Out of plane equilibrium points locations and the forbidden movement regions in the restricted three-body problem with variable mass
- 161 Downloads
This work aims to present an analytical study on the dynamics of a third body in the restricted three-body problem. We study this model in the context of the third body having variable-mass changes according to Jeans’ law. The equation of motion is constructed when the variation of the mass is non-isotropic. We find an appropriate approximation for the locations of the out-of-plane equilibrium points in the special case of a non-isotropic variation of the mass. Moreover, some graphical investigations are shown for the effects of the parameters which characterize the variable mass on the locations of the out-of-plane equilibrium points, the regions of possible and forbidden motions of the third body. This model has many applications, especially in the dynamics behavior of small objects such as cosmic dust and grains. It also has interesting applications for artificial satellites, future space colonization or even vehicles and spacecraft parking.
KeywordsRestricted three-body problem Variable mass Out of plane equilibrium points
This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (857-71-D1435). The authors, therefore, acknowledge with thanks DSR technical and financial support.
- Bekov, A.A., Mukhametkalieva, R.K.: On the stability of coplanar libration points of the restricted three-body problem of variable mass. Problems of celestial mechanics and stellar dynamics pp. 12–18 (1990) Google Scholar
- Khanna, M., Bhatnagar, K.B.: Existence and stability of libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid. Indian J. Pure Appl. Math. 7, 721–733 (1999) Google Scholar
- Meshcherskii, I.V.: Studies on the Mechanics of Bodies of Variable Mass. GITTL, Moscow (1949) Google Scholar
- Meshcherskii, I.V.: Works on the Mechanics of Bodies of Variable Mass. GITTL, Moscow (1952) Google Scholar