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

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

Interstellar Object Uncertainty Evolution and Effect on Fast Flyby Delivery and Required Delta-V

Interstellar objects (ISOs) are small bodies that can travel through our solar system from other star systems. When present in our solar system, they represent an opportunity to study the properties and origins of these objects, as well as the potential for cross-pollination of material between star systems. With current propulsion technology, rendezvous with these objects is likely infeasible, and thus the maximum science return results from a rapid response flyby and impactor. However, while trajectories to ISOs may be feasible, their potentially high ephemeris uncertainties and high-speed hyperbolic orbits present significant challenges to navigation. In this paper we assess these challenges by modeling the uncertainties of reachable synthetic ISOs as a function of time, as derived by measurements from ground observatories and an approaching spacecraft. From these uncertainties we derive the final delivery accuracy of fast flyby spacecraft to the ISO and required statistical delta-v for navigation. We find that these two challenges can lead to hundreds of meters-per-second or even kilometers-per-second of required statistical delta-v for navigation, reduce delivery accuracy to hundreds of kilometers, and make autonomous navigation a requirement