Computation of the perturbed locations of L1 for all Sun-Planet RTBP systems with oblate primaries

Abstract

The location of the equilibrium point ΔL1 in the restricted three body problem with oblate primaries is investigated. The zonal harmonic coefficients are retained up to the fourth harmonic coefficient of both primaries. The perturbed mean motion is determined. The perturbed location of L1 is computed for eight restricted three body systems within the solar system as well as two restricted three body lunar systems. The nondimensionalized and dimensionalized locations for different combinations of perturbing oblateness parameters of the primaries are obtained. The linear stability is investigated. The study shows that the equilibrium point is unstable for the whole considered systems.