Abstract
An exoplanet, or extrasolar planet, is a planet that does not orbit the Sun, but is around a different star, stellar remnant, or brown dwarf. Up to now, about 1900 exoplanets were discovered. To better understand the dynamics of these exoplanets, a study with respect to possible collisions of the planet with the central star is shown here. We present an expanded model in a small parameter that takes into account up to the fifth order to analyze the effect of this potential in the orbital elements of the extrasolar planet. Numerical simulations were also performed using the N-body simulations, using the software Mercury, to compare the results with the ones obtained by the analytical model. The numerical simulations are presented in two stages: one considering the celestial bodies as point masses and the other one taking into account their dimensions. This analysis showed that the planet collided with the central star in the moment of the first inversion for orbits with high inclinations in various situations. The results of the simulations of the equations developed in this study are consistent with the N-body numerical simulations. We analyze also the flip of the inclination taking into account the coupling of the perturbations of the third body, effect due to the precession of periastron and the tide effect. In general, we find that such perturbations combined delay the time of first inversion, but do not keep the planet in a prograde or retrograde orbit.
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Acknowledgments
Sponsored by CNPq—Brazil. The authors are grateful to CNPq (National Council for Scientific and Technological Development)—Brazil for contracts 306953/2014-5, 304700/2009-6, 303070/2011-0, FAPESP (Foundation to Support Research in So Paulo State) under the contracts No. 2011/05671-5, 2012/21023-6, 2014/06688-7, 2011/08171-3, 2011/13101-4 SP-Brazil and CAPES.
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Communicated by Dr. Elbert E. N. Macau, Dr. Antônio Fernando Bertachini de Almeida Prado and Dr. Cristiano Fiorilo de Melo.
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Carvalho, J.P.S., de Moraes, R.V., Prado, A.F.B.A. et al. Analysis of the orbital evolution of exoplanets. Comp. Appl. Math. 35, 847–863 (2016). https://doi.org/10.1007/s40314-015-0270-z
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DOI: https://doi.org/10.1007/s40314-015-0270-z