Trajectory Design with Hybrid Low-Thrust Propulsion System

A novel mission concept based on a hybrid low-thrust propulsion system is proposed and discussed. A solar electric propulsion thruster is coupled with an auxiliary system providing an inverse square radial thrust In this way the spacecraft is virtually subjected to a reduced gravitational solar force. The primary purpose of this paper is to quantify the impact of the reduced solar force on the propellant consumption for an interplanetary mission. To this end the steering law that minimizes the propellant consumption for a circle-to-circle rendezvous problem is found using an indirect approach. The hybrid system is compared with a conventional solar electric thruster in terms of payload mass fraction deliverable for a given mission. A tradeoff between payload size and trip time is established

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

Thrust and torque vector characteristics of axially-symmetric E-sail

The Electric Solar Wind Sail is an innovative propulsion system concept that gains propulsive acceleration from the interaction with charged particles released by the Sun. The aim of this paper is to obtain analytical expressions for the thrust and torque vectors of a spinning sail of given shape. Under the only assumption that each tether belongs to a plane containing the spacecraft spin axis, a general analytical relation is found for the thrust and torque vectors as a function of the spacecraft attitude relative to an orbital reference frame. The results are then applied to the noteworthy situation of a Sun-facing sail, that is, when the spacecraft spin axis is aligned with the Sun-spacecraft line, which approximatively coincides with the solar wind direction. In that case, the paper discusses the equilibrium shape of the generic conducting tether as a function of the sail geometry and the spin rate, using both a numerical and an analytical (approximate) approach. As a result, the structural characteristics of the conducting tether are related to the spacecraft geometric parameters

Venus-Centered Heliosynchronous Orbits with Smart Dusts

This paper deals with the problem of determining an analytical control law capable of maintaining highly elliptical heliosynchronous polar orbits around Venus. The problem is addressed using the Smart Dust concept, a propellantless propulsion system that extracts momentum from the solar radiation pressure using a reflective coating. The modulation of the thrust magnitude is performed by exploiting the property of electrochromic materials of changing their optical characteristics through the application of a suitable electrical voltage. The propulsive acceleration can, therefore, be switched from a minimum to a maximum value (or vice versa) so as to obtain a simple on–off control law. The required Smart Dust performance is described in closed form as a function of the semimajor axis and eccentricity of the working orbit. The soundness of the analytical control law is validated through a numerical integration of the equations of motion, in which the orbital perturbations due to the oblateness of Venus and to the gravitational attraction of the Sun are also included

Optimal Planetary Rendezvous with an Electric Sail

The aim of this paper is to discuss Electric Solar Wind Sail-based missions towards Venus and Mars. The analysis takes into account the real three-dimensional shape of the starting and arrival orbits and the planetary ephemeris constraints, using the JPL planetary ephemerides model DE405/LE405

Optimal solar sail transfers to circular Earth-synchronous displaced orbits

The aim of this paper is to evaluate the minimum flight time of a solar sail-based spacecraft towards Earth-synchronous (heliocentric) circular displaced orbits. These are special displaced non-Keplerian orbits characterized by a period of one year, which makes them suitable for the observation of Earth’s polar regions. The solar sail is modeled as a flat and purely reflective film with medium-low performance, that is, with a characteristic acceleration less than one millimeter per second squared. Starting from a circular parking orbit of radius equal to one astronomical unit, the optimal steering law is sought by considering the characteristic acceleration that is required for the maintenance of the target Earth-synchronous displaced orbit. The indirect approach used for the calculation of the optimal transfer trajectory allows the minimum flight time to be correlated with several Earth-synchronous displaced orbits, each one being characterized by given values of Earth- spacecraft distance and displacement over the ecliptic. The proposed mathematical model is validated by comparison with results available in the literature, in which a piecewise-constant steering law is used to find the optimal flight time for a transfer towards a one-year Type I non-Keplerian orbit

Solar Sail Optimal Transfer Between Heliostationary Points

This Note analyzes the transfer between two heliostationary points that are the same distance from the sun. The problem is addressed within an optimal framework in which a constraint is enforced on the minimum sun–spacecraft distance along the transfer trajectory

Time-optimal formation establishment around a slowly rotating asteroid

A study is conducted to find a solution to the problem of time-optimal formation establishment around a slowly rotating asteroid, whose gravity is approximated as a second-degree and second-order gravitational field (SDSOGF). Similar to the methodology used for identifying the classical J2-invariant relative orbits, two necessary conditions are analytically derived to guarantee bounded relative motion in an SDSOGF. In particular, it is shown that when the nonspherical harmonic coefficients of the asteroid gravity are first-order small, the resulting necessary conditions are consistent with the recent literature results. Based on the analytically obtained constraints, the problem of time-optimal formation establishment is then emphasized via an indirect approach, in which the initial unknown costate vector is calculated with a scaling technique to alleviate its sensitivity to the initial guess problem

Electric sail phasing maneuvers for constellation deployment

The aim of this work is to investigate heliocentric phasing maneuvers performed by a spacecraft propelled by an Electric Solar Wind Sail, that is, an innovative propellantless propulsion system that consists of a spinning grid of charged tethers that uses solar wind momentum to produce thrust. It is assumed that the Electric Solar Wind Sail may be controlled by varying its attitude with respect to a classical orbital reference frame, and by switching the tether grid off to obtain Keplerian arcs along its phasing trajectory. The analysis is conducted within an optimal framework, the aim of which is to find both the optimal control law and the minimum-time phasing trajectory for a given angular drift along the (assigned) working orbit. A typical phasing scenario is analyzed, by considering either a drift ahead or a drift behind maneuver on a circular, heliocentric orbit of given radius. The paper also investigates the possibility of using an Electric Solar Wind Sail-based deployer to place a constellation of satellites on the same working orbit. In that case, the optimal flight time is obtained in a compact, semianalytical form as a function of both the propulsion system performance and the number of the sail-deployed satellites

Solar Sail Simplified Optimal Control Law for Reaching High Heliocentric Distances

The aim of this paper is to analyze optimal trajectories of a solar sail-based spacecraft in missions towards the outer Solar System region. The paper proposes a simplified approach able to estimate the minimum flight time required to reach a given (sufficiently high) heliocentric distance. In particular, the effect of a set of solar photonic assists on the overall mission performance is analyzed with a simplified numerical approach. A comparison with results taken from the existing literature show the soundness of the proposed approach