Abstract
We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this system in the framework of the circular and elliptic restricted threebody problem, when the motion of the giant planet describes circular and elliptic orbits, respectively. Originating from the circular family, families of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 meanmotion resonances are continued in the circular and the elliptic problems. New bifurcation points from the circular to the elliptic problem are found for each of the above resonances, and thus, new families continued from these points are herein presented. Stable segments of periodic orbits were found at high eccentricity values of the already known families considered as whole unstable previously. Moreover, new isolated (not continued from bifurcation points) families are computed in the elliptic restricted problem. The majority of the new families mainly consists of stable periodic orbits at high eccentricities. The families of the 5/1 resonance are investigated for the first time in the restricted threebody problems. We highlight the effect of stable periodic orbits on the formation of stable regions in their vicinity and unveil the boundaries of such domains in phase space by computing maps of dynamical stability. The longterm stable evolution of the terrestrial planets or asteroids is dependent on the existence of regular domains in their dynamical neighbourhood in phase space, which could host them for longtime spans. This study, besides other celestial architectures that can be efficiently modelled by the circular and elliptic restricted problems, is particularly appropriate for the discovery of terrestrial companions among the singlegiant planet systems discovered so far.
Original language  English 

Article number  41 
Number of pages  30 
Journal  Celestial Mechanics & Dynamical Astronomy 
Volume  130 
Issue number  6 
DOIs  
Publication status  Published  1 Jun 2018 
Keywords
 Astrophysics  Earth and Planetary Astrophysics
 periodic orbits
 circular family
 meannotion resonance
 orbital stability
 threebody problem
 high eccentricity
 Circular family
 Meanmotion resonance
 Periodic orbits
 Threebody problem
 Orbital stability
 High eccentricity
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Champagne, B. (Manager)
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