Camilla Colombo

Multicriteria comparison among several mitigation strategies for dangerous near-Earth objects

In this paper a comparative assessment of the effectiveness of different deviation methods for Near Earth Objects is presented. Specifically, solar collector, nuclear interceptor, kinetic impactor, low-thrust propulsion, mass driver and gravity tug are modelled and compared. For each method, a mathematical model is developed in order to compute the achievable deviation. A multi-criteria optmization method is then used to construct the set of Pareto optimal solutions, minimizing the mass of the spacecraft at departure from the Earth and the warning time, i.e., the time from launch to the foreseen impact of the asteroid with the Earth, while at the same time maximizing the deviation. A dominance criterion is defined and used to compare all the Pareto sets for all the various mitigation strategies. Finally a Technology Readiness Level factor is associated to each strategy in order to estimate the required technological development.

Optimal impact strategies for asteroid deflection

This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple analytical formulas are derived from proximal motion equations. The proposed analytical formulation allows for an analysis of the optimal direction of the deviating impulse transferred to the asteroid. This ideal optimal direction cannot be achieved for every asteroid at any time; therefore, an analysis of the optimal launch opportunities for deviating a number of selected asteroids was performed through the use of a global optimization procedure. The results in this paper demonstrate that the proximal motion formulation has very good accuracy in predicting the actual deviation and can be used with any deviation method because it has general validity. Furthermore, the characterization of optimal launch opportunities shows that a significant deviation can be obtained even with a small spacecraft.

Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects

This paper presents a semi-analytical solution of the asteroid deviation problem when a low-thrust action, inversely proportional to the square of the distance from the sun, is applied to the asteroid. The displacement of the asteroid at the minimum orbit interception distance from the Earths orbit is computed through proximal motion equations as a function of the variation of the orbital elements. A set of semi-analytical formulas is then derived to compute the variation of the elements: Gauss planetary equations are averaged over one orbital revolution to give the secular variation of the elements, and their periodic components are approximated through a trigonometric expansion. Two formulations of the semi-analytical formulas, latitude and time formulation, are presented along with their accuracy against a full numerical integration of Gauss equations. It is shown that the semi-analytical approach provides a significant savings in computational time while maintaining a good accuracy. Finally, some examples of deviation missions are presented as an application of the proposed semi-analytical theory. In particular, the semi-analytical formulas are used in conjunction with a multi-objective optimization algorithm to find the set of Pareto-optimal mission options that minimizes the asteroid warning time and the spacecraft mass while maximizing the orbital deviation.

Electrochromic orbit control for smart-dust devices

Recent advances in MEMS (micro electromechanical systems) technology are leading to spacecraft which are the shape and size of computer chips, so-called SpaceChips, or ‘smart dust devices’. These devices can offer highly distributed sensing when used in future swarm applications. However, they currently lack a feasible strategy for active orbit control. This paper proposes an orbit control methodology for future SpaceChip devices which is based on exploiting the effects of solar radiation pressure using electrochromic coatings. The concept presented makes use of the high area-to-mass ratio of these devices, and consequently the large force exerted upon them by solar radiation pressure, to control their orbit evolution by altering their surface optical properties. The orbital evolution of Space Chips due to solar radiation pressure can be represented by a Hamiltonian system, allowing an analytic development of the control methodology. The motion in the orbital element phase space resembles that of a linear oscillator, which is used to formulate a switching control law. Additional perturbations and the effect of eclipses are accounted for by modifying the linearized equations of the secular change in orbital elements around an equilibrium point in the phase space of the problem. Finally, the effectiveness of the method is demonstrated in a test case scenario.

Impact hazard protection efficiency by a small kinetic impactor

In this paper the ability of a small kinetic impactor spacecraft to mitigate an Earth-threatening asteroid is assessed by means of a novel measure of efficiency. This measure estimates the probability of a space system to deflect a single randomly generated Earth-impacting object to a safe distance from the Earth. This represents a measure of efficiency that is not biased by the orbital parameters of a test-case object. A vast number of virtual Earth-impacting scenarios are investigated by homogenously distributing in orbital space a grid of 17,518 Earth-impacting trajectories. The relative frequency of each trajectory is estimated by means Opik’s theory and Bottke’s near-Earth objects model. A design of the entire mitigation mission is performed and the largest deflected asteroid computed for each impacting trajectory. The minimum detectable asteroid can also be estimated by an asteroid survey model. The results show that current technology would likely suffice against discovered airburst and local damag...

Wave-like patterns in an elliptical satellite ring

Satellite constellations are families of orbits selected to provide useful coverage patterns for telecommunications, Earth observation and navigation services. Such constellations are often assembled from families of circular orbits, which ensures a uniform spacing between satellites in each circular ring. However, there is a large class of elliptical orbits which are of practical interest including Molniya-like orbits and so-called Magic orbits [1,2]. Constellations of satellites using such elliptical orbits will then exhibit a time varying spacing between satellites as the orbital angular velocity experienced by each satellites varies around the elliptical ring. While current constellations use relatively modest numbers of satellites, future microspacecraft [3] or ‘smart dust’ type devices [4,5] may enable constellations with extremely large numbers of nodes. In this Note a continuum approach is used to model the dynamics of such constellations. A continuity equation is formed to describe the evolution of the number density of nodes as a function of both true anomaly and time. For small eccentricities, the continuity equation can be solved analytically to provide closed-form solutions which describe the evolution of the constellation for some initial distribution of nodes. The closed-form solutions can then be used to investigate pattern formation in elliptical rings. Wave-like patterns are found which circulate around the elliptical ring, with peaks in density which can in principle be used to provide enhanced coverage. A similar continuum approach with a continuity equation has been used in previous studies to develop closed-form solutions which model the time evolution of the radial distribution of constellations of microspacecraft under the action of air drag [6,7].

Solar Radiation Pressure-Augmented Deorbiting: Passive End-of-Life Disposal from High-Altitude Orbits

A deorbiting strategy for small satellites is proposed that exploits the effect of solar radiation pressure to increase the spacecraft orbit eccentricity so that the perigee falls below an altitude where atmospheric drag will cause the spacecraft orbit to naturally decay. This is achieved by fitting the spacecraft with an inflatable reflective balloon. Once this is fully deployed, the overall area-to-mass ratio of the spacecraft is increased; hence, solar radiation pressure and aerodynamic drag have a greatly increased effect on the spacecraft orbit. An analytical model of the orbit evolution due to solar radiation pressure and the J2 effect as a Hamiltonian system show the evolution of an initially circular orbit. The maximum reachable orbit eccentricity as a function of semimajor axis and area-to-mass ratio is found analytically for deorbiting from circular equatorial orbits of different altitudes. The analytical planar model is then adapted for sun-synchronous orbits. The model is validated numerically...

Orbital dynamics of Earth-orbiting 'smart dust' spacecraft under the effects of solar radiation pressure and aerodynamic drag

This paper investigates how the perturbations due to asymmetric solar radiation pressure, in presence of Earths shadow, and atmospheric drag can be balanced to obtain long-lived Earth centered orbits for swarms of SpaceChips, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where a Sun-synchronous apse-line precession is achieved passively. The long-term evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Therefore, long-lived orbits can be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the short life-time of high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the end-of life decay of SpaceChips, thus preventing long-lived orbit debris.

Optimal law for inclination change in an atmosphere through solar sailing

The aim of this paper is to devise a local optimal strategy for the orbital inclination change of solar sail spacecraft in low Earth orbit, combining the effects of the solar radiation pressure and atmospheric forces. The spacecraft is modeled as a reflective flat plate. The acceleration due to effects of atmospheric forces and solar radiation pressure is computed, depending on the orbital parameters and attitude of the sail. Then, the attitude that maximizes the instantaneous orbital inclination change is found through Gauss’ equations. When either one of these effects dominates over the other (and so, one can be neglected), the analytic expressions are found. When both effects are considered, a numerical optimization is used. An additional constraint is introduced to avoid a decrease in the orbital semimajor axis, and therefore prevent losses of orbital energy, while increasing the inclination. Different regions are identified, depending on whether the atmospheric effects dominate, the solar radiation p...

Solar Radiation Pressure Hamiltonian Feedback Control for Unstable Libration-Point Orbits

This work investigates a Hamiltonian structure-preserving control that uses the acceleration of solar radiation pressure for the stabilization of unstable periodic orbits in the circular restricted...