Abstract

This paper deals with the planar circular restricted three-body problem when both the primaries are sources of radiation and oblate spheroids with their equatorial planes coincident with the plane of motion. A new mean motion is utilized which includes the secular effects of the oblateness of the primary on mean anomaly (M), the argument of perigee (ω), and right ascension of ascending node (Ω).1 The value of the critical mass ratio (μc) is obtained in the series form. It is found that it further decreases with the increase in oblateness of the primaries as well with their radiation effect. The angular frequencies of the long-periodic orbits (s4) and short-periodic orbits (s5) around the triangular Lagrangian point (L4) are computed in series form. It is observed that (s4) increases with mass ratio μ, oblateness, and radiation pressure of both the primaries, while (s5) decreases with mass ratio, oblateness, and radiation pressure of both the primaries. The eccentricities are also computed in the series form. It is observed that the eccentricity of long-periodic orbits (e4) decreases with mass ratio, oblateness, and radiation pressure of both the primaries, whereas the eccentricity of short-periodic orbits (e5) increases with mass ratio, oblateness, and radiation pressure of both the primaries. These results are confirmed with the numerical values. Comparisons of these solutions are made with the results of Singh and Ishwar2 Abouelmagd and El-Shaboury,3 Arohan and Sharma,4 and Jency et al.5

Keywords

Restricted Three Body Problem, Oblateness, Radiation Pressure, Perturbations, Equilateral Points, Critical mass ratio, Periodic Orbits, Angular Frequencies, Eccentricities, Time Periods