A simple derivation of capture probabilities for the J+1:J and J+2:J orbit-orbit resonance problems (original) (raw)

Abstract

We present a simplified analytic derivation of the capture probabilities for the j+1∶j and j+2∶j orbital resonances. We apply Henrard's method which is based on an extension of the theory of adiabatic invariants and recover the results originally obtained by Yoder.

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References

• Goldreich, P.: 1965,Monthly Notices Roy. Astron. Soc. 130, 159.
  Google Scholar
• Goldreich, P. and Peale, S.: 1966,Astron. J. 71, 425.
  Google Scholar
• Greenberg, R.: 1973,Astron. J. 78, 338.
  Google Scholar
• Henrard, J.: 1982,Celest. Mech. 27, 3.
  Google Scholar
• Henrard, J. and Lemaitre, A.: 1983,Celest. Mech. 30, 197.
  Google Scholar
• Peale, S. J.:Ann. Rev. Astron. Astrophys. 14, 215.
• Sinclair, A. T.: 1972,Monthly Notices Roy. Astron. Soc. 160, 169.
  Google Scholar
• Yoder, C. F.: 1973, ‘On the Establishment and Evolution of Orbit-Orbit Resonances’, Ph.D. thesis, University of California, Santa Barbara, 303 pp.
  Google Scholar
• Yoder, C. F.: 1979,Celest. Mech. 19, 3.
  Google Scholar

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Authors and Affiliations

1. NASA-Ames Research Center, 94035, Moffett Field, CA, USA
   Nicole Borderies
2. Division of Geological and Planetary Sciences, California Institute of Technology, 91125, Pasadena, CA, USA
   Peter Goldreich

Authors

1. Nicole Borderies
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2. Peter Goldreich
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Additional information

Contribution number 3874 from the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, U.S.A.

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Borderies, N., Goldreich, P. A simple derivation of capture probabilities for the J+1:J and J+2:J orbit-orbit resonance problems.Celestial Mechanics 32, 127–136 (1984). https://doi.org/10.1007/BF01231120

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• Received: 04 March 1983
• Accepted: 26 September 1983
• Issue Date: February 1984
• DOI: https://doi.org/10.1007/BF01231120

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