Error Covariance Analysis of a Karhunen-Loeve Random Field Estimator

An error covariance analysis of a two-dimensional Karhunen-Loeve random field estimator (KLE) for gridded gravity data is presented without actually using the data. Attention is focused particularly on the north-south deflection component of the disturbance vector so that the rms value of its residual error may not exceed 3 percent of the signal rms for grid spacing of not less than 5 nm, when signal-to-noise ratio in the data is varied within reasonable limits. To achieve this rather stringent goal, a discrete KLE derived entirely from a two-dimensional grid configuration is needed. The KLE for geodesy applications was developed initially by Bose. Using continuous measurements and the orthogonality relations of the Karhunen-Loeve (KL) eigenvectors in a continuous domain, continuous KL gain coefficients ?mnj and consequently the continuous KL gain vector Kmn were obtained; thus a satisfactory continuous KLE was achieved. However the discrete version of the KLE was then given by keeping the old (continuous) ?mnj, and simply computing the KL eigenvectors on the grid coordinates to evaluate the discrete KL gain vector Kmn. Clearly this is not a satisfactory discrete KLE since , ?mnj are not constants but rather depend on the measurement noise variances. So if the measurements are now going to be discrete, one must rederive ?mnj for this situation.     

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune–Triton system

The problem of a spacecraft orbiting the Neptune–Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune’s satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a × I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton’s orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L₂, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincaré section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method.     

On the planetary ionospheric vortex electric fields

The paper presents a physical mechanism of large-scale vortex electric field generation in the ionospheric E- and F-layers. It shows that the planetary-scale, synoptic short-period (from several second to several hours) and fast processes (with propagation velocity higher than 1 km/s) produce a planetary-scale internal vortex electric field. Its value may far exceed that of the dynamo-field generated in the same ionospheric layer by local wind motion. We found, that an ionospheric source of the vortex electric field is spatial inhomogeneity of the geomagnetic field.     

Small-Scale Solar Magnetic Fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.     

Mathematical description of the NaK model for MASTER-2005

The release of NaK droplets has been modeled for the new version of the European Meteoroid and Space Debris Terrestrial Environment Reference model MASTER-2005. Previously published versions of the model have been revised. The parameters of the model are introduced and discussed. NaK droplets consist of eutectic sodium–potassium alloy and have been released during RORSAT reactor core ejections. They contributed to the space debris environment in the centimeter and millimeter size regime. Sixteen nuclear powered RORSATs launched between 1980 and 1988 activated a reactor core ejection system in Sufficiently High Orbits (SHO), mostly between 900 and 950 km altitude. The core ejection caused an opening of the primary coolant circuit. The liquid coolant has been released into space during these core ejections. The outflow is considered as a discrete event for each of the sixteen core ejections in total. The NaK coolant has been forming droplets up to a diameter of 5.5 cm. NaK releases are restricted to a very narrow region near 65° inclination. This paper gives the parameters of the NaK release model as it is implemented in MASTER-2005. The quantitative values of all model parameters including characteristic diameter and uniformity parameter are presented. The ratio of the characteristic droplet size to the orifice diameter is discussed. It is estimated that altogether 128 kg of NaK-78 (8 kg per RORSAT) was released on orbit. Simulation runs show that there are still 45,000 droplets with a total mass of 97 kg in orbit at the reference epoch 1 May 2005, whereas the smallest droplet has a diameter of 5 mm. Results of orbit propagation simulation runs are presented in terms of spatial density.     

Permanent-Magnet Linear Alternators Part 1: Fundamental Equations

Powered by free-piston Stirling engines, linear alternators are proposed for space power stations as well as for isolated domestic applications, automotive, and on-Earth solar power plants. As the literature on the subject is sparse and base-design oriented, we present the general equations for both three-phase and single-phase winding configurations having permanent-magnet field excitations.     

An Adaptive Multiple-Beam Transmitter for Satellite Communications

A multiple-beam satellite communications system that can adaptbeam power to varying beam traffic is proposed. A new type active-array fed, single reflector antenna design and an S band, 5-beamsystem concept including interbeam exchange are described. Basedon these concepts, a high EIRP multiple-beam system with trafficadaptability similar to a single-beam system is realized.     

Software intensive systems safety analysis

Two important elements in the avionics suite of modern aircraft are: the flight control system (FCS) and the flight management system (FMS). The FCS provides the capability to stabilize and control the aircraft, while the FMS is responsible for flight planning and navigation. A clear trend in the aerospace industry is to place greater reliance on software systems, and many FCS and FMS subsystems are implemented primarily in software. For example, within the FCS is the flight guidance system (FGS) that generates roll and pitch guidance commands. Similarly, within the FMS is the vertical navigation (VNAV) function that acts like a third crew member in the cockpit, ordering mode change requests and resetting target altitude values to enable the aircraft to track the vertical flight plan. We have developed formal, executable models of the requirements for the mode logic of a FGS and for portions of the VNAV functionality. We have also conducted a comprehensive software safety analysis on the FGS mode logic model, and are completing the analysis of the VNAV model. This analysis uses as its starting point several "traditional" safety analysis techniques such as a functional hazard assessment (FHA), a fault tree analysis (FTA), and a failure mode effects analysis (FMEA). However, we are also using formal methods techniques known as model checking and theorem proving to verify the presence of safety properties in the model. This paper summarizes the (now completed) safety analysis that was performed on the FGS model, and highlights the similarities and differences with the (still on-going) safety analysis of the FMS model. In particular, we summarize progress made to date in the use of formal methods to verify the presence of the required safety properties in the models themselves.