Periodic Orbits in the Photogravitational Elliptic Restricted Three-Body Problem

Periodic orbits in the elliptic restricted three-body problem are studied by considering the photogravitational and oblateness effects of the larger and smaller primary, respectively. The mean motion is derived with the help of averaging the distance r between the primaries over a revolution in terms of the mean anomaly. Collinear points L1, L2, L3 are studied for some of the Sun and its planet systems. The value of the critical mass μc is found, which decreases with the increase in radiation pressure and oblateness. The stability of the triangular points is studied using the analytical technique of Bennett. This is based on Floquet's theory for determination of characteristic exponents for periodic coefficients. Transition curves bounding the regions of stability in the μ-e plane, accurate to O(e2) are generated. Tadpole orbits, a combination of long-short periodic orbits, are produced for Sun-Jupiter and Sun-Saturn systems.