Systematic ranging and late warning asteroid impacts

We describe systematic ranging, an orbit determination technique especially suitable to assess the near-term Earth impact hazard posed by newly discovered asteroids. For these late warning cases, the time interval covered by the observations is generally short, perhaps a few hours or even less, which leads to severe degeneracies in the orbit estimation process. The systematic ranging approach gets around these degeneracies by performing a raster scan in the poorly-constrained space of topocentric range and range rate, while the plane of sky position and motion are directly tied to the recorded observations. This scan allows us to identify regions corresponding to collision solutions, as well as potential impact times and locations. From the probability distribution of the observation errors, we obtain a probability distribution in the orbital space and then estimate the probability of an Earth impact. We show how this technique is effective for a number of examples, including 2008 TC3 and 2014 AA, the only two asteroids to date discovered prior to impact

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

Constraints on the near-Earth asteroid obliquity distribution from the Yarkovsky effect

Aims. From lightcurve and radar data we know the spin axis of only 43 near-Earth asteroids. In this paper we attempt to constrain the spin axis obliquity distribution of near-Earth asteroids by leveraging the Yarkovsky effect and its dependence on an asteroid’s obliquity. Methods. By modeling the physical parameters driving the Yarkovsky effect, we solve an inverse problem where we test different simple parametric obliquity distributions. Each distribution results in a predicted Yarkovsky effect distribution that we compare with a X2 test to a dataset of 125 Yarkovsky estimates. Results. We find different obliquity distributions that are statistically satisfactory. In particular, among the considered models, the best-fit solution is a quadratic function, which only depends on two parameters, favors extreme obliquities, consistent with the expected outcomes from the YORP effect, has a 2:1 ratio between retrograde and direct rotators, which is in agreement with theoretical predictions, and is statistically consistent with the distribution of known spin axes of near-Earth asteroids

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 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