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 towards a Near Earth Asteroid.
► A semi-analytical approach to electric sail mission analysis is proposed. ► The spacecraft uses a purely radial, outward, propulsive acceleration. ► Maximum and minimum attainable distance from the Sun can be easily estimated. ► The optimal strategy required to reach a heliocentric Keplerian orbit is provided. ► A nodal mission towards a Near Earth Asteroid is discussed.
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.
•This paper analyzes the in-orbit repositioning of an E-sail-based vehicle.•The problem is studied by evaluating the minimum flight time.•A mission towards Sun–Earth triangular Lagrangian points is discussed.
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.
•The paper analyzes the Electric Sail transit within the Sun−Earth+Moon CRTBP.•The time-optimal transfer between equilibrium points is investigated.•The symmetric structure arising from the optimal trajectory is discussed.•A mission involving the tour of a subset of Lagrangian points is studied.
•This paper presents an extension of the method by Alfano for heliocentric transfer.•A circle-to-circle, coplanar, orbit transfer for a SEP spacecraft is analyzed.•The numerical results are arranged ...into contour plots in a parametric way.•A semi-analytical model for preliminary mission analysis purposes is also discussed.
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 3000s (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 8.3years) 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.
This paper discusses the generation, stability, and control of artificial equilibrium points for a solar balloon spacecraft in the α 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 solar balloon may displace the equilibrium points of the α Centauri system.•Two families of artificial equilibrium points may be generated.•Most of the L1-type points may be stabilized with a proportional-derivative control law.•The requirements of a balloon spacecraft for a mission around an equilibrium point are estimated.
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 1mm/s2, an optimal Earth–Venus transfer may be completed within about 380 days.
•A magnetic sail (Magsail) is an advanced thruster for deep space mission.•This paper develops a mathematical model of a Magsail for mission analysis.•Optimal and locally optimal steering laws are derived using an indirect approach.•An optimal Earth–Venus transfer and a Solar System escape mission are discussed.
This 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.
Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical ...model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.
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