TWO MORE SOLUTIONS OF NON-COLLINEAR LIBRATION POINTS IN A PLANAR RESTRICTED THREE-BODY PROBLEM WHEN LESS MASSIVE PRIMARY IS AN OBLATE SPHEROID

Abstract

In this paper the stability of non-collinear libration points in circular restricted three-body problem has been analyzed considering less massive primary as an oblate spheroid. We have considered two cases to find out the location and stability of non-collinear libration points. In case I, it is observed that there exist infinite numbers of non-collinear libration points on the unit circle centered at oblate body and out of these libration points only those lying in the interval  57˚ ≤ ψ ≤ 60˚ are stable for different values of critical mass parameter µ_c, where ψ is the angle between m₃, m₂ and m₁ in the same plane. In case II, the non-collinear libration points exist only in the interval 0˚ ≤ φ ≤ 140˚ are stable for different values of critical mass parameter µ_c, during the analysis we got a collinear libration point which is stable for µ_c ≤ 0.127284… .

Key Words: Celestial Mechanics, Restricted three-body problem, Libration points, Linear stability.