High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem
Terms in the analytic expansion of the doubly averaged disturbing function for the circular restricted three-body problem using the Legendre polynomial are explicitly calculated up to the fourteenth order of semimajor axis ratio (α) between perturbed and perturbing bodies in the inner case (α<1),...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Advances in Astronomy |
| Online Access: | http://dx.doi.org/10.1155/2016/8945090 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555872972177408 |
|---|---|
| author | Takashi Ito |
| author_facet | Takashi Ito |
| author_sort | Takashi Ito |
| collection | DOAJ |
| description | Terms in the analytic expansion of the doubly averaged disturbing function for the circular restricted three-body problem using the Legendre polynomial are explicitly calculated up to the fourteenth order of semimajor axis ratio (α) between perturbed and perturbing bodies in the inner case (α<1), and up to the fifteenth order in the outer case (α>1). The expansion outcome is compared with results from numerical quadrature on an equipotential surface. Comparison with direct numerical integration of equations of motion is also presented. Overall, the high-order analytic expansion of the doubly averaged disturbing function yields a result that agrees well with the numerical quadrature and with the numerical integration. Local extremums of the doubly averaged disturbing function are quantitatively reproduced by the high-order analytic expansion even when α is large. Although the analytic expansion is not applicable in some circumstances such as when orbits of perturbed and perturbing bodies cross or when strong mean motion resonance is at work, our expansion result will be useful for analytically understanding the long-term dynamical behavior of perturbed bodies in circular restricted three-body systems. |
| format | Article |
| id | doaj-art-9d9f5f1c680d41d29232903f41e27abc |
| institution | Kabale University |
| issn | 1687-7969 1687-7977 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Astronomy |
| spelling | doaj-art-9d9f5f1c680d41d29232903f41e27abc2025-02-03T05:47:03ZengWileyAdvances in Astronomy1687-79691687-79772016-01-01201610.1155/2016/89450908945090High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body ProblemTakashi Ito0National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, JapanTerms in the analytic expansion of the doubly averaged disturbing function for the circular restricted three-body problem using the Legendre polynomial are explicitly calculated up to the fourteenth order of semimajor axis ratio (α) between perturbed and perturbing bodies in the inner case (α<1), and up to the fifteenth order in the outer case (α>1). The expansion outcome is compared with results from numerical quadrature on an equipotential surface. Comparison with direct numerical integration of equations of motion is also presented. Overall, the high-order analytic expansion of the doubly averaged disturbing function yields a result that agrees well with the numerical quadrature and with the numerical integration. Local extremums of the doubly averaged disturbing function are quantitatively reproduced by the high-order analytic expansion even when α is large. Although the analytic expansion is not applicable in some circumstances such as when orbits of perturbed and perturbing bodies cross or when strong mean motion resonance is at work, our expansion result will be useful for analytically understanding the long-term dynamical behavior of perturbed bodies in circular restricted three-body systems.http://dx.doi.org/10.1155/2016/8945090 |
| spellingShingle | Takashi Ito High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem Advances in Astronomy |
| title | High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem |
| title_full | High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem |
| title_fullStr | High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem |
| title_full_unstemmed | High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem |
| title_short | High-Order Analytic Expansion of Disturbing Function for Doubly Averaged Circular Restricted Three-Body Problem |
| title_sort | high order analytic expansion of disturbing function for doubly averaged circular restricted three body problem |
| url | http://dx.doi.org/10.1155/2016/8945090 |
| work_keys_str_mv | AT takashiito highorderanalyticexpansionofdisturbingfunctionfordoublyaveragedcircularrestrictedthreebodyproblem |