Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential
We study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of α and λ on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where α∈...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4072418 |
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| author | M. Javed Idrisi Teklehaimanot Eshetie Tenaw Tilahun Mitiku Kerebh |
| author_facet | M. Javed Idrisi Teklehaimanot Eshetie Tenaw Tilahun Mitiku Kerebh |
| author_sort | M. Javed Idrisi |
| collection | DOAJ |
| description | We study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of α and λ on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where α∈−1,1 is the coupling constant of Yukawa force to gravitational force, and λ∈0,∞ is the range of Yukawa force. It is observed that as λ⟶∞, the mean-motion of the primaries n⟶1+α1/2 and as λ⟶0, n⟶1. Further, it is observed that the mean-motion is unity, i.e., n=1 for α=0, n>1 if α>0 and n<1 when α<0. The triangular equilibria are not affected by α and λ and remain the same as in the classical case of restricted three-body problem. But, α and λ affect the stability of these triangular equilibria in linear sense. It is found that the triangular equilibria are stable for a critical mass parameter μc=μ0+fα,λ, where μ0=0.0385209⋯ is the value of critical mass parameter in the classical case of restricted three-body problem. It is also observed that μc=μ0 either for α=0 or λ=0.618034, and the critical mass parameter μc possesses maximum (μcmax) and minimum (μcmin) values in the intervals −1<α<0 and 0<α<1, respectively, for λ=1/3. |
| format | Article |
| id | doaj-art-68d6afde6a2c4e1e82d1d0c643da88d0 |
| institution | OA Journals |
| issn | 1687-0042 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-68d6afde6a2c4e1e82d1d0c643da88d02025-08-20T02:35:25ZengWileyJournal of Applied Mathematics1687-00422022-01-01202210.1155/2022/4072418Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian PotentialM. Javed Idrisi0Teklehaimanot Eshetie1Tenaw Tilahun2Mitiku Kerebh3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsWe study the triangular equilibrium points in the framework of Yukawa correction to Newtonian potential in the circular restricted three-body problem. The effects of α and λ on the mean-motion of the primaries and on the existence and stability of triangular equilibrium points are analyzed, where α∈−1,1 is the coupling constant of Yukawa force to gravitational force, and λ∈0,∞ is the range of Yukawa force. It is observed that as λ⟶∞, the mean-motion of the primaries n⟶1+α1/2 and as λ⟶0, n⟶1. Further, it is observed that the mean-motion is unity, i.e., n=1 for α=0, n>1 if α>0 and n<1 when α<0. The triangular equilibria are not affected by α and λ and remain the same as in the classical case of restricted three-body problem. But, α and λ affect the stability of these triangular equilibria in linear sense. It is found that the triangular equilibria are stable for a critical mass parameter μc=μ0+fα,λ, where μ0=0.0385209⋯ is the value of critical mass parameter in the classical case of restricted three-body problem. It is also observed that μc=μ0 either for α=0 or λ=0.618034, and the critical mass parameter μc possesses maximum (μcmax) and minimum (μcmin) values in the intervals −1<α<0 and 0<α<1, respectively, for λ=1/3.http://dx.doi.org/10.1155/2022/4072418 |
| spellingShingle | M. Javed Idrisi Teklehaimanot Eshetie Tenaw Tilahun Mitiku Kerebh Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential Journal of Applied Mathematics |
| title | Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential |
| title_full | Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential |
| title_fullStr | Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential |
| title_full_unstemmed | Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential |
| title_short | Triangular Equilibria in R3BP under the Consideration of Yukawa Correction to Newtonian Potential |
| title_sort | triangular equilibria in r3bp under the consideration of yukawa correction to newtonian potential |
| url | http://dx.doi.org/10.1155/2022/4072418 |
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