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.     

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.     

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.     

Power-limited low-thrust trajectory optimization with operation point detection

The power-limited solar electric propulsion system is considered more practical in mission design. An accurate mathematical model of the propulsion system, based on experimental data of the power generation system, is used in this paper. An indirect method is used to deal with the time-optimal and fuel-optimal control problems, in which the solar electric propulsion system is described using a finite number of operation points, which are characterized by different pairs of thruster input power. In order to guarantee the integral accuracy for the discrete power-limited problem, a power operation detection technique is embedded in the fourth-order Runge-Kutta algorithm with fixed step. Moreover, the logarithmic homotopy method and normalization technique are employed to overcome the difficulties caused by using indirect methods. Three numerical simulations with actual propulsion systems are given to substantiate the feasibility and efficiency of the proposed method.     

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.     

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.     

Artificial halo orbits for low-thrust propulsion spacecraft

We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L ₁ and L ₂ in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L ₁ and beyond L ₂ where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L ₁ decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L ₂ in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases and then decreases after the thrust acceleration exceeds 0.415 mm/s². Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s².     

Sun-perturbed earth-to-moon transfers with low energy and moderate flight time

We construct a spacecraft transfer with low cost and moderate flight time from the Earth to the Moon. The motion of the spacecraft is modeled by the planar circular restricted three-body problem including a perturbation due to the solar gravitation. Our approach is to reduce computation of optimal transfers to a non-linear boundary value problem. Using a computer software called AUTO, we solve it and continue its solutions numerically to obtain the optimal transfers. Our result also shows that the use of the solar gravitation can further lower the transfer cost drastically.     

Symmetries in the Optimal Control of Solar Sail Spacecraft

The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods perform the terminal fine tuning of the optimization parameters.     

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 long-duration balloon payload for hard X-ray and gamma-ray observations of the sun

We describe a balloon payload designed to study the processes of energy release, particle acceleration, and heating of the active corona, in hard X-ray microflares and normal flares. An array of liquid nitrogen-cooled germanium detectors together with large area phoswich scintillation detectors provide the highest sensitivity (∼500 cm²) and energy resolution (≤0.7 keV) ever achieved for solar hard X-ray (∼15–600 keV) measurements. These detectors were flown in February 1987 from Australia on a long duration RAdiation COntrolled balloON (RACOON) flight (LDBF) which provided 12 days of observations before cutdown in Brazil. The payload includes solar cells for power, pointing and navigation sensors, a microprocessor controlled data system with VCR tape storage, and transmitters for GOES and ARGOS spacecraft. This successful flight illustrates the potential of LDBF's for solar flare studies.

     

Solar sail time-optimal interplanetary transfer trajectory design

The fuel consumption associated with some interplanetary transfer trajectories using chemical propulsion is not affordable. A solar sail is a method of propulsion that does not consume fuel. Transfer time is one of the most pressing problems of solar sail transfer trajectory design. This paper investigates the time-optimal interplanetary transfer trajectories to a circular orbit of given inclination and radius. The optimal control law is derived from the principle of maximization. An indirect method is used...     

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.     

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.     

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.     

Some peculiarities of the power spectrum of the 5-min solar brightness oscillations

Several results of the solar irradiance observations carried out with the IPHIR experiment on board the Soviet spacecraft within the PHOBOS Project are considered. The time variations of the power spectrum of 5-min solar oscillations is discussed. It is found that the lines are generated inhomogeneously in the spectrum as a whole. Each of the frequencies is excited separately at a definite time interval. The duration of active periods does not exceed 2 or 3 hours.     

A multi-objective approach to the design of low thrust space trajectories using optimal control

In this article, we introduce a novel three-step approach for solving optimal control problems in space mission design. We demonstrate its potential by the example task of sending a group of spacecraft to a specific Earth L ₂ halo orbit. In each of the three steps we make use of recently developed optimization methods and the result of one step serves as input data for the subsequent one. Firstly, we perform a global and multi-objective optimization on a restricted class of control functions. The solutions of this problem are (Pareto-)optimal with respect to ΔV and flight time. Based on the solution set, a compromise trajectory can be chosen suited to the mission goals. In the second step, this selected trajectory serves as initial guess for a direct local optimization. We construct a trajectory using a more flexible control law and, hence, the obtained solutions are improved with respect to control effort. Finally, we consider the improved result as a reference trajectory for a formation flight task and compute trajectories for several spacecraft such that these arrive at the halo orbit in a prescribed relative configuration. The strong points of our three-step approach are that the challenging design of good initial guesses is handled numerically by the global optimization tool and afterwards, the last two steps only have to be performed for one reference trajectory.     

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).