Wisdom system: Dynamics in the adiabatic approximation

A simple approximate model of the asteroid dynamics near the 3:1 mean–motion resonance with Jupiter can be described by a Hamiltonian system with two degrees of freedom. The phase variables of this system evolve at different rates and can be subdivided into the ‘fast’ and ‘slow’ ones. Using the averaging technique, wisdom obtained the evolutionary equations which allow to study the long-term behavior of the slow variables. The dynamic system described by the averaged equations will be called the ‘Wisdom system’ below. The investigation of the, wisdom system properties allows us to present detailed classification of the slow variables’ evolution paths. The validity of the averaged equations is closely connected with the conservation of the approximate integral (adiabatic invariant) possessed by the original system. Qualitative changes in the behavior of the fast variables cause the violations of the adiabatic invariance. As a result the adiabatic chaos phenomenon takes place. Our analysis reveals numerous stable periodic trajectories in the region of the adiabatic chaos.     

On the circular Sitnikov problem: the alternation of stability and instability in the family of vertical motions

This paper is devoted to the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the primaries (so called periodic vertical motions). The main goal of the paper is to study the stability of these periodic motions in the linear approximation. A special attention is given to the alternation of stability and instability within the family of periodic vertical motions, whenever their amplitude is varied in a continuous monotone manner.     

Long-term ocean simulations in FESOM: evaluation and application in studying the impact of Greenland Ice Sheet melting

The Finite Element Sea-ice Ocean Model (FESOM) is formulated on unstructured meshes and offers geometrical flexibility which is difficult to achieve on traditional structured grids. In this work, the performance of FESOM in the North Atlantic and Arctic Ocean on large time scales is evaluated in a hindcast experiment. A water-hosing experiment is also conducted to study the model sensitivity to increased freshwater input from Greenland Ice Sheet (GrIS) melting in a 0.1-Sv discharge rate scenario. The variability of the Atlantic Meridional Overturning Circulation (AMOC) in the hindcast experiment can be explained by the variability of the thermohaline forcing over deep convection sites. The model also reproduces realistic freshwater content variability and sea ice extent in the Arctic Ocean. The anomalous freshwater in the water-hosing experiment leads to significant changes in the ocean circulation and local dynamical sea level (DSL). The most pronounced DSL rise is in the northwest North Atlantic as shown in previous studies, and also in the Arctic Ocean. The released GrIS freshwater mainly remains in the North Atlantic, Arctic Ocean and the west South Atlantic after 120 model years. The pattern of ocean freshening is similar to that of the GrIS water distribution, but changes in ocean circulation also contribute to the ocean salinity change. The changes in Arctic and sub-Arctic sea level modify exchanges between the Arctic Ocean and subpolar seas, and hence the role of the Arctic Ocean in the global climate. Not only the strength of the AMOC, but also the strength of its decadal variability is notably reduced by the anomalous freshwater input. A comparison of FESOM with results from previous studies shows that FESOM can simulate past ocean state and the impact of increased GrIS melting well.     

Some properties of the dumbbell satellite attitude dynamics

The dumbbell satellite is a simple structure consisting of two point masses connected by a massless rod. We assume that it moves around the planet whose gravity field is approximated by the field of the attracting center. The distance between the point masses is assumed to be much smaller than the distance between the satellite’s center of mass and the attracting center, so that we can neglect the influence of the attitude dynamics on the motion of the center of mass and treat it as an unperturbed Keplerian one. Our aim is to study the satellite’s attitude dynamics. When the center of mass moves on a circular orbit, one can find a stable relative equilibrium in which the satellite is permanently elongated along the line joining the center of mass with the attracting center (the so called local vertical). In case of elliptic orbits, there are no stable equilibrium positions even for small values of the eccentricity. However, planar periodic motions are determined, where the satellite oscillates around the local vertical in such a way that the point masses do not leave the orbital plane. We prove analytically that these planar periodic motions are unstable with respect to out-of-plane perturbations (a result known from numerical investigations cf. Beletsky and Levin Adv Astronaut Sci 83, 1993). We provide also both analytical and numerical evidences of the existence of stable spatial periodic motions.     

Long-term attitude dynamics of space debris in Sun-synchronous orbits: Cassini cycles and chaotic stabilization

Comprehensive analysis of space debris rotational dynamics is vital for active debris removal missions that require physical capture or detumbling of a target. We study the attitude motion of large space debris objects that admittedly pose an immediate danger to space operations in low Earth orbits. Particularly, we focus on Sun-synchronous orbits (SSO) with altitude range 600–800 km, where the density of space debris is maximal. Our mathematical model takes into account the gravity-gradient torque and the torque due to eddy currents induced by the interaction of conductive materials with the geomagnetic field. Using perturbation techniques and numerical methods, we examine the deceleration of the initial fast rotation and the subsequent transition to a relative equilibrium with respect to the local vertical. A better understanding of the latter phase is achieved owing to a more accurate model of the eddy-current torque than in most prior research. We show that SSO precession is also a crucial factor influencing the motion properties. One of its effects is manifested at the deceleration stage as oscillations of the angular momentum vector about the direction to the south celestial pole.     

The eccentric Kozai–Lidov effect as a resonance phenomenon

Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (Planet Space Sci 9:719–759, 1962) and, independently, Kozai (Astron J 67:591–598, 1962) discovered coupled oscillations of eccentricity and inclination (the KL cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL cycles can be established (Ford et al. in Astrophys J 535:385–401, 2000; Naoz et al. in Nature 473:187–189, 2011; Katz et al. in Phys Rev Lett 107:181101, 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a nonzero eccentricity, the term “eccentric Kozai–Lidov effect” (or EKL effect) was proposed by Lithwick and Naoz (Astrophys J 742:94, 2011) to specify such behavior. We demonstrate that the EKL effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of “action-angle” variables emerging in the integrable Kozai–Lidov model. It turns out that for some initial values the resonance is degenerate and the usual “pendulum” approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space.     

On the rotation of comet Borrelly’s nucleus

We consider the secular effect of outgassing torques on the rotation of a comet nucleus. An averaging method is applied to obtain evolutionary equations which allow us to study the long-term variations in the nucleus spin state. Since the spin axis direction of 19P/Borrelly’s nucleus is close to the line of apsides direction, a simplified version of these equations can be written to analytically study the most important qualitative effects. In particular, a correlation between the drift of the rotation axis direction and the possible spin up/spin down of the nucleus is revealed.     

On the impact of atmospheric vs oceanic resolutions on the representation of the sea surface temperature in the South Eastern Tropical Atlantic

Climate Dynamics - Despite the efforts of the modelling community to improve the representation of the sea surface temperature (SST) over the South Eastern Tropical Atlantic, warm biases still...