Stability of libration points in the restricted four-body problem with variable mass

作者：Mittal Amit^*; Aggarwal Rajiv; Suraj Md Sanam; Bisht Virender Singh

来源：Astrophysics and Space Science, 2016, 361(10): 329.

DOI：10.1007/s10509-016-2901-2

• Restricted four-body problem
• Variable mass
• Libration points
• Zero velocity surfaces

We have investigated the stability of the Lagrangian solutions for the restricted four-body problem with variable mass. It has been assumed that the three primaries with masses m(1), m(2) and m(3) form an equilateral triangle, wherein m(2) = m(3). According to Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), the infinitesimal body varies its mass m with time. The space-time transformations of Meshcherskii (Studies on the Mechanics of Bodies of Variable Mass, GITTL, Moscow, 1949) are used by taking the values of the parameters q = 1/2, k = 0, n = 1. The equations of motion of the infinitesimal body with variable mass have been determined. The equations of motion of the current problem differ from the ones of the restricted four-body problem with constant mass. There exist eight libration points, out of which two are collinear with the primary m1 and the rest are non-collinear for a fixed value of parameters gamma (m at time t/m at initial time, 0 < gamma <= 1), alpha (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0 <= alpha <= 2.2) and mu = 0.019 (the mass parameter). All the libration points are found to be unstable. The zero velocity surfaces (ZVS) are also drawn and regions of motion are discussed.

• 出版日期2016-10