  The magnetic moment of a particle orbiting a straight current-carrying wire
may precess rapidly enough in the wire's magnetic field to justify an adiabatic
approximation, eliminating the rapid time dependence of the magnetic moment and
leaving only the particle position as a slow degree of freedom. To zeroth order
in the adiabatic expansion, the orbits of the particle in the plane
perpendicular to the wire are Keplerian ellipses. Higher order post-adiabatic
corrections make the orbits precess, but recent analysis of this `vector Kepler
problem' has shown that the effective Hamiltonian incorporating a
post-adiabatic scalar potential (`geometric electromagnetism') fails to predict
the precession correctly, while a heuristic alternative succeeds. In this paper
we resolve the apparent failure of the post-adiabatic approximation, by
pointing out that the correct second-order analysis produces a third
Hamiltonian, in which geometric electromagnetism is supplemented by a tensor
potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown
to be a canonical transformation of the correct adiabatic Hamiltonian, to
second order. The transformation has the important advantage of removing a
$1/r^3$ singularity which is an artifact of the adiabatic approximation.
