The limits of Earth orbital calculations for geological time-scale use

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 357, Issue 1757, 1999, Pages 1735-1759

  Laskar, Jacques ^a  

^a Bureau des Longitudes   (France)

Author keywords

Chaos; Milankovitch cycles; Obliquity; Orbital evolution; Palaeoclimates; Precession; Solar System

Indexed keywords

EID: 0346968494     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1999.0399     Document Type: Article

References (59)

1. Berger, A. 1976 Obliquity and precession for the last 5,000,000 years. Astron. Astrophys. 51, 127-135.
2. Berger, A. 1978 Long-term variations of daily insolation and quaternary climatic changes. J. Atmos. Sci. 35, 2362-2367.
3. Berger, A., Loutre, M. F. & Dehant, V. 1989 Influence of the changing lunar orbit on the astronomical frequencies of pre-quaternary insolation patterns. Paleoceanography 4, 555-564.
4. Bills, B. G. 1994 Obliquity-oblateness feedback: are climatically sensitive values of obliquity dynamically unstable? Geophys. Res. Lett. 21, 177-180.
5. Bois, E. & Girard, J. F. 1998 Impact of the quadrupole moment of the Sun on the dynamics of the Earth-Moon system. Preprint.
6. Bretagnon, P. 1974 Termes à longue périodes dans le système solaire. Astron. Astrophys. 30, 141-154.
7. Bretagnon, P. 1984 Amélioration des théories planétaires analytiques. Celest. Mech. 34, 193-201.
8. Brouwer, D. & Van Woerkoni, A. J. J. 1950 The secular variations of the orbital elements of the principal planets. Astron. Papers Am. Ephem. 13(II), 81-107.
9. Campbell, L. & Moffat, J. W. 1983 Quadrupole moment of the Sun and the planetary orbits. Astrophys. J. 275, L77-L79.
10. Darwin, G. H. 1880 On the secular change in the elements of a satellite revolving around a tidally distorted planet. Phil. Trans. R. Soc. Lond. 171, 713-891.
11. Dickey, J. O. (and 11 others) 1994 Lunar laser ranging: a continuating legacy of the Apollo program. Science 265, 182-190.
12. Forte, A. & Mitrovica, J. X. 1997 A resonance in the Earth's obliquity and precession over the past 20 Myr driven by mantle convection. Nature 390, 676-680.
13. Goldreich, P. 1966 History of the lunar orbit. Rev. Geophys. 4, 411-439.
14. Goldreich, P. & Peale, S. 1966 Spin orbit coupling in the Solar System. Astron. J. 71, 425-438.
15. Goldreich, P. & Peale, S. 1967 Spin-orbit coupling in the Solar System. II. The resonant rotation of Venus. Astron. J. 72, 662-668.
16. Goldreich, P. & Soter, S. 1966 Q in the Solar System. Icarus 5, 375-389.
17. Greenspan, H. P. & Howard, L. N. 1963 J. Fluid Mech. 17, 385.
18. Hill, G. 1897 On the values of the eccentricities and longitudes of the perihelia of Jupiter and Saturn for distant epochs. Astron. J. 17(11), 81-87.
19. Ito, T., Masuda, K., Hamano, Y. & Matsui, T. 1995 Climate friction: a possible cause for secular drift of Earth's obliquity. J. Geophys. Res. 100, 15147-15161.
20. Jurgens, R. F., Rojas, F., Slade, M. A. & Standish, E. M. 1998 Mercury radar ranging data from 1987 to 1997. Astron. J. 116, 486-488.
21. Kaula, W. 1964 Tidal disipation by solid friction and the resulting orbital evolution. J. Geophys. Res. 2, 661-685.
22. Lambeck, K. 1979 On the orbital evolution of the Martian satellites. J. Geophys. Res. B 84, 5651-5658.
23. Lambeck, K. 1980 The Earth's variable rotation. Cambridge University Press.
24. Landgraf, W. 1992 An estimation of the oblateness of Sun from the motion of Icarus. Solar Physics 142, 403-406.
25. Laskar, J. 1984 Theorie générale planétaire: eléments orbitaux des planètes sur 1 million d'années. Thèse, Observatoire de Paris, France.
26. Laskar, J. 1985 Accurate methods in general planetary theory. Astron. Astrophys. 144, 133-146.
27. Laskar, J. 1986 Secular terms of classical planetary theories using the results of general theory. Astron. Astrophys. 157, 59-70.
28. Laskar, J. 1988 Secular evolution of the Solar System over 10 million years. Astron. Astrophys. 198, 341-362.
29. Laskar, J. 1989 A numerical experiment on the chaotic behaviour of the Solar System. Nature 338, 237-238.
30. Laskar, J. 1990 The chaotic motion of the Solar System: a numerical estimate of the size of the chaotic zones. Icarus 88, 266-291.
31. Laskar, J. 1992 A few points on the stability of the Solar System. In Chaos, resonance and collective dynamical phenomena in the Solar System (ed. S. Ferraz-Mello), pp. 1-16. IAU Symposium 152. Kluwer.
32. Laskar, J. & Robutel, P. 1993 The chaotic obliquities of the planets. Nature 301, 608-612.
33. Laskar, J., Joutel, F. & Boudin, F. 1993a Orbital, precessional, and insolation quantities for the Earth from -20 Myr to +10 Myr. Astron. Astrophys. 270, 522-533.
34. Laskar, J., Joutel, F. & Robutel, P. 1993b Stabilization of the Earth's obliquity by the Moon. Nature 361, 615-617.
35. Le Verrier, U. 1856 Ann. Obs. Paris, vol. II. Paris: Mallet-Bachelet.
36. Le Verrier, U. 1858 Ann. Obs. Paris, vol. IV. Paris: Mallet-Bachelet.
37. Lourens, L. J., Hilgen, F. J., Zachariasse, W. J., Van Hoof, A. A. M., Antonarakou, A. & Vergnaud-Grazzini, C. 1996 Evaluation of the Plio-Pleistocene astronomical time scale. Paleoceanography 11, 391-413.
38. Lumb, L. I. & Aldridge, K. D. 1991 On viscosity estimates for the Earth's fluid outer core and core-mantle coupling. J. Geomagn. Geoelectr. 43, 93-110.
39. MacDonald, G. J. F. 1964 Tidal friction. J. Geophys. Res. 2, 467-541.
40. Mignard, F. 1979 The evolution of the lunar orbit revisited. I. Moon Planets 20, 301-315.
41. Mignard, F. 1980 The evolution of the lunar orbit revisited. II. Moon Planets 23, 185-206.
42. Mignard, F. 1981 The evolution of the lunar orbit revisited. III. Moon Planets 24, 189-207.
43. Mitrovica, J. X. & Forte, A. 1995 Pleistocene glaciation and the Earth's precession constant. Geophys. J. Int. 121, 21-32.
44. Néron de Surgy, O. & Laskar, J. 1997 On the long term evolution of the spin of the Earth. Astron. Astrophys. 318, 975-989.
45. Paternó, L., Sofia, S. & DiMauro, M. P. 1996 The rotation of the Sun's core. Astron. Astrophys. 314, 940-946.
46. Peltier, W. R. & Jiang, X. 1994 Precession constant of the Earth: variations through the ice-age. Geophys. Res. Lett. 21, 2299-2302.
47. Pijpers, F. P. 1998 Helioseismic determination of the solar gravitational quadrupole moment. Mon. Notes R. Astr. Soc. 297, L76-L80.
48. Quinn, T. R., Tremaine, S. & Duncan, M. 1991 A three million year integration of the Earth's orbit. Astron. J. 101, 2287-2305.
49. Rochester, M. G. 1976 The secular decrease of obliquity due to dissipative core-mantle coupling. Geophys. J. R. Astr. Soc. 46, 109-126.
50. Rubincam, D. P. 1990 Mars: change in axial tilt due to climate? Science 248, 720-721.
51. Rubincam, D. P. 1995 Has climate changed Earth's tilt? Paleoceanography 10, 365-372.
52. Sharav, S. G. & Boudnikova, N. A. 1967a On secular perturbations in the elements of the Earth's orbit and their influence on the climates in the geological past. Bull. ITA 11, 231-265.
53. Sharav, S. G. & Boudnikova, N. A. 1967b Secular perturbations in the elements of the Earth's orbit and the astronomical theory of climate variations. Trud. ITA 14, 48-84.
54. Soffel, M. H. 1989 Relativity in astrometry, celestial mechanics and geodesy. Springer.
55. Standish, E. M. 1998 JPL planetary and lunar ephemerides. DE405/LE405, JPL-IOM, 312F-98-048.
56. Thomson, D. J. 1990 Quadratic-inverse spectrum estimates: applications to palaeoclimatology. Phil. Trans. R. Soc. Lond. A 332, 539-597.
57. Touma, J. & Wisdom, J. 1994 Evolution of the Earth-Moon system. Astron. J. 108, 1943-1961.
58. Ward, W. R. 1982 Comments on the long-term stability of the Earth's obliquity. Icarus 50, 444-448.
59. Williams, D. M., Kasting, J. F. & Frakes, L. A. 1998 Low-latitude glaciation and rapid changes in the Earth's obliquity explained by obliquity-oblateness feedback. Nature 396, 453-455.