Optimization of the trajectory of the spacecraft insertion into the system of heliocentric orbits

The possibility of the spacecraft insertion into the system of operational heliocentric orbits has been analyzed. It has been proposed to use a system of several operational heliocentric orbits. On each orbit, the spacecraft makes one or more revolutions around the Sun. These orbits are characterized by a relatively small perihelion radius and relatively high inclination, which allows one to investigate the polar regions of the Sun. The transition of the spacecraft from one orbit to another has been performed using an unpowered gravity assist maneuver near Venus and does not require the cruise propulsion operation. Each maneuver transfers the spacecraft into the sequence of operational heliocentric orbits. We have analyzed several systems of operational heliocentric orbits into which the spacecraft can be inserted by means of the considered transportation system with electric propulsion (EP). The mass of the spacecraft delivered to these systems of operational orbits has been estimated.     

Optimization of transfer trajectories to the Apophis asteroid for spacecraft with high and low thrust

The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid’s satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft’s hyperbolic velocity “at infinity” during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft’s final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.     

Space patrol: Variants of the optical barrier scheme

Different variants of the space patrol system to be designed for discovering and cataloging space objects hazardous for the Earth have been investigated. The basic idea of this system is to create an optical barrier using the telescopes deployed in a heliocentric orbit. Difficulties (as well as ways of overcoming them) of this program are analyzed, associated with form and position of the orbit of a space object relative to the patrol spacecraft, determination of orbit parameters, and mutual motion of space objects and the telescopes on spacecraft. The barrier’s schemes with scanning vertical or horizontal belts are considered. Some examples of observational conditions are presented for space objects crossing the barrier region: angular positions, velocities, distances, and numbers of days during which they are observed in the barrier region. The barrier’s characteristics are given for telescopes deployed in the orbits of the Earth and Venus.     

Mission analysis and systems design of a near-term and far-term pole-sitter mission

This paper provides a detailed mission analysis and systems design of a near-term and far-term pole-sitter mission. The pole-sitter concept was previously introduced as a solution to the poor temporal resolution of polar observations from highly inclined, low Earth orbits and the poor high-latitude coverage from geostationary orbit. It considers a spacecraft that is continuously above either the north or south pole and, as such, can provide real-time, continuous and hemispherical coverage of the polar regions. Being on a non-Keplerian orbit, a continuous thrust is required to maintain the pole-sitter position. For this, two different propulsion strategies are proposed, which result in a near-term pole-sitter mission using solar electric propulsion (SEP) and a far-term pole-sitter mission where the SEP thruster is hybridized with a solar sail. For both propulsion strategies, minimum propellant pole-sitter orbits are designed. In order to maximize the spacecraft mass at the start of the operations phase of the mission, the transfer from Earth to the pole-sitter orbit is designed and optimized assuming either a Soyuz or an Ariane 5 launch. The maximized mass upon injection into the pole-sitter orbit is subsequently used in a detailed mass budget analysis that will allow for a trade-off between mission lifetime and payload mass capacity. Also, candidate payloads for a range of applications are investigated. Finally, transfers between north and south pole-sitter orbits are considered to overcome the limitations in observations due to the tilt of the Earth's rotational axis that causes the poles to be alternately situated in darkness. It will be shown that in some cases these transfers allow for propellant savings, enabling a further extension of the pole-sitter mission.     

Two-craft tether formation relative equilibria about circular orbits and libration points

The relative equilibria of a two spacecraft tether formation connected by line-of-sight elastic forces moving in the context of a restricted two-body system and a circularly restricted three-body system are investigated. For a two spacecraft formation moving in a central gravitational field, a common assumption is that the center of the circular orbit is located at the primary mass and the center of mass of the formation orbits around the primary in a great-circle orbit. The relative equilibrium is called great-circle if the center of mass of the formation moves on the plane with the center of the gravitational field residing on it; otherwise, it is called a nongreat-circle orbit. Previous research shows that nongreat-circle equilibria in low Earth orbits exhibit a deflection of about a degree from the great-circle equilibria when spacecraft with unequal masses are separated by 350 km. This paper studies these equilibria (radial, along-track and orbit-normal in circular Earth orbit and Earth–Moon Libration points) for a range of inter-craft distances and semi-major axes of the formation center of mass. In the context of a two-spacecraft Coulomb formation with separation distances on the order of dozens of meters, this paper shows that the equilibria deflections are negligible (less than 10^?6°) even for very heterogeneous mass distributions. Furthermore, the nongreat-circle equilibria conditions for a two spacecraft tether structure at the Lagrangian libration points are developed.     

Application of periodic solutions of three-dimensional three-body problem to designing the orbit of a space telescope

A method of constructing three-dimensional orbits with a necessary evolution in the system the Sun — (Earth + Moon) is described. The orbit (promising from the viewpoint of solving formulated research problems) of the Millimetron spacecraft is suggested. Feasibility of such an orbit is demonstrated, as well as a possibility to observe with its help the majority of objects on the celestial sphere and to transmit the data to the Earth.     

One optimization problem for trajectories of spacecraft rendezvous mission to a group of asteroids

The optimization problem is considered for the trajectory of a spacecraft mission to a group of asteroids. The ratio of the final spacecraft mass to the flight time is maximized. The spacecraft is controlled by changing the value and direction of the jet engine thrust (small thrust). The motion of the Earth, asteroids, and the spacecraft proceeds in the central Newtonian gravitational field of the Sun. The Earth and asteroids are considered as point objects moving in preset elliptical orbits. The spacecraft departure from the Earth is considered in the context of the method of a point-like sphere of action, and the excess of hyperbolic velocity is limited. It is required sequentially to have a rendezvous with asteroids from four various groups, one from each group; it is necessary to be on the first three asteroids for no less than 90 days. The trajectory is finished by arrival at the last asteroid. Constraints on the time of departure from the Earth, flight duration, and final mass are taken into account in this problem.     

Locally Optimal Laws of Control of a Spacecraft Motion with an Electrodynamic Engine at Circumterrestrial Orbits

The motion of a spacecraft under the action of Ampére force is investigated. This force arises as a result of the interaction of the current in a rigid rod, at whose ends the devices which close the electric circuit through the circumterrestrial plasma are located, with the magnetic field of the Earth. The locally optimal laws of control by this rod orientation are found, when one of the elements of the orbit gains the maximum increment under the action of this engine. Numerical estimates of the gained increments are obtained, and it is demonstrated that this engine is a promising tool for the execution of light spacecraft maneuvers at low circumterrestrial orbits.     

Optimal flights to near-Earth asteroid

The spacecraft flights to the Near-Earth asteroid in order to give an impact influence on the asteroid, correct its orbit and prevent the asteroid’s collision with the Earth are analyzed.In the first part, the impulse flights are analyzed in the Lambert approach. There are determined the optimal trajectories maximizing the asteroid deviation from the Earth.In the second part, the flights with the chemical and electric-jet engines are analyzed. The high thrust is used to launch the spacecraft from the geocentric orbit, and the low thrust is applied for the heliocentric motion. On the base of optimal impulse transfer, the optimal low thrust trajectories are determined using Pontryagin maximum principle.The numerical results are given for the flight to the asteroid Toutatis. Parameters of the spacecraft impact on the asteroid are determined. The asteroid deviation from the Earth caused by the spacecraft influence is presented.     

Halo orbits in the vicinity of the L 2 libration point in the Sun-Earth system

Methods are proposed for constructing the orbits of spacecraft remaining for long periods of time in the vicinity of the L ₂ libration point in the Sun-Earth system (so-called halo orbits), and the trajectories of uncontrolled flights from low near-Earth orbits to halo orbits. Halo orbits and flight trajectories are constructed in two stages: A suitable solution to a circular restricted three-body problem is first constructed and then transformed into the solution for a restricted four-body problem in view of the real motions of the Sun, Earth, and Moon. For a halo orbit, its prototype in the first stage is a combination of a periodic Lyapunov solution in the vicinity of the L ₂ point and lying in the plane of large-body motion, with the solution for the linear second-order system describing small deviations of the spacecraft from this plane along the periodic solution. The desired orbit is found as the solution to the three-body problem best approximating the prototype in the mean square. The constructed orbit serves as a similar prototype in the second stage. In both stages, the approximating solution is constructed by continuation along a parameter that is the length of the approximation interval. Flight trajectories are constructed in a similar manner. The prototype orbit in the first stage is a combination of a solution lying in the plane of large-body motion and a solution for a linear second-order system describing small deviations of the spacecraft from this plane. The planar solution begins near the Earth and over time tends toward the Lyapunov solution existing in the vicinity of the L ₂ point. The initial conditions of both prototypes and the approximating solutions correspond to the spacecraft’s departure from a low near-Earth orbit at a given distance, perigee, and inclination.     

Electric transfer optimization for mars sample return mission

The aim of this paper is to analyse an alternative scenario for Mars Sample Return Orbiter mission, where electric propulsion is used for Earth-Mars and Mars-Earth heliocentric cruises and for Mars orbit insertion / escape transfers, whereas chemical propulsion is used for final Mars rendezvous. The problem consists in minimizing the initial vehicle mass to obtain a specific final dry mass in reasonable time. The planetocentric phases correspond to continuous low-thrust trajectories, spiraling around Mars between a low orbit and the influence sphere altitude. The heliocentric phases consist of a succession of low-thrust and coasting arcs with specific departure and arrival conditions at the Earth. For these two types of transfer, efficient optimal control tools exist based on Pontryagin's maximum principle. Thanks to the coordination between planetocentric and heliocentric phases, the solution obtained with these two separate tools gives a good upper bound of the optimal solution in terms of propellant consumption and duration. This optimization procedure is described and finally applied to the proposed mission. The numerical results are presented and compared with the baseline chemical mission solution. The electric option could allow to decrease the spacecraft departure mass but may lead to rather long mission duration.     

Applications of multi-body dynamical environments: The ARTEMIS transfer trajectory design

The application of forces in multi-body dynamical environments to permit the transfer of spacecraft from Earth orbit to Sun–Earth weak stability regions and then return to the Earth–Moon libration (L₁ and L₂) orbits has been successfully accomplished for the first time. This demonstrated that transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecrafts into Earth–Moon libration orbits by means of these applications.     

Design of optimal earth pole-sitter transfers using low-thrust propulsion

Recent studies have shown the feasibility of an Earth pole-sitter mission using low-thrust propulsion. This mission concept involves a spacecraft following the Earth's polar axis to have a continuous, hemispherical view of one of the Earth's poles. Such a view will enhance future Earth observation and telecommunications for high latitude and polar regions. To assess the accessibility of the pole-sitter orbit, this paper investigates optimum Earth pole-sitter transfers employing low-thrust propulsion. A launch from low Earth orbit (LEO) by a Soyuz Fregat upper stage is assumed after which solar electric propulsion is used to transfer the spacecraft to the pole-sitter orbit. The objective is to minimize the mass in LEO for a given spacecraft mass to be inserted into the pole-sitter orbit. The results are compared with a ballistic transfer that exploits manifold-like trajectories that wind onto the pole-sitter orbit. It is shown that, with respect to the ballistic case, low-thrust propulsion can achieve significant mass savings in excess of 200 kg for a pole-sitter spacecraft of 1000 kg upon insertion. To finally obtain a full low-thrust transfer from LEO up to the pole-sitter orbit, the Fregat launch is replaced by a low-thrust, minimum time spiral, which provides further mass savings, but at the cost of an increased time of flight.     

The Use of a Solar Electrojet Propulsion System for Jupiter Satellite Injection

The problem of optimization of the interplanetary trajectory of flight for a multistage spacecraft with high- and low-thrust engines into the Jupiter satellite orbit is considered. Low-thrust engines (stationary plasma engines) are used on a heliocentric flight segment. Their operation is maintained with electric power supply from solar batteries. The principal feasibility of the realization of such a project is shown, and estimations of the mass of a spacecraft placed into Jupiter's satellite orbit are presented.     

Asteroidal resources for space manufacturing

Earth-approaching asteroids (Apollos and Amors) may be competitive candidates as raw materials for space manufacturing. The total energy per unit mass required to transfer material from some of these bodies to high Earth orbit is comparable to that for lunar material. Recent optical studies suggest ordinary and carbonaceous chondrite compositions for these asteroids, with some containing large quantities of metallic iron and nickel, and others, carbon, hydrogen and nitrogen. Discoveries of several new candidate asteroids over the next few years will allow for a better selection of materials and mission possibilities. Material from one of these asteroids, either in raw or manufactured form, could be returned to the vicinity of the Earth by a solar-powered mass-driver reaction engine. With a requirement of ～60 shuttle flights, and with minimal development costs, an automated mission to a 200-m dia. (10⁷ ton) metal-rich asteroid could be carried out by a mass-driver tug assembled in low Earth orbit using shuttle tankage as reaction mass. Such a tug could, within a few years, move the asteroid into high Earth orbit for the manufacturing of ～ 20 satellite power stations using a portion of the asteroid itself as reaction mass. In the next few years over 100 asteroids in this size range could be discovered, orbits determined and composition types classified using existing earthbased and spaceborne search techniques.     

欧空局今后十年空间探测战略

欧空局目前正在研究今后十年的空间探测任务,这些任务可以分为两大类,一类是具有研究性的地球探测任务,另一类是可供使用的地球观察任务。这些研究要求的卫星质量不同,小的不足1000kg,大的可达3000kg;功率不同,小的不到500W,大的超过1500W;轨道高度也不同,从500km到800km。除降雨量观测任务由于飞行器结构和系统的限制是在低倾角轨道上执行外,其他大部分任务将在太阳同步轨道上执行。     

A model for the evolution of the on-orbit man-made debris environment

A model for the evolution of the low Earth orbit man-made debris population is presented and the results of several test cases discussed. Debris sources include normal operations in space, explosions occurring on spacecraft in orbit, and collisions between objects in orbit; the stochastic occurrence of these deposition events is modeled using Monte Carlo techniques. A technique for discriminating between objects populating long-life vs rapid-decay orbits is discussed and applied to the analysis of debris contributions from collisions of comparable sized objects. In varying degrees, each of the cases presented indicate there is cause for concern for spacecraft and space operations from the 1990s onward-man-made debris will play a role which may vary from presenting a considerable hazard to certain operations or certain spacecraft to effectively prohibiting the use of certain spaceccraft or space operations.     

General solution for the optimal trajectory of an AFE-type spacecraft

The aeroassisted flight experiment (AFE) refers to an experimental spacecraft to be launched and then recovered by the Space Shuttle. It simulates a transfer from a geosynchronous Earth orbit (GEO) to a low Earth orbit (LEO). In this paper, with reference to an AFE-type spacecraft, an actual GEO-to-LEO transfer is considered under the following assumptions: the GEO and LEO orbital planes are identical; both the initial and final orbits are circular; the initial phase angle is given, while the final phase angle is free. The aeroassisted orbital transfer trajectory involves three branches: a preatmospheric branch, GEO-to-entry; an atmospheric branch, entry-to-exit; a post-atmospheric branch, exit-to-LEO. The optimal trajectory is determined by minimizing the total characteristic velocity. The optimization is performed with respect to the velocity impulses at GEO, LEO, and the time history of the angle of bank during the atmospheric pass. It is assumed that the entry path inclination is free and that the angle of attack is constant, = 17.0 deg. The sequential gradient-restoration algorithm is used to compute the optimal trajectory and it is shown that the best atmospheric pass is to be performed with constant angle of bank. The resulting optimal trajectory constitutes an ideal nominal trajectory for the generation of guidance trajectories for two reasons: the fact that the low value of the characteristic velocity is accompanied by relatively low values of the peak heating rate and the peak dynamic pressure; and the simplicity of the control distribution, requiring constant angle of bank.     

On solving the problems of optimization of trajectories of many-revolution orbit transfers of spacecraft

The problem of optimal control over many-revolution spacecraft orbit transfers between circular coplanar orbits of satellites is considered. The spacecraft flight is controlled by a thrust vector of a jet engine with restricted thrust (JERT). The mass expenditure is minimized at a limited time of flight. The optimal control problem is solved based on the maximum principle. The boundary value problem of the maximum principle is solved numerically using the shooting method. A modified computation scheme of the shooting method is suggested (multi-point shooting), as well as a method (correlated with the scheme) of choosing the initial approximation with the use of a solution to the optimization problem in the impulse formulation. The scheme and method allow one to construct many-revolution spacecraft orbit transfers.     

On the features of long-term evolution of a high-apogee orbit of the SPECTR-R spacecraft

The practical tasks related to qualitative investigation of long-term evolution of high-apogee orbits of artificial Earth satellites (AES), for which the main perturbing factors are gravitational perturbations from the Moon and the Sun, are considered. Attention is given to the problem of the ballistic lifetime of similar orbits, and the issues associated with possibilities of the correction of orbits for ensuring the required duration of their ballistic lifetime are considered. The orbit of the SPECTR-R spacecraft launched in July of 2011 is considered as an example.