New developments for modern celestial mechanics - I. General coplanar three-body systems. Application to exoplanets

Monthly Notices of the Royal Astronomical Society

Volumn 435, Issue 3, 2013, Pages 2187-2226

  Mardling, Rosemary A ^a,b  

^a MONASH UNIVERSITY   (Australia)

^b UNIVERSITÉ DE GENÈVE   (Switzerland)

Author keywords

Celestial mechanics; Chaos; Methods: analytical; Planets and satellites: dynamical evolution and stability

Indexed keywords

EID: 84885799962     PISSN: 00358711     EISSN: 13652966     Source Type: Journal    
DOI: 10.1093/mnras/stt1438     Document Type: Article

References (97)

1. Arnol'd V. I., 1963, Russ. Math. Surv., 18, 9
2. Ballard S. et al., 2011, ApJ, 743, 200
3. Batalha N. M., et al. 2013, ApJS, 204, 24
4. Batygin K. Morbidelli A., 2013, AJ, 145, 1
5. Batygin K., Bodenheimer P., Laughlin G., 2009, ApJ, 704, L49
6. Borucki W. J., et al. 2011, ApJ, 736, 19
7. Brouwer D., Clements G. M., 1961, Methods of Celestial Mechanics. Academic Press, New York
8. Chirikov B. V., 1979, Phys. Rep., 52, 263
9. Correia A. C. M., Udry S., Mayor M., Laskar J., Naef D., Pepe F., Queloz D., Santos N. C., 2005, A&A, 440, 751
10. Correia A. C. M., et al. 2010, A&A, 511, A21
11. Delisle J.-B., Laskar J., Correia A. C. M., Boué G., 2012, A&A, 546, A71
12. Doyle L. R., et al. 2011, Sci, 333, 1602
13. Dumusque X., et al. 2012, Nat, 491, 207
14. Ellis K. M., Murray C. D., 2000, Icarus, 147, 129
15. Fabrycky D., Tremaine S., 2007, ApJ, 669, 1298
16. Fabrycky D. C., et al. 2012, ApJ, 750, 114
17. Ford E. B., Kozinsky B., Rasio F. A., 2000, ApJ, 535, 385
18. Fortney J. J., Marley M. S., 2007, ApJ, 666, L45
19. Giuppone C. A., Leiva A. M., Correa-Otto J., Beaugé C., 2011, A&A, 530, A103
20. Goldreich P., Tremaine S., 1979, ApJ, 233, 857
21. Gradstein I. S., Ryzhik I. M., 1980, Table of Integrals, Series, and Products. Academic Press, New York
22. Henrard J., Lemaitre A., 1983, Celest. Mech., 30, 197
23. Holman M., Touma J., Tremaine S., 1997, Nat, 386, 254
24. Holman M. J., et al. 2010, Sci, 330, 51
25. Hori G., 1966, PASJ, 18, 287
26. Hughes S., 1981, Celest. Mech., 25, 101
27. Innanen K. A., Zheng J. Q., Mikkola S., Valtonen M. J., 1997, AJ, 113, 1915
28. Jackson J. D., 1975, Classical Electrodynamics, 2nd edn. Wiley, New York
29. Kalas P., et al. 2008, Sci, 322, 1345
30. Kaula W. M., 1961, Geophys. J. Roy. Astron. Soc., 5, 104
31. Kaula W. M., 1962, AJ, 67, 300
32. Kiseleva L. G., Eggleton P. P., Mikkola S., 1998, MNRAS, 300, 292
33. Kolmogorov A. N., 1954, Dokl. Akad. Nauk. SSSR, 98, 527
34. Kozai Y., 1962, AJ, 67, 591
35. Lagrange A.-M., et al. 2009, A&A, 493, L21
36. Landau L. D., Lifshitz E. M., 1969, Course of Theoretical Physics. Pergamon Press, Oxford
37. Laskar J., 1988, A&A, 198, 341
38. Laskar J., 1996, Celest. Mech. Dyn. Astron., 64, 115
39. Laskar J., Boué G., 2010, A&A, 522, A60
40. Laskar J., Robutel P., 1995, Celest. Mech. Dyn. Astron., 62, 193
41. Laskar J., Boué G., Correia A. C. M., 2012, A&A, 538, A105
42. Le Verrier U.-J., 1855, Ann. Obs. Paris, 1, 258
43. Lin D. N. C., Papaloizou J., 1979, MNRAS, 188, 191
44. Lin D. N. C., Bodenheimer P., Richardson D. C., 1996, Nat, 380, 606
45. Lissauer J. J., et al. 2011, Nat, 470, 53
46. Lithwick Y., Wu Y., 2012, ApJ, 756, L11
47. Lovis C., et al. 2011, A&A, 528, A112
48. Mardling R.A. 2007, MNRAS, 382, 1768
49. Mardling R. A., 2008, in Aarseth S. J., Tout C. A., Mardling R. A., eds, Lecture Notes in Physics, Vol. 760, The Cambridge N-Body Lectures. Springer-Verlag, Berlin, p. 59
50. Mardling R. A., 2010, MNRAS, 407, 1048
51. Mardling R. A., 2013, submitted (Paper II)
52. Marois C., Macintosh B., Barman T., Zuckerman B., Song I., Patience J., Lafrenière D., Doyon R., 2008, Sci, 322, 1348
53. Marois C., Zuckerman B., Konopacky Q. M., Macintosh B., Barman T., 2010, Nat, 468, 1080
54. Mayor M., Queloz D., 1995, Nat, 378, 355
55. Mayor M., et al. 2009, A&A, 507, 487
56. Mayor M., et al. 2011, preprint (arXiv:1109.2497)
57. McArthur B. E., Benedict G. F., Barnes R., Martioli E., Korzennik S., Nelan E., Butler R. P., 2010, ApJ, 715, 1203
58. Meisner T., Wurm G., Teiser J., 2012, A&A, 544, A138
59. Meschiari S., 2012a, ApJ, 752, 71
60. Meschiari S., 2012b, ApJ, 761, L7
61. Mordasini C., Alibert Y., Benz W., Naef D., 2009, A&A, 501, 1161
62. Moser J., 1962, Nachr. Akad. Wiss. Goett. II, 1, 1
63. Murray C. D., Dermott S. F., 2000, Solar System Dynamics. Cambridge Univ. Press, Cambridge
64. Naef D., et al. 2001, A&A, 375, L27
65. Naoz S., Farr W. M., Lithwick Y., Rasio F. A., Teyssandier J., 2011, MNRAS, 431, 2155
66. Nayfeh A. H., 1973, Perturbation Methods. Wiley, New York
67. Nesvorný D., Kipping D. M., Buchhave L. A., Bakos G. Á, Hartman J., Schmitt A. R., 2012, Sci, 336, 1133
68. Neyfeh A. H., Mook D. T., 1979, Nonlinear Oscillations. Wiley, New York
69. Okuzumi S., Tanaka H., Kobayashi H., Wada K., 2012, ApJ, 752, 106
70. Orosz J. A. A., et al. 2012a, Sci, 337, 1511
71. Orosz J. A., et al. 2012b, ApJ, 758, 87
72. Paardekooper S.-J., Leinhardt Z. M., Thébault P., Baruteau C., 2012, ApJ, 754, L16
73. Papaloizou J. C. B., 2011, Celest. Mech. Dyn. Astron., 111, 83
74. Peale S. J., 1976, ARA&A, 14, 215
75. Pelupessy F. I., Portegies Zwart S., 2013, MNRAS, 429, 895
76. Pepe F., Lovis C., Ségransan D., et al. 2011, A&A, 534, A58
77. Pillitteri I., Wolk S. J., Cohen O., Kashyap V., Knutson H., Lisse C. M., Henry G. W., 2010, ApJ, 722, 1216
78. Poincaré H., 1892, Les Méthode Nouvelle de la Mécanique Céleste. Gauthier-Villars, Paris
79. Pollard H., 1966, Mathematical Introduction to Celestial Mechanics. Prentice-Hall, Englewood Cliffs, NJ
80. Rasio F. A., Ford E. B., 1996, Sci, 274, 954
81. Richardson L. J., Harrington J., Seager S., Deming D., 2006, ApJ, 649, 1043
82. Rivera E. J., et al. 2005, ApJ, 634, 625
83. Robutel P., 1995, Celest. Mech. Dyn. Astron., 62, 219
84. Sahlmann J., Ségransan D., Queloz D., Udry S., 2011, in Sozzetti A., Lattanzi M. G., Boss A. P., eds, Proc. IAU Symp. 276, The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution. Cambridge Univ. Press, Cambridge, p. 117
85. Seager S., Deming D., 2010, ARA&A, 48, 631
86. Steffen J. H., et al. 2012, MNRAS, 421, 2342
87. Takeuchi T., Ida S., 2012, ApJ, 749, 89
88. Torres G., et al. 2011, ApJ, 727, 24
89. Triaud A. H. M. J., et al. 2010, A&A, 524, A25
90. Udry S., Santos N. C., 2007, ARA& A, 45, 397
91. Welsh W. F., et al. 2012, Nat, 481, 475
92. Winn J. N., Fabrycky D., Albrecht S., Johnson J. A., 2010, ApJ, 718, L145
93. Wisdom J., 1980, AJ, 85, 1122
94. Wisdom J., 1982, AJ, 87, 577
95. Wolfram Research Inc., 2010, Mathematica, Version 8.0, Champaign, IL
96. Wolszczan A., Frail D. A., 1992, Nat, 355, 145
97. Wu Y., Goldreich P., 2002, ApJ, 564, 1024