Multiple solutions for asteroid orbits: Computational procedure and applications

We describe the Multiple Solutions Method, a one-dimensional sampling of the six-dimensional orbital confidence region that is widely applicable in the field of asteroid orbit determination. In many situations there is one predominant direction of uncertainty in an orbit determination or orbital prediction, i.e., a ``weak'' direction. The idea is to record Multiple Solutions by following this, typically curved, weak direction, or Line Of Variations (LOV). In this paper we describe the method and give new insights into the mathematics behind this tool. We pay particular attention to the problem of how to ensure that the coordinate systems are properly scaled so that the weak direction really reflects the intrinsic direction of greatest uncertainty. We also describe how the multiple solutions can be used even in the absence of a nominal orbit solution, which substantially broadens the realm of applications. There are numerous applications for multiple solutions; we discuss a few problems in asteroid orbit determination and prediction where we have had good success with the method. In particular, we show that multiple solutions can be used effectively for potential impact monitoring, preliminary orbit determination, asteroid identification, and for the recovery of lost asteroids

Orbit determination of space objects based on sparse optical data

While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained at different times. This correlation step is the most computationally intensive, and becomes more and more difficult as the number of objects to be discovered increases. In this paper we tested two different algorithms (and the related prototype software) recently developed to solve the correlation problem for objects in geostationary orbit (GEO), including the accurate orbit determination by full least squares solutions with all six orbital elements. Because of the presence in the GEO region of a significant subpopulation of high area to mass objects, strongly affected by non-gravitational perturbations, it was actually necessary to solve also for dynamical parameters describing these effects, that is to fit between 6 and 8 free parameters for each orbit. The validation was based upon a set of real data, acquired from the ESA Space Debris Telescope (ESASDT) at the Teide observatory (Canary Islands). We proved that it is possible to assemble a set of sparse observations into a set of objects with orbits, starting from a sparse time distribution of observations, which would be compatible with a survey capable of covering the region of interest in the sky just once per night. This could result in a significant reduction of the requirements for a future telescope network, with respect to what would have been required with the previously known algorithm for correlation and orbit determination.Comment: 20 pages, 8 figure

Orbit Determination with the two-body Integrals

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results from the observation error statistics. The performance of this method has been investigated by using a large set of simulated observations of the Pan-STARRS project.Comment: 23 pages, 1 figur

Frequency based localization of structural discrepancies

The intent of modal analysis is to develop a reliable model of a structure by working with the analytical and experimental modal properties of frequency, damping and mode shape. In addition to identifying these modal properties, it would be desirable to determine spatially which parts of the structure are modelled poorly or well. It is shown how the pattern of discrepancies in the analytical and experimental test values for the pole and the driving point zero frequencies of a structure can be linked to discrepancies in the mass or stiffness of the structural elements. The success of the procedure depends on the numerical conditioning of a modal reference matrix. Strategies to insure adequate numerical conditioning require a formulation which avoids geometric and energy storage symmetries of the structure, and ignores structural elements which contribute negligibly small potential or kinetic energy to the excited modes. Physical insight into the numerical conditioning problem is provided by a numerical example and by localization of a mass discrepancy in a real structure based on lab tests

Innovative methods of correlation and orbit determination for space debris

We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the $J_2$ effect.Comment: 18 page

Semi-analytical mechanical model for FRCM-to-substrate shear bond tests

The debonding process of an FRCM reinforcing system from the substrate is studied in a semi-analytical fashion. FRCM is modeled considering independently the central elastic fiber grid and the two thick upper and lower matrix layers, assumed elasto-fragile; matrix and fiber are considered in a monoaxial state of stress; they mutually exchange shear stresses at the interface, this latter characterized by a softening stress-slip relationship; the reinforcement system is then bonded with a rigid substrate by means of a further elastic interface. Under such hypotheses, a simple system of first order non-linear and coupled differential equations is derived and solved by means of a semi-analytical approach. Independent variables are the axial displacements of the three layers (upper and lower matrix, central fiber) and the corresponding axial stresses. The approach is successfully validated against two experimental datasets available in the literature, relying into different FRCM strengthening systems bonded to rigid substrates and subjected to single lap shear tests. The model is able to capture not only the global debonding behavior but also the local one, with a precise prediction along the bond length of the shape of the axial stresses into the different layers, of the interface shear stresses and of the location of the cracks inside the matrix

Comparison of the fluctuation influence on the resistive properties of the mixed state of BiSrCaCuO and of thin films of conventional superconductor

The resistive properties of layered HTSC BiSrCaCuO in the mixed state are compared with those of thin films of conventional superconductors with weak disorders (amorphous Nb_{1-x}0_{x} films) and with strong disorders (Nb_{1-x}O_{x} films with small grain structure). The excess conductivity is considered as a function of superconducting electron density and phase coherence length. It is shown that the transition to the Abrikosov state differs from the ideal case both in BiSrCaCuO and Nb_{1-x}O_{x} films, i.e. the appearance of long-range phase coherence is continuous transition in both cases. The quantitative difference between thin films with weak and strong disorders is greater than the one between layered HTSC and conventional superconductors, showing that the dimensionality of the system, rather than the critical temperature, is the key factor ruling fluctuation effectsComment: 17 pages, 5 figure

Vulcanization degree influence on the mechanical properties of Fiber Reinforced Elastomeric Isolators made with reactivated EPDM

Rubber is well known as the basic material for some structural devices, such as seaport fenders and seismic isolators. In practice, to seismically isolate a structure it is necessary to interpose between the foundation and the superstructure a rubber device that increases the period of the superstructure, a feature that allows the structure to be “transparent” to the seismic excitation. A seismic isolator is constituted typically by a package of several rubber pads 1–2 cm thick vertically interspersed with either steel laminas or FRP dry textiles suitably treated. In this latter case the isolator is called FREI (Fiber Reinforced Elastomeric Isolator). FREIs exhibit light weight, easy installation and low cost. In this study, recycled rubber in the form of reactivated EPDM has been used to produce very low cost FREIs, combined with glass fiber reinforcement. To be ready for structural application, the rubber used must be vulcanized correctly to properly create the polymer crosslinking. However, all rubber mechanical properties are strongly affected by curing temperature and curing time. Here, the mechanical properties of a typology of FREI conceived and produced by the authors in prototypes are evaluated through a series of experimental tests and numerical computations, taking into account the different levels of vulcanization degree. Shore A hardness test, uniaxial tensile test, and relaxation test have been conducted and verified through Finite Element (FE) modeling. All collected data allow to precisely determine the curing time and temperature to use in the industrial production to obtain optimal output mechanical properties for FREIs

Light-time computations for the BepiColombo radioscience experiment

The radioscience experiment is one of the on board experiment of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian (PN) parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the space-time coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations.Comment: 14 pages, 7 figures, corrected reference