Non-linear stability of L 4 in the restricted problem when the primaries are finite straight segments under resonances
- Resource Type
- Authors
- Ruchika Jain; Deepa Sinha
- Source
- Astrophysics and Space Science. 353:73-88
- Subject
- Physics
Range (mathematics)
Fourth order
Classical mechanics
Space and Planetary Science
Mathematical analysis
Resonance
Lagrangian point
Astronomy and Astrophysics
Stability (probability)
Non linear stability
Celestial mechanics
Cosmology
- Language
- ISSN
- 1572-946X
0004-640X
The non-linear stability of L 4 in the restricted three-body problem when both primaries are finite straight segments in the presence of third and fourth order resonances has been investigated. Markeev’s theorem (Markeev in Libration Points in Celestial Mechanics and Astrodynamics, 1978) is used to examine the non-linear stability for the resonance cases 2:1 and 3:1. It is found that the non-linear stability of L 4 depends on the lengths of the segments in both resonance cases. It is also found that the range of stability increases when compared with the classical restricted problem. The results have been applied in the following asteroids systems: (i) 216 Kleopatra–951 Gaspara, (ii) 9 Metis–433 Eros, (iii) 22 Kalliope–243 Ida.