Analytic expansions of luni-solar gravity perturbations along rotating axes for trajectory optimization—Part 2: The multipliers system and simulations

An efficient self-contained trajectory optimization software is generated by making use of de Pontécoulant's analytic lunar theory removing the need for an outside third body ephemeris program to compute the lunar and solar position vectors at each integration step. The accelerations being further resolved along the rotating Euler–Hill frame after expansion to third order in the spacecraft radial distance, the adjoint differential equations are derived in a direct manner complementing the generation of the dynamic system of equations for full compatibility. Because the variation of parameters equations are cast in terms of the nonsingular equinoctial elements with the perturbation accelerations resolved in their analytic form along the rotating axes, the adjoint equations are also derived in the same manner providing a highly efficient and accurate system of equations for rapid computations in conjunction with Aerospace Corporation's NLP2 nonlinear programming codes to search for the initial values of the multipliers that steer the spacecraft towards its target orbit in minimum time. Numerical simulations show that the solutions obtained by the analysis developed in this paper are essentially identical to the more indirect approach based on the use of inertial accelerations obtained from a separate ephemeris generator and subsequent conversions to the thrust frame and equinoctial system.     

Solution to the problem of stability of regular precessions of a symmetrical gyrostat in Newtonian field

The constraints imposed on parameters of a force field and of a symmetrical gyrostat in it are determined, at which regular precession of this gyrostat demonstrate Lyapunov stability (or, respectively, instability).     

Transformation of the Spectrum of a Signal in Communication between Relativistically Moving Inertial Frames

Future space exploration may involve communications between spacecraft moving at relativistic velocities. One of the significant problems associated with such communication is spectral distortion of signals which are propagated between relativistic frames. This distortion is generated by both changing propagation distances and purely relativistic electromagnetic field transformations. In this paper a linear integral transformation is formulated for relating the Fourier spectra of the source antenna excitation current and the resulting incident electric field at the receiving antenna. The kernel of the transformation is evaluated for the case of a steerable source antenna tracking on the advanced receiver position. The transformation is then applied to the case of an ideal thin-wire half-wave dipole source antenna excited by a narrowband, double-sideband modulated current. The specific distortions of spectral spreading and translation are then related to increased bandwidth and upper cutoff frequency requirements of receiving systems in relativistic applications.     

UWB radar detection of targets in foliage using alpha-stableclutter models

We address the problem of detection of targets obscured by a forest canopy using an ultrawideband (UWB) radar. The forest clutter observed in the radar imagery is a highly impulsive random process that is more accurately modeled with the recently proposed class of alpha-stable processes as compared with Gaussian, Weibull, and K-distribution models. With this more accurate model, segmentation is performed on the imagery into forest and clear regions. Further, a region-adaptive symmetric alpha stable (SαS) constant false-alarm rate (CFAR) detector is introduced and its performance is compared with the Weibull and Gaussian CFAR detectors. The results on real data show that the SαS CFAR performs better than the Weibull and Gaussian CFAR detectors in detecting obscured targets     

Consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface

Possible consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface are described. The methodological basis of classification of consequences is the solution of meteor physics equations characterizing the trajectory of a body in the atmosphere, namely, the dependence of the body’s velocity and mass on the flight altitude. The solution depends on two dimensionless parameters characterizing the drag altitude and the role of mass loss by a meteoroid during its motion in the atmosphere. Depending on values of these parameters, the degree of effect on the planetary surface considerably changes. In particular, the conditions of cratering and meteorite fall on the planetary surface are obtained. The results are presented in a simple analytical form. They quite match to the real events considered in the paper. Recommendations are given on further investigations into the important problem of interaction of cosmic bodies with planetary atmospheres.     

Wave resistance defect in a planar flow over periodic reliefs

The dependence of the wave resistance coefficients for planar periodic reliefs on the similarity parameters is investigated. It is proved that the wave resistance coefficients of the infinite reliefs and their finite analogs in the case of the whole wave numbers coincide, whereas in the case of the fractional wave numbers they differ.     

The effect of geocenter motion on Jason-2 orbits and the mean sea level

We compute a series of Jason-2 GPS and SLR/DORIS-based orbits using ITRF2005 and the std0905 standards ( Lemoine et al., 2010). Our GPS and SLR/DORIS orbit data sets span a period of 2 years from cycle 3 (July 2008) to cycle 74 (July 2010). We extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. We compare the annual terms of these time-series to the annual terms of two different geocenter motion models where biases and trends have been removed. Subsequently, we include the annual terms of the modeled geocenter motion as a degree-1 loading displacement correction to the GPS and SLR/DORIS tracking network of the POD process. Although the annual geocenter motion correction would reflect a stationary signal in time, under ideal conditions, the whole geocenter motion is a non-stationary process that includes secular trends. Our results suggest that our GSFC Jason-2 GPS-based orbits are closely tied to the center of mass (CM) of the Earth consistent with our current force modeling, whereas GSFC’s SLR/DORIS-based orbits are tied to the origin of ITRF2005, which is the center of figure (CF) for sub-secular scales. We quantify the GPS and SLR/DORIS orbit centering and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the annual term of the geocenter correction. We find that for the SLR/DORIS std0905 orbits, currently used by the oceanographic community, only the negligence of the annual term of the geocenter motion correction results in a – 4.67 ± 3.40 mm error in the Z-component of the orbit frame which creates 1.06 ± 2.66 mm of systematic error in the MSL estimates, mainly due to the uneven distribution of the oceans between the North and South hemisphere.     

Vibrations of a shell with the discretely attached dynamic subsystem

A problem on low vibrations of a thin spherical shell is considered. A solid of finite dimensions is discretely attached to the shell by means of an elastic rod system. The calculation examples are presented.