TY - JOUR
T1 - On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems
AU - Libert, Anne-Sophie
AU - Sansottera, Marco
PY - 2013/10/1
Y1 - 2013/10/1
N2 - We study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincaré canonical variables, we determine the fundamental frequencies of the motion and compute analytically the long-term evolution of the Keplerian elements. Our study clearly shows that, for systems close to a mean-motion resonance, the second order approximation describes their secular evolution more accurately than the usually adopted first order one. Moreover, this approach takes into account the influence of the mean anomalies on the secular dynamics. Finally, we set up a simple criterion that is useful to discriminate between three different categories of planetary systems: (i) secular systems (HD 11964, HD 74156, HD 134987, HD 163607, HD 12661 and HD 147018); (ii) systems near a mean-motion resonance (HD 11506, HD 177830, HD 9446, HD 169830 and υ Andromedae); (iii) systems really close to or in a mean-motion resonance (HD 108874, HD 128311 and HD 183263).
AB - We study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincaré canonical variables, we determine the fundamental frequencies of the motion and compute analytically the long-term evolution of the Keplerian elements. Our study clearly shows that, for systems close to a mean-motion resonance, the second order approximation describes their secular evolution more accurately than the usually adopted first order one. Moreover, this approach takes into account the influence of the mean anomalies on the secular dynamics. Finally, we set up a simple criterion that is useful to discriminate between three different categories of planetary systems: (i) secular systems (HD 11964, HD 74156, HD 134987, HD 163607, HD 12661 and HD 147018); (ii) systems near a mean-motion resonance (HD 11506, HD 177830, HD 9446, HD 169830 and υ Andromedae); (iii) systems really close to or in a mean-motion resonance (HD 108874, HD 128311 and HD 183263).
KW - Extrasolar systems
KW - n-Body problem
KW - Normal forms method
KW - Proximity to mean-motion resonances
KW - Secular dynamics
KW - Upsilon Andromedae
UR - http://www.scopus.com/inward/record.url?scp=84884673628&partnerID=8YFLogxK
U2 - 10.1007/s10569-013-9501-z
DO - 10.1007/s10569-013-9501-z
M3 - Article
AN - SCOPUS:84884673628
SN - 0923-2958
VL - 117
SP - 149
EP - 168
JO - Celestial Mechanics & Dynamical Astronomy
JF - Celestial Mechanics & Dynamical Astronomy
IS - 2
ER -