The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary
The study investigates the collinear positions and stability in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary for Luhman 16 and HD188753 systems. Our study has established four collinear equilibrium points (L1,2,3,6) which are greatly affected...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-03-01
|
| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023009155 |
| _version_ | 1827972710599229440 |
|---|---|
| author | Jagadish Singh Richard K. Tyokyaa |
| author_facet | Jagadish Singh Richard K. Tyokyaa |
| author_sort | Jagadish Singh |
| collection | DOAJ |
| description | The study investigates the collinear positions and stability in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary for Luhman 16 and HD188753 systems. Our study has established four collinear equilibrium points (L1,2,3,6) which are greatly affected by the parameters under review. The collinear position L1 move away and closer as the parameters increase and decrease respectively. For the collinear positions L2andL3, we witnessed a uniform space movement away from the origin in the negative direction while L6 seems to be moving closer to the origin from the negative part of the origin. We observed changes in the movements of the collinear positions (L1,2,3,6) as a result of the half distance between the mass dipoles and the oblateness of the primary for the problem under review. The movements away and closer to the origin from collinear positions do not change the status of the collinear points as they remain unstable and unchanged. It is also found that as the half distance between mass dipoles and oblateness of the primary increase, the region of stability of the collinear positions decreases for the aforementioned binary systems. The collinear equilibrium point (L3) is stable for the characteristic roots (λ1,2) for Luhman 16 system. This is evidenced by at least one characteristic root, a positive real part and a complex root. The stability of collinear points in most cases are unstable for the stated binary systems in Lyapunov. |
| first_indexed | 2024-04-09T19:25:45Z |
| format | Article |
| id | doaj.art-98695bbfb4be4c7d837ffa2e16e78020 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-09T19:25:45Z |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-98695bbfb4be4c7d837ffa2e16e780202023-04-05T08:15:52ZengElsevierHeliyon2405-84402023-03-0193e13708The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondaryJagadish Singh0Richard K. Tyokyaa1Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, NigeriaDepartment of Mathematical Sciences, Faculty of Physical Sciences, Federal University Dutsin-Ma, Katsina, Nigeria; Corresponding author.The study investigates the collinear positions and stability in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary for Luhman 16 and HD188753 systems. Our study has established four collinear equilibrium points (L1,2,3,6) which are greatly affected by the parameters under review. The collinear position L1 move away and closer as the parameters increase and decrease respectively. For the collinear positions L2andL3, we witnessed a uniform space movement away from the origin in the negative direction while L6 seems to be moving closer to the origin from the negative part of the origin. We observed changes in the movements of the collinear positions (L1,2,3,6) as a result of the half distance between the mass dipoles and the oblateness of the primary for the problem under review. The movements away and closer to the origin from collinear positions do not change the status of the collinear points as they remain unstable and unchanged. It is also found that as the half distance between mass dipoles and oblateness of the primary increase, the region of stability of the collinear positions decreases for the aforementioned binary systems. The collinear equilibrium point (L3) is stable for the characteristic roots (λ1,2) for Luhman 16 system. This is evidenced by at least one characteristic root, a positive real part and a complex root. The stability of collinear points in most cases are unstable for the stated binary systems in Lyapunov.http://www.sciencedirect.com/science/article/pii/S2405844023009155OblatenessPositionsStabilityDipole mass and elliptic restricted synchronous three-body problem |
| spellingShingle | Jagadish Singh Richard K. Tyokyaa The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary Heliyon Oblateness Positions Stability Dipole mass and elliptic restricted synchronous three-body problem |
| title | The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary |
| title_full | The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary |
| title_fullStr | The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary |
| title_full_unstemmed | The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary |
| title_short | The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary |
| title_sort | collinear equilibrium points in the elliptic restricted synchronous three body problem under an oblate primary and a dipole secondary |
| topic | Oblateness Positions Stability Dipole mass and elliptic restricted synchronous three-body problem |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023009155 |
| work_keys_str_mv | AT jagadishsingh thecollinearequilibriumpointsintheellipticrestrictedsynchronousthreebodyproblemunderanoblateprimaryandadipolesecondary AT richardktyokyaa thecollinearequilibriumpointsintheellipticrestrictedsynchronousthreebodyproblemunderanoblateprimaryandadipolesecondary AT jagadishsingh collinearequilibriumpointsintheellipticrestrictedsynchronousthreebodyproblemunderanoblateprimaryandadipolesecondary AT richardktyokyaa collinearequilibriumpointsintheellipticrestrictedsynchronousthreebodyproblemunderanoblateprimaryandadipolesecondary |