Evaluating the impact of space activities in low earth orbit

Abstract The evolution of cataloged orbital debris in low Earth orbit (LEO) over the last quarter of century was analyzed in detail, to gather insights on the development of space activities, on the effectiveness of the debris mitigation measures recommended in the meantime, and on the environmental impact of fragmentations, in particular collisions, both intentional and accidental. The main conclusion was that the observed evolution matched on the whole the predictions of the unmitigated business-as-usual scenarios simulated twenty years ago, and that the benefits caused by the progressive worldwide adoption of mitigation measures were unfortunately offset by a couple of catastrophic collisions and prolonged weak solar activity. Concerning the recorded growth of cataloged fragmentation debris, nowhere have the signs of an exponential increase been revealed so far. Nevertheless, the overall picture has worsened during the last quarter of a century and extreme care is required in planning and conducting new space activities from now on, especially in a phase of increased and ever more rapid exploitation. In order to assess the sustainability of space activities, especially over the next 10–30 years, several environmental criticality indexes have been introduced and discussed, estimating their current values in LEO, as well as their magnitudes associated with specific scenarios of debris growth. They could provide simple tools for evaluating the relative and absolute impact on the debris environment, either in LEO as a whole or in specific altitude shells, of new spacecraft deployments and operations, as in the case of mega-constellations of satellites. The main result of this preliminary analysis was that all indexes were consistent in indicating that from one third to one half of the LEO capacity to sustain long-term space activities – as they are currently conceived – has already been saturated. The 2020s, with their many planned launches, will therefore be crucial years for enforcing more effective debris mitigation and remediation measures

Evolution of the Debris Cloud Generated by the Fengyun-1C Fragmentation Event

The cloud of cataloged debris produced in low earth orbit by the fragmentation of the Fengyun-1C spacecraft was propagated for 15 years, taking into account all relevant perturbations. Unfortunately, the cloud resulted to be very stable, not suffering substantial debris decay during the time span considered. The only significant short term evolution was the differential spreading of the orbital planes of the fragments, leading to the formation of a debris shell around the earth approximately 7-8 months after the breakup, and the perigee precession of the elliptical orbits. Both effects will render the shell more "isotropic" in the coming years. The immediate consequence of the Chinese anti-satellite test, carried out in an orbital regime populated by many important operational satellites, was to increase significantly the probability of collision with man-made debris. For the two Italian spacecraft launched in the first half of 2007, the collision probability with cataloged objects increased by 12% for AGILE, in equatorial orbit, and by 38% for COSMO-SkyMed 1, in sun-synchronous orbit

A minimalistic approach for fast computation of geodesic distances on triangular meshes

The computation of geodesic distances is an important research topic in Geometry Processing and 3D Shape Analysis as it is a basic component of many methods used in these areas. In this work, we present a minimalistic parallel algorithm based on front propagation to compute approximate geodesic distances on meshes. Our method is practical and simple to implement and does not require any heavy pre-processing. The convergence of our algorithm depends on the number of discrete level sets around the source points from which distance information propagates. To appropriately implement our method on GPUs taking into account memory coalescence problems, we take advantage of a graph representation based on a breadth-first search traversal that works harmoniously with our parallel front propagation approach. We report experiments that show how our method scales with the size of the problem. We compare the mean error and processing time obtained by our method with such measures computed using other methods. Our method produces results in competitive times with almost the same accuracy, especially for large meshes. We also demonstrate its use for solving two classical geometry processing problems: the regular sampling problem and the Voronoi tessellation on meshes.Comment: Preprint submitted to Computers & Graphic

Dictionary Learning-based Inpainting on Triangular Meshes

The problem of inpainting consists of filling missing or damaged regions in images and videos in such a way that the filling pattern does not produce artifacts that deviate from the original data. In addition to restoring the missing data, the inpainting technique can also be used to remove undesired objects. In this work, we address the problem of inpainting on surfaces through a new method based on dictionary learning and sparse coding. Our method learns the dictionary through the subdivision of the mesh into patches and rebuilds the mesh via a method of reconstruction inspired by the Non-local Means method on the computed sparse codes. One of the advantages of our method is that it is capable of filling the missing regions and simultaneously removes noise and enhances important features of the mesh. Moreover, the inpainting result is globally coherent as the representation based on the dictionaries captures all the geometric information in the transformed domain. We present two variations of the method: a direct one, in which the model is reconstructed and restored directly from the representation in the transformed domain and a second one, adaptive, in which the missing regions are recreated iteratively through the successive propagation of the sparse code computed in the hole boundaries, which guides the local reconstructions. The second method produces better results for large regions because the sparse codes of the patches are adapted according to the sparse codes of the boundary patches. Finally, we present and analyze experimental results that demonstrate the performance of our method compared to the literature

Class, type and position of 9148 surgically removed third molars in 3206 patients : a retrospective study

Objective: To investigate the class, type, position, diagnosis and most common procedures used in the surgical removal of third molars, and evaluate the sex and age distribution in a representative sample of Mexican patients. Study Design: A retrospective descriptive study was made covering the period 1993-2008 in relation to 9148 extracted third molars in 3206 patients treated in the Dental School of Salle Bajío University, A.C. (Mexico). Patients of either sex and aged 11-59 years, with at least one third molar programmed for surgical removal, were included in the study. A descriptive statistical study was made. Results: The mean patient age was 27.6 ± 10.6 years. There were 2093 females (65.3%) and 1111 males (34.6%). In relation to the 4025 upper molars, extraction was decided for prophylactic reasons in 3827 cases (95.08%). Type A presentations were recorded in 1929 cases (47.9%), with a vertical position in 1931 teeth (48%). In relation to the 5123 lower third molars, extraction was likewise most often indicated for prophylactic reasons (4424 cases, 86.36%). A total of 2353 teeth corresponded to type A (45.9%), 2545 were class I cases (49.7%), and a mesioangular position was observed in 1850 cases (36.1%). Conclusions: The present study shows that in Mexican patients, upper third molars most often correspond to type A and class I, with a vertical position, while lower third molars predominantly correspond to type A and class I, with a mesioangular position. This information can help dental surgeons take better decisions before and after surgery, to the benefit of their patients

Testing gravitation with satellite laser ranging and the LARASE experiment

The International Laser Ranging Service (ILRS) provides range measurements of pas- sive satellites around the Earth through the powerful Satellite Laser Ranging (SLR) technique. These very precise measurements of the distance between an on-ground laser station and a satellite equipped with cube corner retro-reflectors (CCRs) make possible precise tests and measurements in fundamental physics and, in particular, in gravitational physics. The LAGEOS (NASA 1976) and LAGEOS II (NASA/ASI 1992) satellites are outstanding examples of very good test particles because of their very low area-to-mass ratio as well as the high quality of their tracking data and, consequently, of the precise orbit determination (POD) we can obtain after a refined modeling of their orbit. The aim of our research program LARASE (LAser RAnged Satellites Experi- ment) is to go a step further in testing gravitation in the field of Earth by means of the joint analysis of the orbits of the two LAGEOS satellites together with that of the most recently launched LARES (ASI, 2012) satellite. Therefore, our work falls in the so-called weak field and slow motion (WFSM) limit of Einstein’s general relativity (GR) where, in terms of Newtonian physics, relativistic effects appear as two new fields to be added to the classical gravitational field: the gravitoelectric and the gravitomagnetic fields. A fundamental ingredient to reach such a goal is to provide high-quality updated models for the perturbing non-gravitational perturbations (NGP) acting on the surface of these satellites. In fact, regardless of their minimization thanks to a smaller value for the area-to-mass ratio, the subtle and complex to model perturbing effects of the NGP play a crucial role in the POD of the considered satellites, especially in the case of the thermal thrust effects. A large amount of SLR data of LAGEOS and LAGEOS II has been worked out using a set of dedicated models for the satellite dynamics and the related post-fit residuals have been analyzed. A parallel work was performed with LARES, although at a preliminary stage. Our recent work on the orbit modeling and on the data analysis of the orbit of such satellites is presented and discussed

A 1% Measurement of the gravitomagnetic field of the earth with laser-tracked satellites

A new measurement of the gravitomagnetic field of the Earth is presented. The measurement has been obtained through the careful evaluation of the Lense-Thirring (LT) precession on the combined orbits of three passive geodetic satellites, LAGEOS, LAGEOS II, and LARES, tracked by the Satellite Laser Ranging (SLR) technique. This general relativity precession, also known as frame-dragging, is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein’s theory of gravitation. The measurement stands out, compared to previous measurements in the same context, for its precision (≃7.4×10−3, at a 95% confidence level) and accuracy (≃16×10−3), i.e., for a reliable and robust evaluation of the systematic sources of error due to both gravitational and non-gravitational perturbations. To achieve this measurement, we have largely exploited the results of the GRACE (Gravity Recovery And Climate Experiment) mission in order to significantly improve the description of the Earth’s gravitational field, also modeling its dependence on time. In this way, we strongly reduced the systematic errors due to the uncertainty in the knowledge of the Earth even zonal harmonics and, at the same time, avoided a possible bias of the final result and, consequently, of the precision of the measurement, linked to a non-reliable handling of the unmodeled and mismodeled periodic effects