Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbits
This paper introduces a different approach to obtain the exact solution of the relative equations of motion of a deputy (follower) satellite with respect to a chief (leader) satellite that both rotate about central body (Earth) in elliptic orbits by using Laplace transformation. Moreover, the paper...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2017-10-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.21042/AMNS.2017.2.00032 |
| _version_ | 1811272152279678976 |
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| author | El-Shaboury S. M. Ammar M.K. Yousef W.M. |
| author_facet | El-Shaboury S. M. Ammar M.K. Yousef W.M. |
| author_sort | El-Shaboury S. M. |
| collection | DOAJ |
| description | This paper introduces a different approach to obtain the exact solution of the relative equations of motion of a deputy (follower) satellite with respect to a chief (leader) satellite that both rotate about central body (Earth) in elliptic orbits by using Laplace transformation. Moreover, the paper will take the perturbation due to the oblateness of the Earth into consideration and simulate this problem with numerical example showing the effect of the perturbation on the Keplerian motion. The solution of such equations in this work is represented in terms of the eccentricity of the chief orbit and its true anomaly as the independent variable. |
| first_indexed | 2024-04-12T22:35:08Z |
| format | Article |
| id | doaj.art-9c8e1ebeb6c3452a8f86d4c585935af1 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-04-12T22:35:08Z |
| publishDate | 2017-10-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-9c8e1ebeb6c3452a8f86d4c585935af12022-12-22T03:13:52ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562017-10-012240341410.21042/AMNS.2017.2.00032Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbitsEl-Shaboury S. M.0Ammar M.K.1Yousef W.M.2Mathematics Dept. Faculty of Science, Ain Shams University, Cairo, EgyptMathematics Dept. Faculty of Science, Helwan University, Cairo, EgyptBasic Science Dept. Canadian International College for Engineering, Cairo, EgyptThis paper introduces a different approach to obtain the exact solution of the relative equations of motion of a deputy (follower) satellite with respect to a chief (leader) satellite that both rotate about central body (Earth) in elliptic orbits by using Laplace transformation. Moreover, the paper will take the perturbation due to the oblateness of the Earth into consideration and simulate this problem with numerical example showing the effect of the perturbation on the Keplerian motion. The solution of such equations in this work is represented in terms of the eccentricity of the chief orbit and its true anomaly as the independent variable.https://doi.org/10.21042/AMNS.2017.2.00032relative motion of two satellitestschauner hempel equationsj2 perturbationlaplace transformation37n0570f15 |
| spellingShingle | El-Shaboury S. M. Ammar M.K. Yousef W.M. Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbits Applied Mathematics and Nonlinear Sciences relative motion of two satellites tschauner hempel equations j2 perturbation laplace transformation 37n05 70f15 |
| title | Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbits |
| title_full | Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbits |
| title_fullStr | Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbits |
| title_full_unstemmed | Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbits |
| title_short | Analytical solutions of the relative orbital motion in unperturbed and in J2 - perturbed elliptic orbits |
| title_sort | analytical solutions of the relative orbital motion in unperturbed and in j2 perturbed elliptic orbits |
| topic | relative motion of two satellites tschauner hempel equations j2 perturbation laplace transformation 37n05 70f15 |
| url | https://doi.org/10.21042/AMNS.2017.2.00032 |
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