Mission Applications for Continuous-Thrust Spacecraft within a Three-Body Problem

This Thesis presents a study of possible mission scenarios for spacecraft propelled by continuous-thrust propulsion systems within a gravitational model of three bodies. The first Part concerns the study of the existence, stability, and control of Artificial Equilibrium Points. A general mathematical model (referred to as Generalized Sail) for the propulsive acceleration of a spacecraft subjected to a continuous and purely radial thrust is proposed. Based on the choice of a coefficient related to the propulsion system and of a parameter (the lightness number) related to the system performance, the propulsive acceleration model encompasses the behavior of different propulsion systems, like Solar Sails, Electric Solar Wind Sails, Magnetic Sails and Electric Thrusters. The continuous propulsive acceleration provided by a Generalized Sail is used to create and maintain Artificial Equilibrium Points. The loci (curves in the space) and the stability of such Artificial Equilibrium Points are discussed both in the Circular and in the Elliptic Restricted Three-Body Problem. Even though similarities between the two problems exist in the description of the geometrical loci, some differences in the stability analysis are shown. Moreover, a Generalized Sail is required to provide a varying lightness number in the elliptical problem to maintain an Artificial Equilibrium Point. The stabilization and control of a interesting class of Artificial Equilibrium Points, the L1-type points, is also discussed to show how a simple Proportional-Derivative feedback control logic, based on the variation of the lightness number, is able to guarantee asymptotical stability. In this respect, two control techniques for Solar Sail based spacecraft are examined: Solar Balloon and Electrochromic Material Panels. A Solar Balloon can provide a passive Proportional control, however, if manufactured with the current technology, it is shown to be unable to stabilize an Artificial Equilibrium Point. Electrochromic Material Panels are, instead, used for an active control system. A suitable dimensioning of such a system provides asymptotical stability for the Artificial Equilibrium Points, when saturation effects are counteracted by means of an anti-windup compensator. In the first Part, the Artificial Equilibrium Points created by an Electric Solar Wind Sail are also investigated. In this case, the radial thrust hypothesis is left, and the Electric Solar Wind Sail is assumed to maintain a constant attitude with respect to an orbital reference frame. This increases the number of attainable Artificial Equilibrium Points, and the loci now become space regions, whose extension depends on the thrust capabilities of the spacecraft. For those points a linear stability analysis is also provided. In the second Part, new frozen orbits are sought for Solar Sail based spacecraft around an oblate planet and under the effects of the Sun’s gravitational attraction. An averaging method of the Hamiltonian that describes the spacecraft motion is used to find new families of displaced frozen orbits, varying the sail lightness number. These orbits are examined both analytically and numerically when Mercury is the reference planet

Electric Solar Wind Sail Optimal Transit in the Circular Restricted Three Body Problem

This paper analyzes the transfer orbits within a Sun-[Earth+Moon] system for a spacecraft whose primary propulsion system is an Electric Solar Wind Sail. The planetary system is approximated through the Circular Restricted Three Body Problem and the spacecraft motion is studied in an optimal framework in which the performance index is the flight time. Minimum time transfers are studied using an indirect approach, and the optimal control law is found in analytical form as a function of the problem parameters. Optimal transfers between equilibrium points are discussed and interesting symmetries in the spacecraft trajectories are pointed out along with an analytical proof of their existence. A mission scenario consistent with the Geostorm concept is analyzed and the effectiveness of the propulsion system is emphasized for missions involving a tour through a subset of the classical Lagrangian points

Artificial Equilibrium Points for Electric Sail with Constant Attitude

Creating and maintaining Artificial Equilibrium Points (AEPs) in the restricted threebody problem is a challenging mission scenario in which a propellantless propulsion system exploits its natural potential. Indeed, in such a problem the acceleration resulting from the sum of centrifugal and gravitational forces can be balanced, for a theoretically unlimited time period, by means of a suitable continuous propulsive thrust. A thorough analysis involving the location and stability of AEPs has been addressed in a recent paper, under the assumption that the propulsion system provides a purely radial thrust with respect to the Sun, and the thrust modulus is a function of the Sun-spacecraft distance only . In that way, with a unified mathematical model, it is possible to analyze the performance of different propulsion systems, as, for example, a photonic solar sail and an Electric Solar Wind Sail (E-Sail). In particular, an E-Sail is known to be able to provide a continuous propulsive acceleration by means of Coulomb’s interaction of a number of positively charged tethers with the solar wind plasma stream

Optimal Control Laws for Heliocentric Transfers with a Magnetic Sail

A magnetic sail is an advanced propellantless propulsion system that uses the interaction between the solar wind and an artificial magnetic field generated by the spacecraft, to produce a propulsive thrust in interplanetary space. The aim of this paper is to collect the available experimental data, and the simulation results, to develop a simplified mathematical model that describes the propulsive acceleration of a magnetic sail, in an analytical form, for mission analysis purposes. Such a mathematical model is then used for estimating the performance of a magnetic sail-based spacecraft in a two-dimensional, minimum time, deep space mission scenario. In particular, optimal and locally optimal steering laws are derived using an indirect approach. The obtained results are then applied to a mission analysis involving both an optimal Earth-Venus (circle-to-circle) interplanetary transfer, and a locally optimal Solar System escape trajectory. For example, assuming a characteristic acceleration of 1 mm/s(2), an optimal Earth-Venus transfer may be completed within about 380 days

Heliocentric Phasing Performance of Electric Sail Spacecraft

We investigate the heliocentric in-orbit repositioning problem of a spacecraft propelled by an Electric Solar Wind Sail. Given an initial circular parking orbit, we look for the heliocentric trajectory that minimizes the time required for the spacecraft to change its azimuthal position, along the initial orbit, of a (prescribed) phasing angle. The in-orbit repositioning problem can be solved using either a drift ahead or a drift behind maneuver and, in general, the flight times for the two cases are different for a given value of the phasing angle. However, there exists a critical azimuthal position, whose value is numerically found, which univocally establishes whether a drift ahead or behind trajectory is superior in terms of flight time it requires for the maneuver to be completed. We solve the optimization problem using an indirect approach for different values of both the spacecraft maximum propulsive acceleration and the phasing angle, and the solution is then specialized to a repositioning problem along the Earth's heliocentric orbit. Finally, we use the simulation results to obtain a first order estimate of the minimum flight times for a scientific mission towards triangular Lagrangian points of the Sun-[Earth+Moon] system

Punti di equilibrio artificiale con spinta radiale nel problema ristretto dei tre corpi

Nell'ambito del Problema dei Tre Corpi Circolare Ristretto (CRTBP) esistono cinque punti di equilibrio detti punti Lagrangiani. Questi sono i punti in cui si bilanciano, sul terzo corpo, le forze gravitazionali, dovute all'azione dei due attrattori, e la forza centrifuga, che agisce nel sistema di riferimento rotante con i due attrattori. Qualsiasi altro punto nello spazio è un punto di non equilibrio in presenza delle suddette forze; è, però, possibile, per mezzo di un sistema di propulsione in grado di fornire una spinta continua, equilibrare la risultante delle forze agenti in un determinato punto ed ottenere, quindi, un punto di equilibrio artificiale (AEP). Scopo della Tesi è studiare i punti di equilibrio artificiali che possono ottenersi con sistemi di propulsione non convenzionali in grado di fornire una accelerazione costante, puramente radiale rispetto all'attrattore principale e che varia con la distanza r come 1/r^n, dove n è un parametro legato al tipo di sistema propulsivo. Dopo aver ripercorso gli aspetti essenziali del problema classico, sottolineando i risultati fondamentali, è stata descritta l'estensione del problema in presenza di una generica accelerazione, dopodiché si è introdotto il modello di accelerazione adottato e ottenuto un integrale di Jacobi generalizzato, oltre alle equazioni necessarie alla descrizione matematica del problema. Si sono, poi, ricavate le equazioni che individuano i punti di equilibrio e determinati i luoghi su cui tali punti debbono trovarsi e il modo in cui si modificano al variare dei parametri caratteristici del sistema propulsivo. Dopo ciò si è linearizzata l'equazione del moto del sistema e studiata la stabilità dei punti di equilibrio ottenuti, determinando quali sono, per una data posizione di equilibrio, le caratteristiche richieste al sistema propulsivo affinché il punto sia stabile o, viceversa, fissate le caratteristiche del sistema propulsivo, quali sono i possibili punti di equilibrio stabile. Infine, si sono applicati i risultati ottenuti a casi di tecnologie propulsive esistenti attualmente o nell'immediato futuro e all'interno del sistema di attrattori Sole-[Terra+Luna], confrontando, quando possibile, i risultati con quelli del caso classico

Artificial Equilibrium Points for a Solar Balloon in the Alpha Centauri System

This paper discusses the generation, stability, and control of artificial equilibrium points for a solar balloon spacecraft in the alpha Centauri A and B binary star system. The continuous propulsive acceleration provided by a solar balloon is shown to be able to modify the position of the (classical) Lagrangian equilibrium points of the three-body system on a locus whose geometrical form is known analytically. A linear stability analysis reveals that the new generated equilibrium points are usually unstable, but part of them can be stabilized with a simple feedback control logic

A Graphical Approach to Electric Sail Mission Design with Radial Thrust

This paper describes a semi-analytical approach to electric sail mission analysis under the assumption that the spacecraft experiences a purely radial, outward, propulsive acceleration. The problem is tackled by means of the potential well concept, a very effective idea that was originally introduced by Prussing and Coverstone in 1998. Unlike a classical procedure that requires the numerical integration of the equations of motion, the proposed method provides an estimate of the main spacecraft trajectory parameters, as its maximum and minimum attainable distance from the Sun, with the simple use of analytical relationships and elementary graphs. A number of mission scenarios clearly show the effectiveness of the proposed approach. In particular, when the spacecraft parking orbit is either circular or elliptic it is possible to find the optimal performances required to reach an escape condition or a given distance from the Sun. Another example is given by the optimal strategy required to reach a heliocentric Keplerian orbit of prescribed orbital period. Finally the graphical approach is applied to the preliminary design of a nodal mission toward a Near Earth Asteroid