A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation

Three methods for the computation of the probability of collision between two space objects are presented. These methods are based on the high order Taylor expansion of the time of closest approach (TCA) and distance of closest approach (DCA) of the two orbiting objects with respect to their initial conditions. The identification of close approaches is first addressed using the nominal objects states. When a close approach is identified, the dependence of the TCA and DCA on the uncertainties in the initial states is efficiently computed with differential algebra (DA) techniques. In the first method the collision probability is estimated via fast DA-based Monte Carlo simulation, in which, for each pair of virtual objects, the DCA is obtained via the fast evaluation of its Taylor expansion. The second and the third methods are the DA version of Line Sampling and Subset Simulation algorithms, respectively. These are introduced to further improve the efficiency and accuracy of Monte Carlo collision probability computation, in particular for cases of very low collision probabilities. The performances of the methods are assessed on orbital conjunctions occurring in different orbital regimes and dynamical models. The probabilities obtained and the associated computational times are compared against standard (i.e. not DA-based) version of the algorithms and analytical methods. The dependence of the collision probability on the initial orbital state covariance is investigated as wel

EVOLUTION OF THE (AERO)SPACE ENGINEERING STUDIES IN ITALY IN THE PAST 20 YEARS

The paper presents the evolution and trends in the Master studies in aerospace engineering in Italy, looking at the last 20 years. In the year 2000, a major reform of the higher education in engineering took place in Italy, with the introduction of the so-called “Bologna system” and the clear separation of Bachelor and Master studies. With this reform, a relatively high flexibility was given to universities to define their program structures. The ministerial rules defined only broad subject areas within which courses and credits should be allocated. This reform allowed to diversify the educational profile within each University and, even more relevant, allowed to create mobility across the country between Bachelor and Master study programs. The paper will show the basic facts and figures in the 6 Italian Universities participating in the PEGASUS network (Politecnico di Milano, Politecnico di Torino, Università di Pisa, Università degli Studi di Napoli “Federico II”, Sapienza Università di Roma, Alma Mater Studiorum - Università di Bologna), elaborating on the impact of the potential workforce for the sector

Rosetta Philae SD2 Drill System and Its Operation on 67p/Churyumov-Gerasimenko

Rosetta Lander Philae approached and landed on the surface of comet 67P/Churyumov-Gerasimenko on the 12th of November 2014. Among the specific Subsystems and instruments carried on board, the Drill, Sample and Distribution System (SD2) which was in charge to drill the surface of the comet, take comet’s soil sample(s) and distribute the collected sample to different instruments. Rosetta has been launched in 2004 and, after very complex orbital trajectories and specific commissioning events, met and carried out a rendezvous with the comet; after ten years cruise and three subsequent touch down, Philae eventually landed on the comet surface. On the 14th of November 2014 SD2 was decided to be operated on the comet. This paper provides an overview of the achievements during the operational phase on the comet and will summarize the basic characteristics and peculiarities of SD2 drill system

An automatic domain splitting technique to propagate uncertainties in highly nonlinear orbital dynamics

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails in highly nonlinear dynamics or long term propagation. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial of the current state is split in two polynomials when its accuracy reaches a given threshold. The resulting polynomials accurately track uncertainties, even in highly nonlinear dynamics. The method is tested on the propagation of (99942) Apophis post-encounter motion

Propagation of Large Uncertainty Sets in Orbital Dynamics by Automatic Domain Splitting

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails when the non-linearities of the dynamics prohibit good convergence of the Taylor expansion in one or more directions. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial expansion of the current state is split into two polynomials whenever its truncation error reaches a predefined threshold. The resulting set of polynomials accurately tracks uncertainties, even in highly nonlinear dynamics. The method is tested on the propagation of (99942) Apophis post-encounter motion