Analytical solutions for J2-perturbed unbounded equatorial orbits

Vladimir Martinusi, Pini Gurfil

Research output: Contribution to journalArticlepeer-review

Abstract

While solutions for bounded orbits about oblate spheroidal planets have been presented before, similar solutions for unbounded motion are scarce. This paper develops solutions for unbounded motion in the equatorial plane of an oblate spheroidal planet, while taking into account only the J2 harmonic in the gravitational potential. Two cases are distinguished: A pseudo-parabolic motion, obtained for zero total specific energy, and a pseudo-hyperbolic motion, characterized by positive total specific energy. The solutions to the equations of motion are expressed using elliptic integrals. The pseudo-parabolic motion unveils a new orbit, termed herein the fish orbit, which has not been observed thus far in the perturbed two-body problem. The pseudo-hyperbolic solutions show that significant differences exist between the Keplerian flyby and the flyby performed under the the J2 zonal harmonic. Numerical simulations are used to quantify these differences.

Original languageEnglish
Pages (from-to)35-57
Number of pages23
JournalCelestial Mechanics and Dynamical Astronomy
Volume115
Issue number1
DOIs
StatePublished - Jan 2013
Externally publishedYes

Keywords

  • Analytical methods
  • Perturbed two-body problem
  • Unbounded orbits
  • Zonal harmonics

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics

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