First order planetary perturbations with elliptic functions View Full Text


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Article Info

DATE

1987-09

AUTHORS

Carol A. Williams, Thomas van Flandern, Edward A. Wright

ABSTRACT

The differential equations of planetary theory are solved analytically to first order for the two-dimensional case, using only Jacobian elliptic functions and the elliptic integrals of the first and second kind. This choice of functions leads to several new features potentially of importance for planetary theory. The first of these is that the solutions do not require the expansion of the reciprocal of the distance between two planets, even for those variables which depend on two angular arguments. A second result is that the solution is free from small divisors with the exception of two special resonances. In fact, not only are the solutions for resonant orbits free from small divisors, the perturbations for all variables are expressible in closed form. A subset of the resonant orbits maintains this form and in addition has the remarkable feature that the first order perturbations are purely periodic; they contain no secular terms. A solution for the 1∶3 resonance case is given as an example. More... »

PAGES

367-391

References to SciGraph publications

  • 1982-02. A third-order intermediate orbit for planetary theory in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1984-09. Motions of the perihelions of Neptune and Pluto in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1984-09. Approximation methods in celestial mechanics. Application to Pluto's motion in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1971. Handbook of Elliptic Integrals for Engineers and Scientists in NONE
  • 1970-03. Expansions of the negative powers of mutual distances between bodies in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1974-01. On the long-term motion of Pluto in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1976-03. Families of periodic planetary-type orbits in the three-body problem and their stability in ASTROPHYSICS AND SPACE SCIENCE
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    http://scigraph.springernature.com/pub.10.1007/bf01235853

    DOI

    http://dx.doi.org/10.1007/bf01235853

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