Abstract
Kepler is a discovery-class mission designed to determine the frequency of Earth-radius planets in and near the habitable zone of solar-type stars. A habitable zone of a star is defined as a range of orbits within which a rocky planet can support liquid water on its surface. The most intriguing question driving the search for habitable planets is whether they host life.
 The aim of this paper is to study the motion of a “test particle” inside the exoplanetary system Kepler-22. This system consists of a sun-like star, Kepler-22, and a terrestrial exoplanet, Kepler-22b. This exoplanet is situated in the habitable zone of its star. Kepler-22b is located about 180 pc from Earth in the constellation of Cygnus. It was discovered by NASA’s Kepler Space Telescope in December 2011 and the planet is about 2.4 times the radius of Earth. Scientists don't yet know if Kepler-22b has a rocky, gaseous or liquid composition.
 In this study, let’s derive Lagrange points and perform several numerical tests to discover different possible orbits around the star Kepler-22. From many numerical tests performed, it is also possible to found two tadpole orbits around the Lagrange points L4 and L5 and a tadpole orbit around the exoplanet Kepler-22b, which encircles the two Lagrange points L1, and L2. Some of these orbits are found in the habitable zone and others outside. We have also examined the possibility of the existence of an exomoon around the terrestrial exoplanet Kepler-22b. In this case we have considered the mass of this exomoon.
 The Circular Restricted Three-Body Problem is used in this study. If it is further assumed that the third body (for example a planet, satellite, an asteroid or just a “test particle”) travels in the same plane as the two larger bodies, then there is the Planar Circular Restricted Three-Body Problem
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