Ring body problem dynamics under the albedo effect

Abstract

This study explores the existence and characteristics of libration points, as well as their linear stability, in the ring-body problem while accounting for additional perturbations from radiation pressure and the albedo effect. Our analysis reveals that even minor variations in the number of peripheral primaries, can lead to significant changes in the system’s dynamics. The mass parameter $\beta$ plays a crucial role in determining the regions associated with libration points. To deepen our understanding, we compare the results of our proposed model with those of the classical $(N+1)$ ring-body problem. This comparison highlights substantial differences in the locations of the libration points and their respective linear stability. Notably, our findings indicate that the libration point $L_0$, positioned at the center alongside the peripheral primary $P_0$, remains unaffected by the considered perturbations. However, with a few exceptions, most identified libration points exhibit unstable behavior. We emphasize that the conducted study is crucial in astrophysics and orbital mechanics, as it helps model planetary ring systems (such as Saturn’s rings), protoplanetary disks, and even certain galactic formations.