Dynamics in the vicinity of (101955) Bennu: Solar radiation pressure effects in equatorial orbits

Here we study the dynamical effects of the solar radiation pressure (SRP) on a spacecraft that will survey the near-Earth rotating asteroid (101955) Bennu when the projected shadow is accounted for. The spacecraft's motion near (101955) Bennu is modelled in the rotating frame fixed at the centre of the asteroid, neglecting the sun gravity effects. We calculate the solar radiation pressure at the perihelion, semi-major axis and aphelion distances of the asteroid from the Sun. The goals of this work are to analyse the stability for both homogeneous and inhomogeneous mass distribution and study the effects of the solar radiation pressure in equatorial orbits close to the asteroid (101955) Bennu. As results, we find that the mascon model divided into ten equal layers seems to be the most suitable for this problem. We can highlight that the centre point $E$8, which was linearly stable in the case of the homogeneous mass distribution, becomes unstable in this new model changing its topological structure. For a Sun initial longitude $\psi_0 = -180^o$, starting with the spacecraft longitude $\lambda = 0$, the orbits suffer fewer impacts and some (between 0.4 and 0.5 km), remaining unwavering even if the maximum solar radiation is considered. When we change the initial longitude of the Sun to $\psi_0 = -135^o$, the orbits with initial longitude $\lambda = 90^0$ appear to be more stable. Finally, when the passage of the spacecraft in the shadow is accounted for, the effects of solar radiation pressure are softened, and we find more stable orbits.Comment: Accepted 2017 May 10. Received 2017 April 29; in original form 2017 January 1

The role of short periodic orbits in quantum maps with continuous openings

We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity functions. This is relevant in many situations that include optical microresonators and more complicated boundary conditions. In a perturbative regime, the shortest periodic orbits belonging to the classical repeller of the open map - a cantor set given by a region of exactly zero reflectivity - prove to be extremely robust in supporting a set of long-lived resonances of the continuously open quantum maps. Moreover, for step like functions a significant reduction in the number needed is obtained, similarly to the completely open situation. This happens despite a strong change in the spectral properties when compared to the discontinuous reflectivity case.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1604.0181