@Article{CarvalhoMouMorPraWin:2015: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, Othon Cabo",
          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 and Dynamical Astronomy",
                 year = "2015",
               volume = "online",
                pages = "1",
             keywords = "Perturba{\c{c}}{\~a}o de Terceiro Corpo, Perturba{\c{c}}{\~a}o 
                         Orbital.",
             abstract = "The eccentric KozaiLidov 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 
                         (\α=a1/a2), where a1 is the semimajor axis of the extrasolar 
                         planet and a2 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 BulirschStoer 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 = "lattes: 7340081273816424 4 CarvalhoMouMorPraWin:2015:SwPrRe",
             language = "en",
           targetfile = "1_carvalho.pdf",
        urlaccessdate = "28 abr. 2024"
}