Out-of-plane equilibrium points in the photogravitational restricted four-body problem - Singh, Jagadish; Vincent, Ekele Aguda (Springer (Astrophys. Space Sc.), 2015)
The photogravitational restricted four-body problem is employed to describe the motion of an inﬁnitesimal particle in the vicinity of three ﬁnite radiating bodies. The fourth body P4 of inﬁnitesimal mass does not affect the motion of the three bodies (P1,P2,P3) that are always at the vertices of an equilateral triangle. We consider that two of the bodies (P2 and P3) have the same radiation and mass value μ while the dominant primary body P1 is of mass 1−2μ. The equilibrium points (Lz 1,Lz 2) lying out of the orbital plane of the primaries as well as the allowed regions of motionasdeterminedbythezerovelocitycurvesarestudied numerically. Finally the stability of these points is studied and they are found to be unstable.
Keywords: Equilibrium points; Restricted four-body problem; MEDICINE::Physiology and pharmacology::Radiological research::Radiation biology; Zero velocity curves; Stability