Collinear Points in the Photogravitational ER3BP with Zonal Harmonics of the Secondary
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Collinear Points in the Photogravitational ER3BP with Zonal Harmonics of the Secondary Rukkayat Suleiman1 · Aishetu Umar2,3 · Jagadish Singh2,3
© Foundation for Scientific Research and Technological Innovation 2017
Abstract The positions and stability of the collinear equilibrium points in the photogravitational ER3BP with zonal harmonics of the secondary is investigated. The effects of the perturbing forces: - oblateness, eccentricity and radiation pressure—on the positions and stability of collinear points (L 1,2,3 ) of an infinitesimal mass in the framework of the photogravitational ER3BP with zonal harmonics of the secondary are established. These effects on the positions of the binary systems Zeta Cygni, 54 Piscium, Procyon A/B and Regulus A are shown graphically and numerically from the analytic results obtained. It is observed that as the zonal harmonic J4 and eccentricity e increase, the collinear points shift towards the origin, while the reverse is observed with increase in the semi-major axis. The stability behavior however is unaffected by the introduction of these parameters, the collinear points remain linearly unstable. Keywords Celestial mechanics · ER3BP · Radiation pressure · Zonal harmonics
Inroduction The motion of three particles in space under their mutual gravitational attraction (according to Newtonian law of gravitation), given their initial conditions and determining their
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Aishetu Umar [email protected] Rukkayat Suleiman [email protected] Jagadish Singh [email protected]
1
Department of Basic Science and General Studies, Federal College of Forestry Mechanization, Forestry Research Institute of Nigeria, Ibadan, Nigeria
2
Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria
3
P.M.B 2273, Afaka, Kaduna, Nigeria
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Differ Equ Dyn Syst
subsequent motions ([10,11], and Chenciner [8]) gave rise to a complicated linear problem and the most celebrated of all dynamical problems called the three-body problem. Various researchers in classical mechanics [4,6,9,28,29,36,37,42,47,60,64–66]) have devoted their time exclusively to the three-body problem as well as its applications. A complete solution of the general three-body problem has remained a formidable challenge to date [20]. A special case of the general three-body arises when one of the participating bodies appears to be very small (infinitesimal mass) compared to the other two (called the primaries), as such, the motion of the two larger bodies (which are in circular/elliptic/hyperbolic/parbolic orbits) is not influenced by the smaller bodies referred to as the restricted three-body problem is one of the most widely studied areas of Space dynamics as well as celestial mechanics. Due to its valuable applications in orbit design and space navigation flights, it covers both analytical and numerical aspects. The relativistic 3-body problem has also received the attention of many researchers [5,19,34,40]. When the primaries move in elliptic orbits around their common barycenter, we ha
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