Effect of Oblateness of the Secondary up to J4 on L4,5 in the Photogravitaional ER3BP

In a synodic-pulsating dimensionless coordinate, with a luminous primary and an oblate secondary, we examine the effects of radiation pressure, oblateness (quadruple and octupolar i.e. ) and eccentricity of the orbits of the primaries on the triangular points in the ER3BP. have been shown to disturb the motion of an infinitesimal body and particularly has significant effects on a satellite’s secular perturbation and orbital precessions. The influence of these parameters on the triangular points of Zeta Cygni, 54 Piscium and Procyon A/B are highlighted in this study. Triangular points are stable in the range and their stability is affected by said parameters.

On the Origins of Eccentric Close-in Planets

Strong tidal interaction with the central star can circularize the orbits of close-in planets. With the standard tidal quality factorQof our solar system, estimated circularization timescales for close-in extrasolar planets are typically shorter than the age of the host stars. While most extrasolar planets with orbital radiia≲ 0.1 AU indeed have circular orbits, some close-in planets with substantial orbital eccentricities have recently been discovered. This new class of eccentric close-in planets implies that either their tidalQfactor is considerably higher, or circularization is prevented by an external perturbation. Here we constrain the tidalQfactor for transiting extrasolar planets by comparing their circularization times with accurately determined stellar ages. Using estimated secular perturbation timescales, we also provide constraints on the properties of hypothetical second planets exterior to the known eccentric close-in planets.

Stability Mechanism of Planetary System of ν Andromedae

Three planets are detected around ν Andromedae. The stability of Upsilon Andromedae Planetary system is maintained by the co rotation of the pericenters of the two outer planets. If the pericenters of the two outer planets move independently, the planetary system becomes unstable. The corotation of the pericenters is explained by the secular perturbation theory. This corotation is not a secular resonance.