Detection of Envisat RA2/ICE-1 retracked radar altimetry bias over the Amazon basin rivers using GPS

Altimetry is now routinely used to monitor stage variations over rivers, including in the Amazon basin. It is desirable for hydrologic studies to be able to combine altimetry from different satellite missions with other hydrogeodesy datasets such as leveled gauges and watershed topography. One requirement is to accurately determine altimetry bias, which could be different for river studies from the altimetry calibrated for deep ocean or lake applications. In this study, we estimate the bias in the Envisat ranges derived from the ICE-1 waveform retracking, which are nowadays widely used in hydrologic applications. As a reference, we use an extensive dataset of altitudes of gauge zeros measured by GPS collocated at the gauges. The thirty-nine gauges are spread along the major tributaries of the Amazon basin. The methodology consists in jointly modeling the vertical bias and spatial and temporal slope variations between altimetry series located upstream and downstream of each gauge. The resulting bias of the Envisat ICE-1 retracked altimetry over rivers is 1.044 ± 0.212 m, revealing a significant departure from other Envisat calibrations or from the Jason-2 ICE-1 calibration.     

Transfer orbits to/from the Lagrangian points in the restricted four-body problem

The well-known Lagrangian points that appear in the planar restricted three-body problem are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L₁, L₂ and L₃) are always unstable and the triangular points (L₄ and L₅) are stable in the present case studied (Earth–Sun system). They are all very good points to locate a space-station, since they require a small amount of ΔV (and fuel), the control to be used, for station-keeping. The triangular points are especially good for this purpose, since they are stable equilibrium points.In this paper, the planar restricted four-body problem applied to the Sun–Earth–Moon–Spacecraft is combined with numerical integration and gradient methods to solve the two-point boundary value problem. This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Earth–Sun system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth.The dynamics given by the restricted four-body problem is used to obtain the trajectory of the spacecraft, but not the position of the equilibrium points. Their position is taken from the restricted three-body model. The goal to use this model is to evaluate the perturbation of the Sun in those important trajectories, in terms of fuel consumption and time of flight. The solutions will also show how to apply the impulses to accomplish the transfers under this force model.The results showed a large collection of transfers, and that there are initial conditions (position of the Sun with respect to the other bodies) where the force of the Sun can be used to reduce the cost of the transfers.     

The knowledge of knots: an interdisciplinary literature review

ABSTRACT

Knots can be found and used in a variety of situations in the 3D world, such as in vines, in the DNA, polymer chains, electrical wires, in mountaineering, seamanship and when ropes or other flexible objects are involved for exerting forces and holding objects in place. Research on knots as topological entities has contributed with a number of findings, not only of interest to pure mathematics, but also to statistical mechanics, quantum physics, genetics, and chemistry. Yet, the cognitive (or algorithmic) aspects involved in the act of tying a knot are a largely uncharted territory. This paper presents a review of the literature related to the investigation of knots from the topological, physical, cognitive and computational (including robotics) standpoints, aiming at bridging the gap between pure mathematical work on knot theory and macroscopic physical knots, with an eye to applications and modeling.     

The perfect boring situation—Addressing the experience of monotony during crewed deep space missions through habitability design

In contemporary orbital missions, workloads are so high and varied that crew may rarely experience stretches of monotony. However, in historical long duration missions, occurrences of monotony were, indeed, reported anecdotally by crew. Of the effective countermeasures that appear to be at hand, many rely on visual or logistical proximity to the Earth, and are not feasible in the remote context of an extended deep space mission scenario. There, particularly in- and outbound cruising stages would be characterised by longer, comparably uneventful periods of low workload, coupled with confinement and unchanging vehicle surroundings.