Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid
The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here ob...
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| Format: | Article |
| Language: | English |
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Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University
2014-05-01
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| Series: | Bibechana |
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| Online Access: | https://www.nepjol.info/index.php/BIBECHANA/article/view/10395 |
| _version_ | 1797194005987983360 |
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| author | RR Thapa |
| author_facet | RR Thapa |
| author_sort | RR Thapa |
| collection | DOAJ |
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The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable τ = ηt. For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m3 has been calculated.
DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10395
BIBECHANA 11(1) (2014) 149-156
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| first_indexed | 2024-04-24T05:49:25Z |
| format | Article |
| id | doaj.art-b9da9d4f4f2d446980370fd4660c67d4 |
| institution | Directory Open Access Journal |
| issn | 2091-0762 2382-5340 |
| language | English |
| last_indexed | 2024-04-24T05:49:25Z |
| publishDate | 2014-05-01 |
| publisher | Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University |
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| series | Bibechana |
| spelling | doaj.art-b9da9d4f4f2d446980370fd4660c67d42024-04-23T13:05:41ZengDepartment of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan UniversityBibechana2091-07622382-53402014-05-011110.3126/bibechana.v11i0.10395Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroidRR Thapa0Department of Mathematics, Post Graduate Campus, Biratnagar Tribhuvan University The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable τ = ηt. For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m3 has been calculated. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10395 BIBECHANA 11(1) (2014) 149-156 https://www.nepjol.info/index.php/BIBECHANA/article/view/10395Characteristic equationNon-trivial solutionOblate spheroidSitnikov's restricted three body problemStability |
| spellingShingle | RR Thapa Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid Bibechana Characteristic equation Non-trivial solution Oblate spheroid Sitnikov's restricted three body problem Stability |
| title | Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid |
| title_full | Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid |
| title_fullStr | Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid |
| title_full_unstemmed | Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid |
| title_short | Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid |
| title_sort | stability of the sitnikov s circular restricted three body problem when the primaries are oblate spheroid |
| topic | Characteristic equation Non-trivial solution Oblate spheroid Sitnikov's restricted three body problem Stability |
| url | https://www.nepjol.info/index.php/BIBECHANA/article/view/10395 |
| work_keys_str_mv | AT rrthapa stabilityofthesitnikovscircularrestrictedthreebodyproblemwhentheprimariesareoblatespheroid |