao, Meng Xiang-chao","doi":"10.1002/CJG2.30046","DOIUrl":null,"url":null,"abstract":"Directly from the second order differential equations of satellite motion, the linearized orbital perturbation differential equations for CHAMP-like satellites are derived after introducing the reference orbit, and then introducing the omitted terms into the linearized orbital perturbation differential equations, the orbital perturbation differential equations with nonlinear corrections are derived. The accuracies for the orbital perturbation differential equations are estimated and the following results are obtained: if the measurement errors of the satellite positions and the non-gravitational accelerations are less than 3 cm and 3 × 10−10 m·s−2 respectively, the linearized orbital perturbation differential equations and the equations with nonlinear corrections can hold the accuracies 3 × 10−10 m·s−2 only when ρ ≤ 4.7 m and ρ ≤ 4.14 × 103 m respectively, where ρ is the distance between the satellite orbit and the reference one. Hence, compared with the linearized orbital perturbation differential equations, the equations with nonlinear corrections are suitable to establish normal system of equations of the gravity field's spherical harmonic coefficients in long time span. The solving method for the orbital perturbation differential equations is also given with the help of the superposition principle in the paper. At last, some imitation examples for CHAMP and GRACE missions are computed, and the results illustrate that the orbital perturbation differential equations with nonlinear corrections have higher accuracies than the linearized ones.","PeriodicalId":55257,"journal":{"name":"地球物理学报","volume":"60 1","pages":"286-299"},"PeriodicalIF":1.6000,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CJG2.30046","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"地球物理学报","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1002/CJG2.30046","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 1

Abstract

Directly from the second order differential equations of satellite motion, the linearized orbital perturbation differential equations for CHAMP-like satellites are derived after introducing the reference orbit, and then introducing the omitted terms into the linearized orbital perturbation differential equations, the orbital perturbation differential equations with nonlinear corrections are derived. The accuracies for the orbital perturbation differential equations are estimated and the following results are obtained: if the measurement errors of the satellite positions and the non-gravitational accelerations are less than 3 cm and 3 × 10−10 m·s−2 respectively, the linearized orbital perturbation differential equations and the equations with nonlinear corrections can hold the accuracies 3 × 10−10 m·s−2 only when ρ ≤ 4.7 m and ρ ≤ 4.14 × 103 m respectively, where ρ is the distance between the satellite orbit and the reference one. Hence, compared with the linearized orbital perturbation differential equations, the equations with nonlinear corrections are suitable to establish normal system of equations of the gravity field's spherical harmonic coefficients in long time span. The solving method for the orbital perturbation differential equations is also given with the help of the superposition principle in the paper. At last, some imitation examples for CHAMP and GRACE missions are computed, and the results illustrate that the orbital perturbation differential equations with nonlinear corrections have higher accuracies than the linearized ones.
类CHAMP卫星的轨道摄动非线性校正微分方程
直接从卫星运动的二阶微分方程出发,在引入参考轨道后,导出了类CHAMP卫星的线性化轨道摄动微分方程,然后将省略的项引入线性化轨道微扰微分方程中,导出了带非线性修正的轨道摄动微分方程。对轨道摄动微分方程的精度进行了估计,得到了以下结果:如果卫星位置和非重力加速度的测量误差分别小于3cm和3×,线性化的轨道摄动微分方程和具有非线性校正的方程只有在ρ≤4.7m和ρ≤4.14×103m时才能分别保持3×10−10m·s−2的精度,其中ρ是卫星轨道与参考轨道之间的距离。因此,与线性化的轨道摄动微分方程相比,具有非线性修正的方程组适用于建立长时间跨度内重力场球谐系数的正规方程组。本文还利用叠加原理给出了轨道摄动微分方程的求解方法。最后,计算了CHAMP和GRACE任务的一些仿真实例,结果表明,具有非线性校正的轨道扰动微分方程比线性化的轨道扰动方程具有更高的精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
地球物理学报
地球物理学报 地学-地球化学与地球物理
CiteScore
3.40
自引率
28.60%
发文量
9449
审稿时长
7.5 months
期刊介绍:
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信