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@Article{CarvalhoMouMorPraWin:2016:SwPrRe,
               author = "Carvalho, Jean P. S. and Mour{\~a}o, D. C. and Moraes, Rodolpho 
                         Vilhena de and Prado, Antonio Fernando Bertachini de Almeida and 
                         Winter, O. C.",
          affiliation = "{Universidade Federal do Rec{\^o}cavo da Bahia (UFRB)} and 
                         {Universidade Estadual Paulista (UNESP)} and {Universidade Federal 
                         de S{\~a}o Paulo (UNIFESP)} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)} and {Universidade Estadual Paulista (UNESP)}",
                title = "Exoplanets in binary star systems: on the switch from prograde to 
                         retrograde orbits",
              journal = "Celestial Mechanics \& Dynamical Astronomy",
                 year = "2016",
               volume = "124",
               number = "1",
                pages = "73--96",
                month = "Jan.",
             keywords = "Three-body problem, Orbital perturbation, Exoplanets, Flip of 
                         inclination, Lidov-Kozai mechanism.",
             abstract = "The eccentric Kozai-Lidov mechanism, based on the secular theory, 
                         has been proposed as a mechanism that plays an important role in 
                         producing orbits that switch from prograde to retrograde. In the 
                         present work we study the secular dynamics of a triple system 
                         composed of a Sun-like central star and a Jupiter-like planet, 
                         which are under the gravitational influence of another perturbing 
                         star (brown dwarf). The perturbation potential is developed in 
                         closed form up to the fifth order in a small parameter (), where 
                         is the semimajor axis of the extrasolar planet and is the 
                         semimajor axis of the perturbing star. To eliminate the 
                         short-period terms of the perturbation potential, the 
                         double-average method is applied. In this work we do not eliminate 
                         the nodes, a standard method in the literature, before deriving 
                         the equations of motion. The main goal is to study the effects of 
                         the higher-order terms of the expansion of the perturbing force 
                         due to the third body in the orbital evolution of the planet. In 
                         particular, we investigate the inclination and the shape 
                         (eccentricity) of these orbits. We show the importance of the 
                         higher-order terms in changing the inversion times of the flip, 
                         i.e., the times where the inclination of the inner planet flips 
                         from prograde to retrograde trajectories. We also show the 
                         dependence of the first flip with respect to the semimajor axis 
                         and eccentricity of the orbit of the planet. The general 
                         conclusion is that the analytical model increases its accuracy 
                         with the inclusion of higher-order terms. We also performed full 
                         numerical integrations using the Bulirsch-Stoer method available 
                         in the Mercury package for comparison with the analytical model. 
                         The results obtained with the equations developed in this work are 
                         in accordance with direct numerical simulations.",
                  doi = "10.1007/s10569-015-9650-3",
                  url = "http://dx.doi.org/10.1007/s10569-015-9650-3",
                 issn = "0923-2958",
                label = "self-archiving-INPE-MCTI-GOV-BR",
             language = "en",
           targetfile = "carvalho.pdf",
        urlaccessdate = "25 nov. 2020"
}


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