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

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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.

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  • Henrard, J. and Lemaitre, A.: 1983,Celest. Mech. 30, 197.

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  • Peale, S. J.:Ann. Rev. Astron. Astrophys. 14, 215.

  • Sinclair, A. T.: 1972,Monthly Notices Roy. Astron. Soc. 160, 169.

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  • Yoder, C. F.: 1973, ‘On the Establishment and Evolution of Orbit-Orbit Resonances’, Ph.D. thesis, University of California, Santa Barbara, 303 pp.

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  • 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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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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  • DOI: https://doi.org/10.1007/BF01231120

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