Effect of oblateness and radiation pressure on angular frequencies at collinear points

Abstract

In the three-dimensional restricted three-body problem, by considering the more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion as well as source of radiation, it is found that the collinear point L 1 comes nearer to the primaries with the increase in oblateness and radiation pressure, while L 2 and L 3 move away from the more massive primary with the increase in oblateness and come nearer to it with the increase in radiation pressure. It is noted that the angular frequency s 1 at L 1 increases with oblateness as well as with radiation pressure. s 2 increases with oblateness and decreases with radiation pressure and s 3 decreases with oblateness and increases with radiation pressure. A study on the norms of the characteristic roots λ and s at L 1 , L 2 and L 3 is carried out.It is established that for certain oblateness and radiation pressure parameters there is a one-to-one commensurability at the collinear points L 2 , L 3 between the planar angular frequencies (s 2,3 ) and the corresponding angular frequency (s z ) in the z-direction, and that at L 1 no such commensurability exists. At L 2 and L 3 , the value of oblateness parameter providing the commensurability decreases with the increase in the radiation pressure. However, the commensurable angular frequencies and eccentricity of the periodic orbits decrease at L 2 and increase at L 3 , with the increase in the radiation pressure.

Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem under Triaxial Luminous Primaries with Poynting-Robertson Drag

“…This circular restricted three-body problem (CR3BP) describes the motion of the infinitesimal mass moving in circular orbits and thus will not sufficiently describe the motion when certain perturbing forces are involved. This led scientists and mathematicians into an extensive study of the circular restricted three-body problem (CR3BP) from which models have been developed on the basis of different perturbing forces [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Stability of triangular equilibrium points in the elliptic restricted three body problem with oblate and triaxial primaries

“…E.g. Tsirogiannis et al (2006), Sharma (1987), Vishnu Namboori et al (2008, Mital et al (2009), Ishwar andKushvah (2006), Singh (2006, 2008), Singh and Ishwar (1999), Kumar and Ishwar (2009), all of these authors treated the restricted three body problem when one or both primaries as sources of radiation or oblate spheroids or both. Most of these studies described their effects on the motion of an infinitesimal mass.…”

Orbit classification in the Copenhagen problem with oblate primaries

“…A plethora of research articles that deal with the motion of the test particle when the two primaries are either oblate spheroid or triaxial rigid bodies is available (see e.g., Beevi and Sharma ; Kalantonis et al ; Sharma and Subba Rao ; Vishnu Namboodiri et al ; Zotos , ). The analysis of the problem, where one of the primaries is an oblate body, has been performed by various researchers: the study of the periodic orbits of second and third kind in this problem (see e.g., Sharma 8; Sharma and Subba Rao ; Sharma ; Sharma ), the periodic orbits generated by Lagrangian solutions using mobile coordinates (see e.g., Mittal et al , ), the linear stability of the libration points (see e.g., Sharma ), the nonlinear stability of the libration point L 4 (see e.g., Subba Rao and Sharma ), the periodic orbits by taking one or both primaries as sources of radiation or oblate spheroids or both (see e.g., Perdios and Kalantonis ; Tsirogiannis et al ) and the fractal basins of convergence, associated with the libration points (see e.g., Zotos ).…”