A primordial origin of the laplace relation among the Galilean satellites

Science

Volumn 298, Issue 5593, 2002, Pages 593-597

  Peale, S J ^a   Lee, Man Hoi ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PLANETS; RESONANCE; TIDES; TORQUE;

STARS;

SATELLITES;

EUROPA; IO; JUPITER; ORBIT DETERMINATION; PLANETARY SATELLITE; VOLCANISM;

ARTICLE; ASTRONOMY; COSMOS; GRAVITY; MEASUREMENT; MIGRATION; MODEL; MOTION; PRIORITY JOURNAL; TELECOMMUNICATION; VELOCITY; VOLCANO;

SIGANUS;

EID: 0037131225     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.1076557     Document Type: Article

References (42)

1. C. F. Yoder, Nature 279, 767 (1979).
2. -, S. J. Peale, Icarus 47, 1 (1981).
3. R. Greenberg, in Satellites of Jupiter, D. Morrison, Ed. (Univ. Arizona Press, Tucson, AZ, 1982), pp. 65-92.
4. R. Greenberg, Icarus 70, 334 (1987).
5. 1 is called the free eccentricity, which can be damped to zero.
6. S. J. Peale, Annu. Rev. Astron. Astrophys. 37, 533 (1999).
7. R. Malhotra, Icarus 94, 399 (1991).
8. A. P. Showman, R. Malhotra, Icarus 127, 93 (1997).
9. A. P. Showman, D. J. Stevenson, R. Malhotra, Icarus 129, 367 (1997).
10. G. W. Ojakangas, D. J. Stevenson, Icarus 66, 341 (1986).
11. S. J. Peale, R. Greenberg, Lunar Planet. Sci. XI, 871 (1980).
12. J. B. Pollack. J. I. Lunine, W. C. Tittemore, in Uranus, J. T. Bergstralh, E. D. Miner, M. S. Matthews, Eds. (Univ. Arizona Press, Tucson, AZ, 1991), pp. 469-512.
13. G. Schubert, T. Spohn, R. T. Reynolds, in Satellites, J. A. Burns, M. S. Matthews, Eds. (Univ. Arizona Press, Tucson, AZ, 1986), pp. 224-292.
14. J. D. Anderson et al., Science 281, 2019 (1998).
15. J. D. Anderson et al., Science 280, 1573 (1998).
16. J. D. Anderson et at., Icarus 153, 157 (2001).
17. D. J. Stevenson, A. W. Harris, J. I. Lunine, in Satellites, J. A. Burns, M. S. Matthews, Eds. (Univ. Arizona Press, Tucson, AZ, 1986), pp. 39-88.
18. D. J. Stevenson, Science 294 71 (2001).
19. R. M. Canup, W. R. Ward, Astron. J., in press.
20. W. R. Ward, J. M. Hahn, in Protostars and Planets IV, V. Mannings, A. P. Boss, S. S. Russell, Eds. (Univ. Arizona Press, Tucson, AZ, 2000), pp. 1135-1158.
21. S. H. Lubow, M. Seibert, P, Artymowicz, Astrophys. J. 526, 1001 (1999).
22. G. Bryden, X. Chen, D. N. C. Lin, R. P. Nelson, J. C. B. Papaloizou, Astrophys. J. S14, 344 (1999).
23. W. Kley, G. D'Angelo, T. Henning, Astrophys. J. 547, 457 (2001).
24. G. D'Angelo, T. Henning, W. Kley, Astron. Astrophys. 385, 647 (2002).
25. W. R. Ward, Icarus 126, 261 (1997).
26. Lee and Peale (29) have shown that capture into the resonances at the 2:1 commensurability during differential migration of the two planets in coplanar orbits about the star GJ 876 occurs easily for a reasonably wide range of initial conditions. Capture and subsequent configuration are independent of the migration rate unless that rate is unreasonably large, and the capture and configuration are independent of the functional dependence of the migration on orbital semimajor axes. The only thing that matters is that the orbits converge.
27. J. Wisdom, M. Holman, Astron. J. 102, 1528 (1991).
28. H. F. Levison, M. J. Duncan, Icarus 108, 18 (1944). Available at: www.boulder.swri.edu/∼hal/swift.html.
29. M. H. Lee, S. J. Peale, Astrophys. J. 567, 596 (2002).
30. We have arbitrarily assigned the full masses to the satellites and assumed that lo and Europa migrate on the same time scale to demonstrate the hypothesis, whereas migration will ensue as the satellites are accreting and lo will generally migrate faster than Europa once its mass exceeds that of the latter. The necessary condition here for the success of the establishment of the Laplace retation is that lo migrate more slowly than Europa after Europa is captured into resonance with Ganymede, which capture accelerates Europa's migration. The migration rate history thus depends on the surface mass density of the disk and the accretion history determining the satellite masses as a function of time. There is enough flexibility in the disk and accretion model to effect the necessary relative rates.
31. P. Artymowicz, Astrophys. J. 419, 166 (1993).
32. H. Tanaka, T. Takeuchi, W. R. Ward, Astrophys. J. 565, 1257 (2002).
33. S. J. Peale, P. Cassen, R. T. Reynolds, Icarus 43, 65 (1980).
34. -, Science 203, 892 (1979).
35. W. C. Tittemore, J. Wisdom, Icarus 78, 63 (1989).
36. P. Goldreich, S. Soter, Icarus 5, 375 (1966).
37. S. J. Goldstein, K. C. Jacobs, Astron. J. 110, 3054 (1995).
38. K. Aksnes, F. A. Franklin, Astron. J. 122, 2734 (2001).
39. J. H. Lieske, Astron. Astrophys. 176, 146 (1987).
40. G. J. Veeder, D. L. Matson, T. V. Johnson, A. G. Davies, D. L. Blaney, AGU Spring Meeting 2002, 28 to 31 May 2002, Washington, DC (American Geophysical Union, Washington, DC, 2002). Available at: www.agu.org/dbasetop.html.
41. The establishment of the Laplace relation is not a certain outcome for differential migration of the satellites, although some type of resonance configuration does seem certain. Minor changes in the initial conditions, migration rates, or eccentricity damping rates sometimes led to other configurations. For example, in one case the system ended up with Ganymede-Europa in 2;1 resonances and Europa-lo in 7:3 resonances. Accretion of the satellites may not have been complete at the time of capture into the resonances, but two identical calculations-one with the full satellite masses and the other with half these masses-led to very similar Laplace configurations. Even if the mass ratios vary during migration, the configuration at the end of migration should be the same. The conditions for the various end configurations and an estimate of the probability of the system selecting the Laplace configuration will be subjects of a future paper.
42. We thank R. Canup and W. Ward for sending us an early preprint of their paper on Galilean satellite origin. This research was supported in part by NASA PGG grants NAG5 3646 and NAG5 11666 and SSO grants NAG5 7177 and NAG5 12087.