Use of Programs for Two-Parameter Multiple Impulse Correction of Altitude and Inclination of Circular Orbits

The paper describes the method for the development of programs for two-parameter multiple impulse correction of altitude and inclination of circular orbits. The considered corrections feature the simultaneous adjustment of altitude and inclination of the orbit under limited thrust of the propulsion system of the spacecraft. Low thrust-to-weight ratio of the spacecraft leads to the need for a correction program consisting of several burns of the propulsion system. Thrust vector orientation, burn time, and its operation duration are determined as propulsion system parameters.     

New Challenges to Trajectory Design by the Use of Electric Propulsion and Other New Means of Wandering in the Solar System

The design of spacecraft trajectories is a crucial part of a space mission design. Often the mission goal is tightly related to the spacecraft trajectory. A geostationary orbit is indeed mandatory for a stationary equatorial position. Visiting a solar system planet implies that a proper trajectory is used to bring the spacecraft from Earth to the vicinity of the planet. The first planetary missions were based on conventional trajectories obtained with chemical engine rockets. The manoeuvres could be considered 'impulsive' and clear limitations to the possible missions were set by the energy required to reach certain orbits. The gravity-assist trajectories opened a new way of wandering through the solar system, by exploiting the gravitational field of some planets. The advent of other propulsion techniques, as electric or ion propulsion and solar sail, opened a new dimension to the planetary trajectory, while at the same time posing new challenges. These 'low thrust' propulsion techniques cannot be considered 'impulsive' anymore and require for their study mathematical techniques which are substantially different from before. The optimisation of such trajectories is also a new field of flight dynamics, which involves complex treatments especially in multi-revolution cases as in a lunar transfer trajectory. One advantage of these trajectories is that they allow to explore regions of space where different bodies gravitationally compete with each other. We can exploit therefore these gravitational perturbations to save fuel or reduce time of flight. The SMART-1 spacecraft, first European mission to the Moon, will test for the first time all these techniques. The paper is a summary report on various activities conducted by the project team in these areas.     

Plasma diagnostics and simulation for the SMART-1 mission

SMART-1 is a technology demonstrator for using primary electric propulsion on interplanetary spacecraft. Hence, studying of the interaction of the plasma emitted by the thruster with the environment and the spacecraft is one of the top priorities during the mission. Two experiments (Electronic propulsion diagnostic package and Spacecraft potential, electron and dust experiment) are available to measure the electron densities and temperatures as well as wave electric fields during the operation of the electric propulsion thruster. Additionally, a retarding potential analyser, a quartz microbalance and a solar-cell sample will analyse data from slow charge-exchange ions which are a potential contamination source. ESTEC is developing a 3D particle-in-cell model in order to study the spacecraft/environment interactions on SMART-1 and interpret the measurements. In the present paper, we will review the contamination effects associated with electric propulsion and how the plasma sensors cover them. We further present preliminary results from the numerical simulation and show how the flight data will be used to validate the modelling code. A successful validation of the simulation will support future interplanetary and commercial missions featuring electric propulsion to reduce the risk of contamination and interference with on board instruments.     

On the problem of designing small spacecraft with electric propulsion power plants for studying minor bodies of the Solar System

Aspects of the design of small spacecraft with electric propulsion power plants for investigating minor bodies in the Solar System are examined. The results of design and ballistic analysis of transfer into an orbit of terrestrial asteroids using electric propulsion thrusters are given. The possible concept design of the spacecraft is determined and the structure of a small spacecraft with an electric propulsion power plant is presented. Parameters of the electric propulsion power plant of a small spacecraft for a flight to the minor bodies of the Solar System are estimated.     

Optimization of the interplanetary trajectories of spacecraft with a solar electric propulsion power plant of minimal power

The problem of optimizing the interplanetary trajectories of a spacecraft (SC) with a solar electric propulsion system (SEPS) is examined. The problem of investigating the permissible power minimum of the solar electric propulsion power plant required for a successful flight is studied. Permissible ranges of thrust and exhaust velocity are analyzed for the given range of flight time and final mass of the spacecraft. The optimization is performed according to Portnyagin’s maximum principle, and the continuation method is used for reducing the boundary problem of maximal principle to the Cauchy problem and to study the solution/ parameters dependence. Such a combination results in the robust algorithm that reduces the problem of trajectory optimization to the numerical integration of differential equations by the continuation method.     

The analysis of ballistic capabilities for countering disturbances associated with temporary emergency electric propulsion shutdown

The paper analyzes the possibility for countering ballistic perturbations of the interplanetary transfer trajectory of the spacecraft with electric propulsion (EP) associated with the temporary impossibility of the normal use of the EP in phases of the heliocentric transfer. The main result of the present study is the method for the determination of a new nominal trajectory, at any point of which the allowed duration of the emergency shutdown of electric propulsion is large enough. The numerical analysis is given for one of the possible scenarios of spacecraft injection into the operational heliocentric orbit for solar research.     

Optimal switching strategy for radially accelerated trajectories

This paper studies the problem of a spacecraft subject to an outward radial thrust, with constant modulus, that may be switched on or off at suitable time intervals. The problem is to find the optimal strategy to guarantee the possibility of transferring the spacecraft from an initial to a final position in a given time interval using the least amount of thrust level. The problem is solved in an optimal framework, using an indirect approach. A number of different mission scenarios are studied in detail: escape missions, flyby missions and rendezvous missions. In the latter case the spacecraft uses a hybrid system comprising an high thrust propulsion system for the final impulsive maneuver. The optimal switching strategy allows one to substantially decrease the thrust level when compared to the continuous case (without thrust modulation).     

Air-Breathing Ramjet Electric Propulsion for Controlling Low-Orbit Spacecraft Motion to Compensate for Aerodynamic Drag

Problems on designing the air-breathing ramjet electric propulsion thruster for controlling loworbit spacecraft motion are examined in the paper. Information for choosing orbits’ altitudes for reasonable application of an air-breathing ramjet electric propulsion thruster and propellant exhaust velocity is presented. Estimates of the probable increase of gas concentration in the area of air-breathing ramjet ionization are presented. The test results of the thruster are also given.     

A new stage in the development of ablative pulsed plasma thrusters at the RIAME

This paper presents an overview of the works on ablative pulsed plasma thrusters (APPTs) carried out at the Research Institute of Applied Mechanics and Electrodynamics (RIAME). The main features of next generation thrusters developed at the RIAME in the 2000s are discussed together with the optimization criteria for APPTs intended for use in correction propulsion systems of small spacecraft, e.g., MKA-FKI (developed by the Lavochkin Association) and Soyuz-Sat-O (developed by Maksimov Space Systems Research Institute and the Production Corporation Polyot).     

Earth–Mars halo to halo low thrust manifold transfers

Application of low thrust propulsion to interconnect ballistic trajectories on invariant manifolds associated with multiple circular restricted three body systems has been investigated. Sun-planet three body models have been coupled to compute the two ballistic trajectories, where electric propulsion is used to interconnect these trajectories as no direct intersection in the Poincarè sections exists. The ability of a low thrust to provide the energy change required to transit the spacecraft between two systems has been assessed for some Earth to Mars transfers. The approach followed consists in a planetary escape on the unstable manifold starting from a periodic orbit around one of the two collinear libration points near the secondary body. Following the planetary escape and the subsequent coasting phase, the electric thruster is activated and executes an ad-hoc thrusting phase. The complete transfer design, composed of the three discussed phases, and possible applications to Earth–Mars missions is developed where the results are outlined in this paper.     

Non-Keplerian orbits for electric sails

An electric sail is capable of guaranteeing the fulfilment of a class of trajectories that would be otherwise unfeasible through conventional propulsion systems. In particular, the aim of this paper is to analyze the electric sail capabilities of generating a class of displaced non-Keplerian orbits, useful for the observation of the Sun’s polar regions. These orbits are characterized through their physical parameters (orbital period and solar distance) and the spacecraft propulsion capabilities. A comparison with a solar sail is made to highlight which of the two systems is more convenient for a given mission scenario. The optimal (minimum time) transfer trajectories towards the displaced orbits are found with an indirect approach.     

New families of Sun-centered non-Keplerian orbits over cylinders and spheres

This paper introduces new families of Sun-centered non-Keplerian orbits (NKOs) that are constrained to a three-dimensional, cylindrical or spherical surface. As such, they are an extension to the well-known families of displaced NKOs that are confined to a two-dimensional plane. The cylindrical and spherical orbits are found by investigating the geometrically constrained spacecraft dynamics. By imposing further constraints on the orbit’s angular velocity and propulsive acceleration, the set of feasible orbits is defined. Additionally, the phase spaces of the orbits are explored and a numerical analysis is developed to find periodic orbits. The richness of the problem is further enhanced by considering both an inverse square acceleration law (mimicking solar electric propulsion) and a solar sail acceleration law to maintain the spacecraft on the three-dimensional surface. The wealth of orbits that these new families of NKOs generate allows for a range of novel space applications.     

The invention that opened the solar system to exploration

The invention of gravity-propelled interplanetary space travel (also known as “gravity-assist trajectories”) in the early 1960s broke the high-energy barrier of classical space travel based on reaction propulsion, and made possible the exploration of the entire solar system with instrumented spacecraft. In this concept, a free-fall spacecraft is launched from a launch planet P₁ to a nearby planet P₂ such that its gravitational field (superimposed on the gravitational field of the Sun) catapults the vehicle to another planet P₃, which in turn is used to repeat the process. Thus, through a series of planetary encounters, a gravity-propelled trajectory P₁-P₂-P₃-P₄-…-P_N is generated. This paper describes how the invention was conceived and how the difficult mathematical problem of computing the trajectories was solved in order to numerically investigate and use the invention in actual missions. The crucial roles played by the UCLA Computing Facility and the Departments of Mathematics and Physics are also described.     

On the detectability of antimatter propulsion spacecraft

It is shown that the NASA Gamma-Ray Observatory will be able to detect large interstellar spacecraft at distances up to 300 pc by the -ray emission from the propulsion system alone. The distance limit is set by the possibility of recognizing such objects by their proper motions.     

Artificial equilibrium points for a generalized sail in the circular restricted three-body problem

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.     

Symmetric theory of probe-plasma interactions

The theory of interactions between a probe and the surrounding plasma at rest is developed in a spherically and in a cylindrically symmetric model (probe theory). The theory is based on the Vlasov-Poisson system; a general numerical program was developed to solve this system by means of an iterative procedure. Various ambient plasma and charged particle emission properties are described by the complete set of boundary conditions for the distribution functions in the phase space. By use of this numerical method, potential and space charge density in the whole surroundings of the probe as well as the current densities of all plasma constituents are calculated self-consistently.Furthermore, the regions of the phase space with particle trajectories of the same kind can be approximated depending on the plasma properties. Then, the current densities can be estimated analytically. This approach to the problem yields self-consistent approximations and is the only stringent derivation of the thick sheath and of the thin sheath approximation of the classical Langmuir theory. These approximations are generalized with respect to the charged particle emission from the surface.The symmetric probe theory is applied to the following problems of spacecraft environment and spacecraft charging: (i) a spacecraft in the ionosphere with very negative surface potential, (ii) a spacecraft in the solar wind with strong photoelectron emission, and (iii) a spacecraft in the transition region of comet Halley with very strong secondary plasma emission.     

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

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.     

Bounded relative motions for formation flying in displaced orbits by low-thrust propulsion

This paper discusses a numerical searching approach for the relative motion of formation flying in displaced orbits by spacecraft with low-thrust propulsion. The nonlinear dynamical model of spacecraft is established in a two-body rotating reference frame with arbitrary polar component of momentum and thrust-induced acceleration. Motions near the stable equilibria are distinguished from each other by means of five-dimensional variables, which can then be compressed uniquely into two-dimensional mapping images characterized by the crossing interval and the angle drifts. The surjective but not injective mapping makes the generation of three configurations of the relative motions possible. The corresponding relative orbits for three kinds of two-spacecraft formation flying are searched and exemplified based on the formation conditions formulized as functions of the crossing interval and the angle drifts. Furthermore, based on the assignment of displaced relative orbits to five-dimensional vector, the working orbit of the deputy for a specific chief can also be searched via the optimization algorithm to generate the bounded relative motion with the minimum thrust acceleration magnitude, which is of certain significance in reducing fuel consumption of formations.     

On target for Venus – set oriented computation of energy efficient low thrust trajectories

Recently new techniques for the design of energy efficient trajectories for space missions have been proposed that are based on the circular restricted three body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space to systematically construct energy efficient flight paths. In this paper, we extend this model in order to account for a continuously applied control force on the spacecraft as realized by certain low thrust propulsion systems. We show how the techniques for the trajectory design can be suitably augmented and compute approximations to trajectories for a mission to Venus.