Exploring out-of-plane equilibrium points in CRTBP: Theoretical insights and empirical observations

This study investigates the presence and stability of out-of-plane equilibrium points within the circular restricted three-body problem (CRTBP), taking into account both albedo effects and the oblateness of the smaller primary. Our findings reveal that when the oblateness factor σ reaches a sufficiently large magnitude, a pair of unstable symmetric equilibrium points exists out of the orbital plane of the primaries. Moreover, the study extends its examination to real planetary systems, where it demonstrates that the small oblateness factor σ confines equilibrium points within the smaller primary, in line with previous research. Consequently, the study concludes that such equilibrium points are absent in real planetary systems unless the oblateness factor σ attains a sufficiently large magnitude. These findings not only validate the results of Douskos and Markellos (2006) and Wu et al. (2018) but also deepen our understanding of dynamic behavior and stability in celestial systems, particularly considering albedo effects and oblateness considerations.