Abstract
Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits. We apply this process to co-orbital motion and systems HD 82943, HD 73526, HD 128311, HD 60532, HD 45364 and HD 108874.
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References
J. Laskar, A.C.M. Correia, A&A 496, L5 (2009)
A.C.M. Correia, J. Couetdic, J. Laskar, X. Bonfils, M. Mayor, J.-L. Bertaux, F. Bouchy, X. Delfosse, T. Forveille, C. Lovis, F. Pepe, C. Perrier, D. Queloz, S. Udry, A&A 511, A21 (2010)
H. Rein, J.C.B. Papaloizou, W. Kley, A&A 510, A4 (2010)
C. Lovis, D. Ségransan, M. Mayor, S. Udry, W. Benz, J.-L. Bertaux, F. Bouchy, A.C.M. Correia, J. Laskar, G. Lo Curto, C. Mordasini, F. Pepe, D. Queloz, N.C. Santos, A&A 528, A112 (2011)
G. Campanella, R.P. Nelson, C.B. Agnor, MNRAS 433, 3190 (2013)
R.A. Wittenmyer, S. Wang, J. Horner, C.G. Tinney, R.P. Butler, H.R.A. Jones, S.J. O’Toole, J. Bailey, B.D. Carter, G.S. Salter, D. Wright, J.-L. Zhou, ApJS 208, 2 (2013)
K.I. Antoniadou, G. Voyatzis, H. Varvoglis, IAUS 310, 82 (2014)
J. Lillo-Box, D. Barrado, L. Mancini, T. Henning, P. Figueira, S. Ciceri, N. Santos, A&A 576, A88 (2015)
F. Marzari, S.J. Weidenschilling, Icarus 156, 570 (2002)
S. Chatterjee, E.B. Ford, S. Matsumura, F.A. Rasio, ApJ 686, 580 (2008)
E.W. Thommes, J.J. Lissauer, ApJ 597, 566 (2003)
M.H. Lee, E.W. Thommes, ApJ 702, 1662 (2009)
A.C.M. Correia, J. Laskar, F. Farago, G. Boué, CeMDA 111, 105 (2011)
S. Ferraz-Mello, C. Beaugé, T.A. Michtchenko, CeMDA 87, 99 (2003)
M.H. Lee, ApJ 611, 517 (2004)
C. Beaugé, T.A. Michtchenko, S. Ferraz-Mello, MNRAS 365, 1160 (2006)
J.D. Hadjidemetriou, G. Voyatzis, CeMDA 107, 3 (2010)
J.D. Hadjidemetriou, G. Voyatzis, IJBC 21, 2195 (2011)
G. Voyatzis, K.I. Antoniadou, K. Tsiganis, CeMDA 119, 221 (2014)
T.A. Michtchenko, C. Beaugé, S. Ferraz-Mello, CeMDA 94, 411 (2006)
G. Voyatzis, T. Kotoulas, J.D. Hadjidemetriou, MNRAS, 395, 2147 (2009)
J.-B. Delisle, J. Laskar, A.C.M. Correia, G. Boué, A&A 546, A71 (2012)
K.I. Antoniadou, G. Voyatzis, CeMDA 115, 161 (2013)
K.I. Antoniadou, G. Voyatzis, ApSS 349, 657 (2014)
J.-B. Delisle, J. Laskar, A.C.M. Correia, A&A 566, A137 (2014)
K.I. Antoniadou, G. Voyatzis, H. Varvoglis, in Proceedings of the 6th International Conference on Numerical Analysis (NumAn2014) (AMCL/TUC, Greece, 2014), p. 7, ISBN: 978-960-8475-22-9
K.I. Antoniadou, Ph.D. thesis, Aristotle University of Thessaloniki, 2014
G. Voyatzis, ApJ 675, 802 (2008)
K.I. Antoniadou, G. Voyatzis, T. Kotoulas, IJBC 21, 2211 (2011)
C. Beaugé, S. Ferraz-Mello, T.A. Michtchenko, ApJ 593, 1124 (2003)
S. Ferraz-Mello, T.A. Michtchenko, C. Beaugé, in Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems, edited by B.A. Steves, A.J. Maciejewski, M. Hendry (Springer, The Netherlands, 2006), p. 255
C. Marchal, The three-body problem (Elsevier, Amsterdam, 1990)
J.D. Hadjidemetriou, in Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems, edited by B.A. Steves, A.J. Maciejewski, M. Hendry (Springer, The Netherlands, 2006), p. 43
J.D. Hadjidemetriou, D. Psychoyos, G. Voyatzis, CeMDA 104, 23 (2009)
J.D. Hadjidemetriou, G. Voyatzis, CeMDA 111, 179 (2011)
P. Robutel, A. Pousse, CeMDA 117, 17 (2013)
C. Froeschlé, E. Lega, R. Gonczi, CeMDA 67, 41 (1997)
X. Tan, M.J. Payne, M.H. Lee, E.B. Ford, A.W. Howard, J.A. Johnson, G.W. Marcy, J.T. Wright, ApJ 777, 101 (2013)
R.A. Wittenmyer, X. Tan, M.H. Lee, J. Horner, C.G. Tinney, R.P. Butler, G.S. Salter, B.D. Carter, H.R.A. Jones, S.J. O’Toole, J. Bailey, D. Wright, J.D. Crane, S.A. Schectman, P. Arriagada, I. Thompson, D. Minniti, M. Diaz, ApJ 780, 140 (2014)
R. Barnes, R. Deitrick, R. Greenberg, T.R. Quinn, S.N. Raymond, ApJ 801, 101 (2015)
S.S. Vogt, R.P. Butler, G.W. Marcy, D.A. Fischer, G.W. Henry, G. Laughlin, J.T. Wright, J.A. Johnson, ApJ 632, 638 (2005)
A.C.M. Correia, S. Udry, M. Mayor, W. Benz, J.-L. Bertaux, F. Bouchy, J. Laskar, C. Lovis, C. Mordasini, F. Pepe, D. Queloz, A&A 496, 521 (2009)
K.I. Antoniadou, G. Voyatzis, MNRAS 461, 3822 (2016)
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Antoniadou, K. Regular and chaotic orbits in the dynamics of exoplanets. Eur. Phys. J. Spec. Top. 225, 1001–1016 (2016). https://doi.org/10.1140/epjst/e2016-02651-6
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DOI: https://doi.org/10.1140/epjst/e2016-02651-6