Generoso Aliasi

Artificial Lagrange Points for Solar Sail with Electrochromic Material Panels

B ECAUSE of its inherent capability of producing thrust without using any propellant consumption, a solar sail is a particularly attractive option for the generation of so-called artificial equilibrium points (AEPs). These points are of great interest for mission applications because the spacecraft can be used to provide new vantage points for scientific observation [1]. Interesting positions for AEPs are those placed along the segment connecting the two primaries in the neighborhood of the classicalL1 Lagrange point. For example, in the sun-(Earth+moon) system, these L1-type AEPs have been suggested as useful locations for space weather observation missions [2] or for geoengineering missions [3,4]. Because L1-type AEPs are intrinsically unstable [5], a suitable control strategy is required to maintain their desired location. This problem has been addressedwith different approaches, whichmainly consider either a pitch and yaw-angle control, or a solar sail area variation [6]. However, both solutions present some drawbacks. A substantial simplification of the control problem is obtained when the solar sail attitude is maintained fixed, in a passive way, using a conically shaped structure [7]. The propulsive thrust is therefore always in the sun–spacecraft direction, but it can be modulated by varying, within a limited range, the ratio of the solar radiation pressure acceleration to the solar gravitational acceleration, that is, the sail lightness number β. Such a solution is commonly referred to as β control. The original idea of a β control applied to a solar-sail-based mission toward an L1-type AEP is due to Biggs and McInnes [4]. An interesting implementation of a β control makes use of electrochromic material panels (EMPs) [8]. These materials have already been employed in space missions, notably for the attitude control of the Japanese solar sail demonstrator interplanetary kitecraft accelerated by radiation of the sun (IKAROS) [9,10]. The aim of this Note is to explore the capabilities of the emerging EMP technology for the active stabilization of L1-type AEPs using a square solar sail with a fixed attitude. The problem is addressed within an elliptic restricted framework, which is a more realistic model with respect to the classical circular case [4]. The main spacecraft parameters, including the sail side and the total spacecraft mass, are defined by means of a simplified mathematical model, as a function of the main mission requirements in terms of maximum allowed sail lightness number variation and AEP position.

Artificial Equilibrium Points for Electric Sail with Constant Attitude

REATINGandmaintainingartificialequilibriumpoints(AEPs)in the restricted three-body problem is a challenging missionscenario in which a propellantless propulsion system exploits itsnatural potential [1]. Indeed, in such a problem, the accelerationresulting from the sum of centrifugal and gravitational forces can bebalanced, for a theoretically unlimited time period, by means of asuitable continuous propulsive thrust.A thorough analysis involving the location and stability of AEPshas been addressed in a recent paper [2], under the assumption thatthe propulsion system provides a purely radial thrust with respect tothe sun, and the thrust modulus is a function of the sun–spacecraftdistance only. In that way, with a unified mathematical model, it ispossibletoanalyzetheperformancesofdifferentpropulsionsystems,as, for example, a photonic solar sail and an electric solar wind sail(ESWS). In particular, an ESWS is known to be able to providea continuous propulsive acceleration by means of Coulomb’sinteraction of a number of positively charged tethers with the solarwind plasma stream [3].As long as the propulsive acceleration is assumed to be radial, asper[2],theESWSnominalplaneisorthogonaltothesun–spacecraftdirection.However,inamoregeneralcase,thespacecraftpropulsiveaccelerationdirectionmaybeinclined(withinprescribedlimits)withrespecttotheradialdirection,andatransversethrustcomponentmaybe generated. The latter, in turn, introduces an additional degree offreedom that can be exploited to expand the region of admissibleAEPs. The study of such a region for an ESWS-based spacecraft isthesubjectofthisNote,forwhichtheaimistoextendtheresultof[2]byremovingtheassumptionoftheradialdirectionforthepropulsiveacceleration. Moreover, this work, dealing with ESWSs, comple-ments the analysis of Baoyin and McInnes [4], which refers tophotonic solar sails.More precisely, to reduce the active attitude control effort, theESWS nominal plane is assumed here to maintain a constantorientation in an orbital reference frame, and the problem ofcalculating the maps of AEPs’ positions as a function of the ESWSattitude and performance is addressed within an elliptical restrictedthree-body problem. A linear stability analysis of AEPs near theLagrange points

Passive Control Feasibility of Collinear Equilibrium Points with Solar Balloons

A = solar balloon’s surface area, m E = Young’s modulus of the skin, Pa h = auxiliary variable, see Eq. (13) i, ĵ, k = unit vectors of rotating frame K = second-order tensor, see Eq. (5) k = gain ‘ = sun–planet distance (with ‘ ≜ 1 AU), astronomical unit m = mass, kg O = center of mass p = internal pressure, Pa R = solar balloon’s radius, m r = absolute position vector, r krk T = spacecraft equilibrium temperature, K T O; x; y; z = rotating reference frame u = vector, see Eq. (6) W = thermal power flux,W=m W = solar constant, 1350 W=m 2 = coefficient of absorptivity = lightness number = variation = coefficient of emissivity = angular coordinate, deg = planet’s dimensionless mass = skin’s Poisson ratio = dimensionless x coordinate = relative position vector, k k = skin’s tensile stress, Pa ~ = Stefan–Boltzmann constant = coefficient of linear expansion, K 1 ! = angular velocity, rad=s

Low-Thrust Earth-Venus Trajectories

The remarkable results obtained by the pioneering Deep Space 1 (DS1) mission (Rayman et al. 2000) have demonstrated the practical possibility of using electric thrusters to successfully perform interplanetary robotic missions.