A torsion-based solution to the hyperbolic regime of the J2-problem

TL;DR

This paper introduces a torsion-based method for solving the hyperbolic regime of the J2-problem, offering an effective alternative to traditional Keplerian approximations in satellite flyby calculations.

Contribution

It develops a torsion-based solution approach for unbounded hyperbolic orbits in the J2-problem, extending the method to higher orders for improved accuracy.

Findings

Torsion-based solutions are effective for hyperbolic orbits.

Extension to higher orders shows convergence to true orbits.

Provides an alternative to Keplerian approximations in flyby computations.

Abstract

A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a torsion. When this reduction process is applied to unbounded orbits the solution is made of Keplerian hyperbolae. For this last case, we show that the torsion-based solution provides an effective alternative to the Keplerian approximation customarily used in flyby computations. Also, we check that the extension of the torsion-based solution to higher orders of the oblateness coefficient yields the expected convergence of asymptotic solutions to the true orbit.