Orbit and Attitude Determination

Stefano Maro, Davide Amato, Helene Ma

The determination of the orbit of an asteroid is a long-standing problem [1]. With new generation surveys, a huge amount of observations need to be processed to produce a catalogue of orbits. One goal is to develop new algorithms for the preliminary computation of orbits from data (tracklets) collected on two different nights of observations (linkage problem). The number of tracklets is very high which causes a problem of computational complexity. New methods for linkage have already been proposed [2]. One solution to decrease the computational complexity is the use of filters to pre-select pairs of tracklets to be tested. Some algorithms to obtain preliminary orbits of space debris with two passes have been proposed for optical observations [2], by using conservation laws of the Kepler problem. The problem has a polynomial formulation and we can use algebraic tools to compute the preliminary orbits with a global control on the solutions. The correlation problem has also been investigated for radar observations; the ranges of observed debris are very accurate but their angular positions are not. Correlation methods have been proposed but they assume a priori more precise information on the angular positions. The rotational motion of asteroids is estimated from the periodic variation of the reflected light (light-curve data analysis). In space measurement, the rotational state of debris and asteroids is fundamental and remains an open point of research.

Objectives. To develop new algorithms for preliminary orbit computation from observation of asteroids and space debris, to revise current techniques for the determination of asteroid rotational state and relate them to the models developed under the other research topics.

Impact Prediction and Risk Analysis

Chiara Tardioli, Stefano Maro, Davide Amato, Helene Ma

Predicting whether a projectile, asteroid or piece of space debris will hit a target over a time span much longer than the orbital period of the object is a challenging problem. In the case of NEAs, the main complicating factor resides in the possible presence of planetary close encounters occurring before the epoch of impact, since our knowledge of the asteroid’s state of motion after each encounter is strongly degraded due to the effects of the encounter itself. Computational strategies able to cope with the chaos induced by close planetary encounters have been devised in order to detect regions of initial conditions leading to impact, in orbital elements space, whose volume is typically one million, or even one billion times smaller than the region occupied by orbits compatible with the available observational record. In the case of space debris there are some simplifications in the dynamical model, since the equivalent of close planetary encounters does not exist in this case. The problem is nevertheless complicated by other factors, like the multitude of possible targets, as well as the presence of peculiar perturbations like those induced by the atmosphere or non-gravitational perturbations. For both asteroids and space debris, all the uncertainties present in the motion and rotation dynamics need to be quantified and propagated in order to generate the solution space of possible impacts. This is normally done by creating families of virtual impactors, then running Monte Carlo simulations to assess the impact area in the b-plane of the impact instants. Recent techniques [3] based on validated integrators or high order expansions represent an interesting possibility that is going to be investigated in this program of research. For both, impact monitoring should be able to identify which asteroids or piece of debris could generate an impact, already in the early phase of orbit determination. Current monitoring programs like the NEODyS, CLOMON or SENTRY need to process large volumes of data and prioritization of asteroids is required. Currently a scoring based on MOID and the orbit uncertainty is used but can be improved by using new criteria, like estimation of crossing times based on the uncertainty and the secular evolution of the MOID [4]. An EU systematic collision avoidance procedure for space debris is still missing and its creation is currently the subject of scientific discussions. The search for colliding pairs must be fast enough to manoeuvre active satellites or to remove of the incoming piece of debris. Some filter chain solutions have been already proposed to quickly identify colliding pairs.

Objectives. To improve: current techniques for impact/collision prediction based on observation and state estimation, current risk and damage assessment tools (SDM, DAMAGE, NEOMiSS); to develop EU collision avoidance procedure, and new prioritisation; to integrate this with deflection/removal techniques.

References

[1] Celletti, Pinzari, Four classical methods for determining planetary elliptic elements: a comparison, Cel. Mech. Dyn. Astr. 93(1), 2005.

[2] Gronchi, Dimare, Milani, Orbit determination with the two-body integrals, Cel. Mech. Dyn. Ast. 107(3), 2010.

[3] Valsecchi, Rossi, Analysis of the Space Debris Impacts Risk on the International Space Station, CMDA 83, 2002.

[4] Gronchi, Tommei, On the uncertainty of the minimal distance between two confocal Keplerian orbits, Dis. and Cont. Dyn. Sys.-Series B 7(4), 2007