Innovative observing strategy and orbit determination for Low Earth Orbit Space Debris

We present the results of a large scale simulation, reproducing the behavior of a data center for the build-up and maintenance of a complete catalog of space debris in the upper part of the low Earth orbits region (LEO). The purpose is to determine the performances of a network of advanced optical sensors, through the use of the newest orbit determination algorithms developed by the Department of Mathematics of Pisa (DM). Such a network has been proposed to ESA in the Space Situational Awareness (SSA) framework by Carlo Gavazzi Space SpA (CGS), Istituto Nazionale di Astrofisica (INAF), DM, and Istituto di Scienza e Tecnologie dell'Informazione (ISTI-CNR). The conclusion is that it is possible to use a network of optical sensors to build up a catalog containing more than 98% of the objects with perigee height between 1100 and 2000 km, which would be observable by a reference radar system selected as comparison. It is also possible to maintain such a catalog within the accuracy requirements motivated by collision avoidance, and to detect catastrophic fragmentation events. However, such results depend upon specific assumptions on the sensor and on the software technologies

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

Nanoscale roughness and morphology affect the IsoElectric Point of titania surfaces

We report on the systematic investigation of the role of surface nanoscale roughness and morphology on the charging behaviour of nanostructured titania (TiO2) surfaces in aqueous solutions. IsoElectric Points (IEPs) of surfaces have been characterized by direct measurement of the electrostatic double layer interactions between titania surfaces and the micrometer-sized spherical silica probe of an atomic force microscope in NaCl aqueous electrolyte. The use of a colloidal probe provides well-defined interaction geometry and allows effectively probing the overall effect of nanoscale morphology. By using supersonic cluster beam deposition to fabricate nanostructured titania films, we achieved a quantitative control over the surface morphological parameters. We performed a systematical exploration of the electrical double layer properties in different interaction regimes characterized by different ratios of characteristic nanometric lengths of the system: the surface rms roughness Rq, the correlation length {\xi} and the Debye length {\lambda}D. We observed a remarkable reduction by several pH units of IEP on rough nanostructured surfaces, with respect to flat crystalline rutile TiO2. In order to explain the observed behavior of IEP, we consider the roughness-induced self-overlap of the electrical double layers as a potential source of deviation from the trend expected for flat surfaces.Comment: 63 pages, including 7 figures and Supporting Informatio

A Possibility to Build Isolated Masonry Housing in High Seismic Zones Using Rubber Seismic Isolators

New residential buildings in developing countries often have inadequate seismic protection, particularly for masonry. Such material is widely preferred because the cost and application are relatively cheap. To decrease the vulnerability, an interesting option is represented by seismic isolation, but the cost should remain relatively low, and this is the reason why rubber isolation with few pads remains the most suitable technical solution to adopt. In this study, we deal with a newly conceived low-cost seismic isolation system for masonry buildings relying on elastomeric bearings. The elastomeric isolator here proposed consists of few layers of rubber pads and fiber lamina, making it cheaper comparing to the conventional isolators. A detailed 3D finite element (FE) analysis to predict the behavior of the low-cost rubber isolator undergoing moderate deformations is carried out. A Yeoh hyperelasticity model with coefficients estimated through available experimental data is assumed for rubber pads. Having so derived the shear behavior, such isolation system is implemented at a structural level into a two stories masonry house prototype, identifying the 3D model with a damped nonlinear spring model, so making the FE analysis computationally inexpensive. For masonry, a concrete damage plasticity (CDP) model available in the commercial FE code Abaqus is adopted. A nonlinear static-pushover analysis is conducted to assess the performance of the isolated building. To simulate a realistic condition under seismic event, a ground motion data is applied to observe the dynamic behavior of the building by monitoring the damage level of masonry. Through a-posterior estimation, it is also possible to monitor the deformation of the isolators during the seismic excitation, to determine whether the isolator is capable of resisting shear deformations in different angles. According to the results obtained, quite good isolation is obtained with the system proposed, with immediate applicability at a structural level

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

The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities

We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular evolution of the orbital elements of the asteroid is computed by averaging the equations of motion over the mean anomalies of the asteroid and the planet. When an orbit crossing with the planet occurs the averaged equations become singular. However, it is possible to define piecewise differentiable solutions by extending the averaged vector field beyond the singularity from both sides of the orbit crossing set. In this paper we improve the previous results, concerning in particular the singularity extraction technique, and show that the extended vector fields are Lipschitz-continuous. Moreover, we consider the distance between the Keplerian trajectories of the small body and of the planet. Apart from exceptional cases, we can select a sign for this distance so that it becomes an analytic map of the orbital elements near to crossing configurations. We prove that the evolution of the 'signed' distance along the averaged vector field is more regular than that of the elements in a neighborhood of crossing times. A comparison between averaged and non-averaged evolutions and an application of these results are shown using orbits of near-Earth asteroids.Comment: 29 pages, 8 figure