Noncollinear Equilibrium Points in CRTBP with Yukawa-Like Corrections to Newtonian Potential under an Oblate Primary Model

Abstract

This study is about the effects of Yukawa-like corrections to Newtonian potential on the existence and stability of noncollinear equilibrium points in a circular restricted three-body problem when bigger primary is an oblate spheroid. It is observed that ∂x0/∂λ = 0 = ∂y0/∂λ at λ0 = 1/2, so we have a critical point λ0 = 1/2 at which the maximum and minimum values of x0 and y0 can be obtained, where λ ∈ (0, ∞) is the range of Yukawa force and (x0, y0) are the coordinates of noncollinear equilibrium points. It is found that x0 and y0 are increasing functions in λ in the interval 0 < λ < λ0 and decreasing functions in λ in the interval λ0 < λ < ∞ for all α ∈ α+. On the other hand, x0 and y0 are decreasing functions in λ in the interval 0 < λ < λ0 and increasing functions in λ in the interval λ0 < λ < ∞ for all α ∈ α−, where α ∈ (−1, 1) is the coupling constant of Yukawa force to gravitational force. The noncollinear equilibrium points are found linearly stable for the critical mass parameter β0, and it is noticed that ∂β0/∂λ = 0 at λ ∗  = 1/3; thus, we got another critical point which gives the maximum and minimum values of β0. Also, ∂β0/∂λ > 0 if 0 < λ <  λ ∗ and ∂β0/∂λ < 0 if λ ∗  < λ < ∞ for all α ∈ α−, and ∂β0/∂λ < 0 if 0 < λ <  λ ∗ and ∂β0/∂λ > 0 if λ ∗  < λ < ∞ for all α ∈ α+. Thus, the local minima for β0 in the interval 0 < λ <  λ ∗ can also be obtained.