Advances in Astrophysics

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Volume 3, Number 3, August 2018

Periodic Orbits in the Photogravitational Elliptic Restricted Three-Body Problem
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154-170

, Pub. Date:August 22, 2018
DOI:

10.22606/adap.2018.33004
**Author(s)**
Y. SHARON RUTH, RAM KRISHAN SHARMA

**Affiliation(s)**
Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore, 641114, India

Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore, 641114, India

**Abstract**
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.

**Keywords**
The elliptic restricted three-body problem, radiation pressure, oblateness, transition
curve, tadpole orbits.

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