Minimum-Time Trajectories of Electric Sail with Advanced Thrust Model

The Electric Solar Wind Sail is an advanced propulsion system concept that, similar to the more conventional solar sail, is able to generate a propulsive thrust without any propellant. The main performances of such a propulsion system have been studied in different mission scenarios and are reported in the literature. However, the analyses available so far are based on a simplified thrust model that neglects the effect of the spacecraft attitude on both the thrust modulus and its direction. The recent availability of a refined thrust model requires a critical reappraisal of the simulation results and a new analysis of the optimal trajectories of a spacecraft equipped with such a propulsion system. The aim of this paper is to review the different thrust models used over the last years for mission analysis purposes, and to illustrate the optimal control law and the corresponding minimum-time trajectories that can be obtained with the new, refined, thrust model. The study highlights new analytical relations for the propulsive thrust as a function of the spacecraft attitude, whereas simple and accurate closed-form equations are also proposed for the study of a classical circle-to-circle coplanar heliocentric orbit transfer

Heliocentric Trajectory Analysis of Sun-pointing Smart Dust with Electrochromic Control

A smart dust is a micro spacecraft, with a characteristic side length on the order of a few millimeters, whose surface is coated with electrochromic material. Its orbital dynamics is controlled by exploiting the differential force due to the solar radiation pressure, which is obtained by modulating the reflectivity coefficient of the electrochromic material within a range of admissible values. A significant thrust level can be reached due to the high values of area-to-mass ratio of such a spacecraft configuration. Assuming that the smart dust is designed to achieve a passive Sun-pointing attitude, the propulsive acceleration due to the solar radiation pressure lies along the Sun-spacecraft direction. The aim of this paper is to study the smart dust heliocentric dynamics in order to find a closed form, analytical solution of its trajectory when the reflectivity coefficient of the electrochromic material can assume two values only. The problem is addressed by introducing a suitable transformation that regularizes the spacecraft motion and translates the smart-dust dynamics into that of a linear harmonic oscillator with unitary frequency, whose forcing input is a boxcar function. The solution is found using the Laplace transform method, and afterwards the problem is generalized by accounting for the degradation of the electrochromic material due to its exposition to the solar radiation. Three spacecraft configurations, corresponding to low, medium and high performance smart dusts, are finally used to quantify the potentialities of these advanced devices in an interplanetary mission scenario

Analysis of Electric Sail Heliocentric Motion under Radial Thrust

The contribution of this Note is to analyze the heliocentric trajectory of an E-sail with an outward radial thrust by reducing the problem, by means of a suitable change of variables, to the dynamics of a known equivalent nonlinear oscillator with a single degree of freedom. An analytical, albeit approximate, expression of the spacecraft heliocentric trajectory is also given in polar form when the motion is periodic. This result is shown to be sufficiently accurate for a preliminary mission analysis and is obtained with a reduced computational time, considerably smaller than what is necessary for a numerical integration of the spacecraft equations of motion

Solar Sail Near-Optimal Circular Transfers with Plane Change

Near-minimum time interplanetary trajectories between circular orbits with different orbital planes are investigated. By assumption, the mission is carried out with a solar sail spacecraft, whose performance takes into account the optical characteristics of the sail film and the maximum temperature constraint. In an effort to obtain a general, albeit approximate, solution, the problem is tackled by dividing the mission in two or three phases, depending on the value of the inclination change between the initial and target orbit. Each phase is analyzed by solving a minimum time problem with an indirect approach, and the whole mission time is estimated as the sum of the contributions of the elementary phases. The obtained results are then collected through graphs and fitting functions that can be used effectively to get a good and quick estimate of the main mission parameters, as well as to quantify their effect on the mission flight time. A comparison of the proposed approach with the optimal results available for the Solar Polar Imager mission confirms the effectiveness of the developed methodology

Optimal Nodal Flyby with Near-Earth Asteroids Using Electric Sail

The aim of this paper is to quantify the performance of an Electric Solar Wind Sail for accomplishing flyby missions toward one of the two orbital nodes of a near-Earth asteroid. Assuming a simplified, two-dimensional mission scenario, a preliminary mission analysis has been conducted involving the whole known population of those asteroids at the beginning of the 2013 year. The analysis of each mission scenario has been performed within an optimal framework, by calculating the minimum-time trajectory required to reach each orbital node of the target asteroid. A considerable amount of simulation data have been collected, using the spacecraft characteristic acceleration as a parameter to quantify the Electric Solar Wind Sail propulsive performance. The minimum time trajectory exhibits a different structure, which may or may not include a solar wind assist maneuver, depending both on the Sun-node distance and the value of the spacecraft characteristic acceleration. Simulations show that over 60% of near-Earth asteroids can be reached with a total mission time less than 100 days, whereas the entire population can be reached in less than 10 months with a spacecraft characteristic acceleration of 1 mm/s(2)

Analysis of spacecraft motion under constant circumferential propulsive acceleration

This paper reassesses the classical circumferential-thrust problem, in which a spacecraft orbiting around a primary body is subjected to a propulsive acceleration of constant modulus, whose direction is in the plane of the parking orbit and orthogonal to the spacecraft-primary line. In particular, a new formulation is proposed to obtain a reduction in the number of differential equations required for the study of the spacecraft propelled trajectory. The mathematical complexity of the problem may be further reduced assuming that both the propulsive acceleration modulus and the spacecraft distance from the primary body are sufficiently small. In that case, an approximate model is able to accurately describe the characteristics of the propelled trajectory when the parking orbit is circular. Finally, using the data obtained by numerical simulations, the approximate model is extended to generate a set of semi-analytical equations for the analysis of a classical escape mission scenario

Constrained Large Angle Reorientation Manoeuvres of a Space Telescope Using Potential Functions and a Variable Control Gain

In this paper we study large angle rotational maneuvers of a space telescope with pointing constraints. The spacecraft attitude control design is formulated and solved by means of potential functions, thus simplifying the problem of frequent reorientation maneuvers. A novel approach is proposed, where a time varying control gain is chosen such that its instantaneous value depends both on the spacecraft kinetic energy and on the distance of the spacecraft from the forbidden directions. As a result, the spacecraft is able to reach points in the potential field arbitrarily close to a constraint and to maneuver with autonomous capability of guidance and control. A case study illustrates the effectiveness of the proposed methodology

Trajectory Approximation for Low-Performance Electric Sail with Constant Thrust Angle

Analytic trajectories for a spacecraft subjected to a low, continuous, propulsive acceleration are available only for very special cases [1–3], even though these solutions find significant utility in preliminary mission design and optimization [4]. If a closed-form trajectory corresponding to a given thrust control law cannot be recovered, a possible option is to resort to a shape-based approach [5–7], or to suitably simplify the differential equations of motion [8–10]. Within the latter context, in this Note an analytical, albeit approximate, expression for the heliocentric trajectory of a spacecraft propelled by a low-performance electric sail [11, 12] is discussed. Using a two-dimensional model and under the assumptions of constant thrust angle and low propulsive acceleration modulus, the spacecraft heliocentric trajectory is obtained in a parametric way as a function of time. The effectiveness of the mathematical model is checked by comparing the analytic solution with a numeric integration of equations of motion

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Electric Sail-Based Displaced Orbits with a Refined Thrust Model

This paper analyzes the performance of an electric solar wind sail for generating and maintaining a heliocentric circular displaced orbit. Previous research on this subject was based on a simplified mathematical model of the spacecraft thrust. However, recent studies have proposed a more accurate algorithm for evaluating both the modulus and the direction of the propulsive thrust as a function of some important parameters related to the spacecraft attitude. Therefore, a reappraisal of the problem is motivated by the need to revise past results, taking into account new information available on the propulsion system. Within this context, this paper focuses on circular displaced orbits that are characterized in terms of orbital period, heliocentric distance and elevation angle. The attitude configuration and the value of the spacecraft characteristic acceleration required for orbital maintenance are calculated. An in-depth analysis of the linear stability of displaced orbits is given. It is shown that displaced orbits are unstable when the elevation angle exceeds about 20 deg