The designation of the customary restricted three-body disturbing potential \Phi as the perturbation Hamiltonian is believed to be the cause of Neptune ring arcs ’ radial offset between theories and observations .
To identify the appropriate perturbation Hamiltonian , the energy integral in the fixed frame of a restricted three-body system , consisting of the central , primary , and test bodies , is reconsidered .
It is shown that the perturbation energy includes the disturbing potential \Phi and the potential arising from the angular momentum terms of the test body .
Both potentials happen to be singular as the test body goes to infinity contradicting to the perturbation nature .
These two potentials can be combined to an energy relevant disturbing potential \Phi ^ { * } = \beta \Phi which is regular at infinity because of the cancellation of the singularities .
For circular orbits of the primary , the energy equation is conservative , and \Phi ^ { * } is identified as the perturbation Hamiltonian .
Applying this result to evaluate the backgrund effect of Triton to the arc-Galatea system of Neptune , it is shown that there is a small difference \Delta \Phi = ( \Phi ^ { * } - \Phi ) which amounts to an outward radial offset of the corotation location of Galatea by 0.3 Km .
The mismatch between the pattern speed of Galatea ’ s corotation potential and the mean motion velocity of the arcs could be resolved by considering the finite mass of Fraternite .
However , by using \Phi ^ { * } , Galatea ’ s eccentricity could be reassessed in terms of the mass of Fraternite . Key Words : Planets : Rings .