Stability and regions of motion in the restricted three-body problem when both the primaries are finite straight segments

作者：Jain Ruchika^*; Sinha Deepa

来源：Astrophysics and Space Science, 2014, 351(1): 87-100.

DOI：10.1007/s10509-013-1698-5

• Restricted three-body problem
• Equilibrium points
• Stability
• Straight segments
• Regions of motion
• Asteroid

In this paper we have studied the locations and stability of the Lagrangian equilibrium points in the restricted three-body problem under the assumption that both the primaries are finite straight segments. We have found that the triangular equilibrium points are conditional stable for 0 <mu <mu (c) , and unstable in the range mu (c) <mu a parts per thousand currency sign1/2, where mu is the mass ratio. The critical mass ratio mu (c) depends on the lengths of the segments and it is observed that the range of mu (c) increases when compared with the classical case. The collinear equilibrium points are unstable for all values of mu. We have also studied the regions of motion of the infinitesimal mass. It has been observed that the Jacobian constant decreases when compared with the classical restricted three-body problem for a fixed value of mu and lengths l (1) and l (2) of the segments. Beside this we have found the numerical values for the position of the collinear and triangular equilibrium points in the case of some asteroids systems: (i) 216 Kleopatra-951 Gaspara, (ii) 9 Metis-433 Eros, (iii) 22 Kalliope-243 Ida and checked the linear stability of stationary solutions of these asteroids systems.

• 出版日期2014-5