Multi-Revolution Transfer for Heliocentric Missions with Solar Electric Propulsion

An extension of the classical method by Alfano, for the analysis of optimal circle-to-circle two-dimensional orbit transfer, is presented for a deep space probe equipped with a solar electric primary propulsion system. The problem is formulated as a function of suitable design parameters, which allow the optimal transfer to be conveniently characterized in a parametric way, and an indirect approach is used to find the optimal steering law that minimizes the required propellant mass. The numerical results, obtained by solving a number of optimal control problems, are arranged into contour plots, characterized by different and well-defined behaviors depending on the value of the initial spacecraft propulsive acceleration, the final orbit radius, and the thruster's specific impulse. The paper presents also a semi-analytical mathematical model for preliminary mission analysis purposes, which is shown to give excellent approximations of the (exact) numerical solutions when the number of revolutions of the spacecraft around the Sun is greater than five. An Earth Mars cargo mission has been thoroughly investigated to validate the proposed approach. In this case, assuming a propulsion system with a specific impulse of 3000 s (comparable to that installed on the Deep Space 1 spacecraft), the results obtained with the semi-analytical model coincide, from an engineering point of view, with the numerical solutions both in terms of total mission time (about 8.3 years) and propellant mass fraction required (about 17.5%). By decreasing the value of the specific impulse, the differences between the results from the semi-analytical model and the numerical simulations tend to increase. However, good results are still possible if the number of revolutions of the spacecraft around the Sun is close to an integer number

Special Orbits for Mercury Observation

Chapter 5, by Generoso Aliasi, Giovanni Mengali and Alessandro A. Quarta, deals with an advanced scientific mission concept in which the existence of suitable positions for the observation and the measurement of the Mercury’s magnetotail are investigated. The scientific mission is based on the use of artificial equilibrium points in the elliptic three-body system, constituted by the Sun, Mercury, and a spacecraft, which is modeled as a massless point. The spacecraft motion in the Sun–Mercury system is first discussed under the assumption that the propulsion system provides a radial continuous thrust with respect to the Sun. In particular, the spacecraft is assumed to have a generalized sail as its primary propulsion system. A generalized sail models the performance of different types of advanced propulsion systems, including a (photonic) solar sail, an electric solar wind sail and an electric thruster, by simply modifying the value of a thrusting parameter. The location of the artificial equilibrium points is derived, and their stability is also investigated. It is shown that that collinear artificial equilibrium points are always unstable, except for a range of L2-type points which are placed far away from Mercury. A similar result is obtained for triangular equilibrium points. A control strategy is introduced to maintain the spacecraft in the neighborhood of an artificial equilibrium point. In this context, a simple and effective way to actively control the spacecraft dynamics is by means of a Proportional-Integral-Derivative feedback control law. The latter control law is finally employed in the magnetotail mission scenario, whose fundamental idea is to continuously and slowly displacing the artificial equilibrium point along the Sun–Mercury direction. Numerical simulations show the effectiveness of the proposed mission strategy

Artificial Equilibrium Points for a Generalized Sail in the Circular Restricted Three-Body Problem

International audienceThis paper introduces a new approach to the study of artificial equilibrium points in the circular restricted three-body problem for propulsion systems with continuous and purely radial thrust. The propulsion system is described by means of a general mathematical model that encompasses the behavior of different systems like a solar sail, a magnetic sail and an electric sail. The proposed model is based on the choice of a coefficient related to the propulsion type and a performance parameter that quantifies the system technological complexity. The propulsion system is therefore referred to as generalized sail. The existence of artificial equilibrium points for a generalized sail is investigated. It is shown that three different families of equilibrium points exist, and their characteristic locus is described geometrically by varying the value of the performance parameter. The linear stability of the artificial points is also discussed

Artificial Periodic Orbits Around L1-Type Equilibrium Points for a Generalized Sail

The contribution of this note is to extend the available results for APOs maintained by a propellantless propulsion system to the case of purely radial (continuous) propulsive acceleration, whose modulus depends on a given power of the Sun–spacecraft distance

Analysis of Smart Dust-Based Frozen Orbits Around Mercury

According to the classical two-body Keplerian model, the orbital parameters of a spacecraft are constant during a mission. However, real-life spacecraft motion is different from a classical Keplerian model due to the presence of perturbing forces, whose effects are usually undesirable, especially for observation and communication spacecraft that require accurate pointing capabilities. Therefore, active control systems are usually required to maintain the working orbit. However, an alternative strategy consists of suitably selecting the initial orbital elements to generate a “frozen orbit”, which on average maintains some of the design orbital elements. The utilization of spacecraft with large area-to-mass ratio could extend the flexibility on the initial choice of orbital parameters. In this context, a novel option is represented by smart dusts (SDs), which are femto-satellites with large area-to-mass ratio (or millimeter-scale solar sails). In this chapter, a double-averaging technique is used to determine planetocentric frozen orbits maintained by SDs. In particular, a numerical analysis of frozen orbits is discussed, with a special application focused on orbits around Mercury, which are fit for an SD-based scenario due to their closeness to the Sun and the absence of atmospheric drag