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Analytical solutions for J 2-perturbed unbounded equatorial orbits

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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 J 2 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 J 2 zonal harmonic. Numerical simulations are used to quantify these differences.

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Correspondence to Pini Gurfil.

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Martinusi, V., Gurfil, P. Analytical solutions for J 2-perturbed unbounded equatorial orbits. Celest Mech Dyn Astr 115, 35–57 (2013). https://doi.org/10.1007/s10569-012-9450-y

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