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The magnetic moment of a particle orbiting a straight current-carrying wiremay precess rapidly enough in the wire's magnetic field to justify an adiabaticapproximation, eliminating the rapid time dependence of the magnetic moment andleaving only the particle position as a slow degree of freedom. To zeroth orderin the adiabatic expansion, the orbits of the particle in the planeperpendicular to the wire are Keplerian ellipses. Higher order post-adiabaticcorrections make the orbits precess, but recent analysis of this `vector Keplerproblem' has shown that the effective Hamiltonian incorporating apost-adiabatic scalar potential (`geometric electromagnetism') fails to predictthe precession correctly, while a heuristic alternative succeeds. In this paperwe resolve the apparent failure of the post-adiabatic approximation, bypointing out that the correct second-order analysis produces a thirdHamiltonian, in which geometric electromagnetism is supplemented by a tensorpotential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shownto be a canonical transformation of the correct adiabatic Hamiltonian, tosecond order. The transformation has the important advantage of removing a$1/r^3$ singularity which is an artifact of the adiabatic approximation.Comment: 9 pages, 10 figure

Failure of geometric electromagnetism in the adiabatic vector Kepler problem