Artificial equilibrium points and their linear stability analysis in the solar sail problem with triaxial second primary

Abstract

Motion of a solar sail or a spacecraft equipped with a solar sail is one of the interesting problem of celestial mechanics. This paper deals with stationary solution of solar sail problem with radiating first primary and triaxial second primary under the frame of circular restricted three body problem (RTBP). First, equations of motion is derived with triaxiality and sail lightness number and then artificial equilibrium points (AEPs) are determined. It is noticed that impact of triaxiality parameters (σ1andσ2) of second primary is less than that of sail lightness number (β) due to which a considerable deviations in the positions of AEPs are occurred. Further, linear stability test is performed for all AEPs and it is found that similar to equilibrium points in classical RTBP, collinear AEPs are unstable for all mass parameter μ∈(0,1/2] and triangular AEPs are stable in the range 0<μ<μc=0.03758902. Moreover, stability range decreases with the values of β and σ1 but increases with σ2. After this we analyze the periodic orbits of the solar sail in the vicinity of AEPs and it is noticed that nature of motion is unaffected but time period is influenced from the sail number β and triaxiality parameters σ1 and σ2. The findings are useful to describe the more generalized solar sail problem with other perturbations such as oblateness, albedo, drag forces etc.