  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.
