The outward radial offset of neptune ring arcs

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It is consensus that the Neptune ring arcs are confined by the 42/43 Lindblad-corotation orbit-orbit resonant interactions with Galatea. Nevertheless, recent observations have indicated that the radial position of the arcs is off the expected resonance location by 1/3 Km outwards. Such radial offset, although very small, is unaccountable by fine tuning the restricted three-body model. In an attempt to resolve this issue, we use a restricted four-body model where the center of mass is anchored by the central body Neptune S and the primary body Triton X. Two minor bodies Galatea G and ring arc s interact with each other while orbiting under the combined XS field. In order to identify the disturbing potential, the equations of motion of s are manipulated to arrive at the energy equation in a frame centered at S with a fixed reference axis. Due to the orbital motions of X and G, the force field acting on s is non-conservative with velocity and time dependences. This non-conservative field is represented in the energy equation in two ways. First, it appears as the energy exchange terms of s with X and G on the right side of the equation. Second, it appears in the potential function on the left side of the equation in a velocity dependent term, which could be removed by going to the SX rotating frame. Rearranging the non-conservative term in the potential function and the sX energy exchange terms gives an angular momentum term of s acted on by a time derivative. This regrouped term can be expressed in terms of the usual disturbing potential V itself multiplied by a coefficient q and becomes conservative. Consequently, the disturbing potential of s read Vs = (1+q)V, and by the same token, we have VG = (1+q)V. The (1+q) factor in Vs represents the effect of the anchoring Triton X on the sG interaction. As a matter of fact, this factor can also be recovered in the restricted three-body system, but has been overlooked so far. With Vs and VG, the resonance relations are preserved while the resonance location is displaced outward due to the additional contribution of X to the corotation secular potential of G that amounts to 0.3 Km.

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