First order stability test of equilibrium points in the planar elliptic restricted four body problem with radiating primaries

Abstract

• Formulation of the planar elliptic restricted four body problems with radiating all primaries. • Existence and computation analysis of equilibrium points. • First order stability test for the equilibrium points. • Significant observations. This paper presents a rigorous analysis of existence of equilibrium points and corresponding their first order stability test in the planar elliptic restricted four body problem under the influence of radiation pressure forces due to radiating primaries. In the presence of radiation pressure of the radiating primaries, a considerable variations in position co-ordinates of the equilibrium points and in their stability ranges have seen. Also, the existence of equilibrium points with respect to the values of eccentricity e and true anomaly f in their respective ranges have analysed and it is found that number of equilibrium points reduces with the increasing value of eccentricity within the range 0 < e < 1 , whereas a random variation is seen in case of true anomaly f ∈ [ 0 , 2 π ] . The results of this study will be helpful to study more generalised problems with different kind of perturbations such as oblateness, solar wind drag, PR drag, Stokes drag etc.