Novel mission concepts for polar coverage: An overview of recent developments and possible future applications

The paper provides a survey of novel mission concepts for continuous, hemispheric polar observation and direct-link polar telecommunications. It is well known that these services cannot be provided by traditional platforms: geostationary satellites do not cover high-latitude regions, while low- and medium-orbit Sun-synchronous spacecraft only cover a narrow swath of the Earth at each passage. Concepts that are proposed in the literature are described, including the pole-sitter concept (in which a spacecraft is stationary above the pole), spacecraft in artificial equilibrium points in the Sun–Earth system and non-Keplerian polar Molniya orbits. Additionally, novel displaced eight-shaped orbits at Lagrangian points are presented. For many of these concepts, a continuous acceleration is required and propulsion systems include solar electric propulsion, solar sail and a hybridisation of the two. Advantages and drawbacks of each mission concept are assessed, and a comparison in terms of high-latitude coverage and distance, spacecraft mass, payload and lifetime is presented. Finally, the paper will describe a number of potential applications enabled by these concepts, focusing on polar Earth observation and telecommunications.     

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.     

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.     

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.     

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.     

About one problem of trajectory optimization

The optimization problem for trajectories of spacecraft flight from the Earth to an asteroid is considered in this paper. The flight is realized in the central Newtonian gravitational field of the Sun with a possibility of gravitational maneuvers near planets. Perturbation maneuvers are taken into account using the method of point area of action with a limitation on the flyby altitude. The spacecraft is controlled by changing the value and direction of the engine thrust. The problem is solved taking into account constraints on the launch time, flight duration, and minimum distance to the Sun.     

The deep space 1 extended mission

The primary mission of Deep Space 1 (DS1), the first flight of the New Millennium program, completed successfully in September 1999, having exceeded its objectives of testing new, high-risk technologies important for future space and Earth science missions. DS1 is now in its extended mission, with plans to take advantage of the advanced technologies, including solar electric propulsion, to conduct an encounter with comet 19P/Borrelly in September 2001. During the extended mission, the spacecraft's commercial star tracker failed; this critical loss prevented the spacecraft from achieving three-axis attitude control or knowledge. A two-phase approach to recovering the mission was undertaken. The first involved devising a new method of pointing the high-gain antenna to Earth using the radio signal received at the Deep Space Network as an indicator of spacecraft attitude. The second was the development of new flight software that allowed the spacecraft to return to three-axis operation without substantial ground assistance. The principal new feature of this software is the use of the science camera as an attitude sensor. The differences between the science camera and the star tracker have important implications not only for the design of the new software but also for the methods of operating the spacecraft and conducting the mission. The ambitious rescue was fully successful, and the extended mission is back on track.     

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.     

Novel orbits of Mercury,Venus and Mars enabled using low-thrust propulsion

Exploration of the inner planets of the Solar System is vital to significantly enhance the understanding of the formulation of the Earth and other planets. This paper therefore considers the development of novel orbits of Mars, Mercury and Venus to enhance the opportunities for remote sensing of these planets. Continuous acceleration is used to extend the critical inclination of highly elliptical orbits at each planet and is shown to require modest thrust magnitudes. This paper also presents the extension of existing sun-synchronous orbits around Mars. However, unlike Earth and Mars, natural sun-synchronous orbits do not exist at Mercury or Venus. This research therefore also uses continuous acceleration to enable circular and elliptical sun-synchronous orbits, by ensuring that the orbit's nodal precession rate matches the planets mean orbital rate around the Sun, such that the lighting along the ground-track remains approximately constant over the mission duration. This property is useful both in terms of spacecraft design, due to the constant thermal conditions, and for comparison of images. Considerably high thrust levels are however required to enable these orbits, which are prohibitively high for orbits with inclinations around 90°. These orbits therefore require some development in electric propulsion systems before becoming feasible.     

微纳卫星在轨温度场快速分析

微纳卫星低成本和方案快速迭代的特点,对其热控系统提出了简化、通用、快速设计等新要求。文章考察分析微纳卫星在热控系统设计方面所面临的困难和技术挑战,针对一般性椭圆地球轨道给出空间外热流随时间变化的计算方法;在此基础上,针对微纳卫星的结构和传热特点,提出整星热平衡方程对真近点角的连续积分方法和卫星温度场的多节点集总参数分析方法,并建立相应的数学模型,对微纳卫星算例进行计算分析和结果验证。结果表明,相对于传统商业软件网格划分建模的分析途径,该方法能对微纳卫星各主要部件的在轨温度变化进行快速建模和计算,可为微纳卫星热控系统的设计和优化提供便捷的初步评估手段。     

低轨航天器磁推进方法

基于地球空间磁场的磁作用效应,提出了一类低轨航天器无工质消耗的磁推进方法,并对航天器的高度保持进行了研究。该方法具有作用机理明晰、物理结构简单、控制策略灵活等特征。以磁场对磁体作用的磁矩理论为基础,建立了带磁航天器飞行的磁推力模型,提出了基于磁力线追踪策略的轨道高度保持方法。利用熟知的IGRF11地磁模型,通过数值仿真计算,验证了磁推进方法对于600～1000km圆轨道航天器进行高度保持的有效性。     

LISA — a study of the ESA cornerstone mission for observing gravitational waves

The primary objective of the Laser Interferometer Space Antenna (LISA) mission is to detect and observe gravitational waves from massive black holes and galactic binaries in the frequency range 10⁻⁴ to 10⁻¹ Hz. This low-frequency range is inaccessible to ground-based interferometers because of the unshieldable background of local gravitational noise and because ground-based interferometers are limited in length to a few km. LISA is an ESA cornerstone mission and recently had a system study (Ref. 1) carried out by a consortium led by Astrium, which confirmed the basic configuration for the payload with only minor changes, and provided detailed concepts for the spacecraft and mission design. The study confirmed the need for a drag-free technology demonstration mission to develop the inertial sensors for LISA, before embarking on the build of the flight sensors. With a technology demonstration flight in 2005, it would be possible to carry out LISA as a joint ESA-NASA mission with a launch by 2010 subject to the funding programmatics. The baseline for LISA is three disc-like spacecraft each of which consist of a science module which carries the laser interferometer payload (two in each science module) and a propulsion module containing an ion drive and the hydrazine thrusters of the AOCS. The propulsion module is used for the transfer from earth escape trajectory provided by the Delta II launch to the operational orbit. Once there the propulsion module is jettisoned to reduce disturbances on the payload. Detailed analysis of thermal and gravitational disturbances, a model of the drag-free control and of the interferometer operation confirm that the strain sensitivity of the interferometer will be achieved.     

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.     

State propagation in an uncertain asteroid gravity field

Various spacecraft have been and will be sent to asteroids to characterize them. Generally, an asteroid's gravity field is very irregular and not accurately known when compared to the gravity field of a major planet, Earth in particular. It has been well studied that the irregularity significantly affects the trajectory of an orbiting spacecraft, and causes it to impact or to escape from the asteroid. Complementary to that, this paper focuses on the influence of the limited knowledge of this gravity field on the evolution of the spacecraft's orbit. It develops a general method by which this influence can be quantified. This method comprises specific Monte Carlo simulations with a discrete set of low-altitude orbits, taking into account the uncertainties in the gravity-field parameters. For illustration purposes, it is applied to two different asteroids. Already after three revolutions, the gravity-field uncertainties propagate to significant position uncertainties; this specifically holds for prograde orbits, and around the smaller asteroid. Applying this robust and accurate method helps mission designers and planners to assess the risk posed by gravity uncertainties, and take appropriate measures such as choosing the most favorable orbital geometries and/or lowering the orbit more slowly.     

Nonlinear feedback control of low-thrust orbital transfer in a central gravitational field

This paper investigates the problem of continuous-thrust orbital transfer using orbital elements feedback from a nonlinear control standpoint, utilizing concepts of controllability, feedback stabilizability and their interaction. Gauss's variational equations (GVEs) are used to model the state-space dynamics of motion under a central gravitational field. First, the notion of accessibility is reviewed. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived which asymptotically steers a spacecraft form an initial elliptic orbit to any given elliptic orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proven, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft onto a parabolic escape trajectory.     

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.     

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.     

Optimization of Flights between the Orbits of Artificial Satellites of Two Planets Using a Combination of High and Low Thrusts

The problem of optimization of the trajectory of an interplanetary flight of a multistaged spacecraft using jet engines with high and low thrust is considered. The issues concerning the problem of choosing the main design parameters of a multistage spacecraft are touched upon. A mathematical model of start-to-finish optimization of all segments of the interplanetary flight trajectory is proposed. Using this model the specific features of flights to the orbits of satellites of Jupiter and Mars are studied.     

面向任务的电推进航天器性能优化与控制

针对电推进(EP)系统的性能与任务耦合优化及控制问题,提出一种基于电推进特征参数模型的耦合优化方法。以入轨有效载荷质量转移率最优为目标,推导出化学-电推进组合任务与多模态全电推进任务的完备形式的拓展火箭方程与最优比冲(Isp)表达式,得到多模态连续电推进最优比冲的计算方法,并得到相关参数对最优比冲的影响规律。结果表明,提出的耦合优化方法与最优比冲公式对求解多模态电推进任务的最优比冲和研究电推进航天器耦合优化控制问题具有指导意义和通用性。     

Quasioptimal control with feedback for multiorbit low-thrust transfer between noncoplanar elliptic and circular orbits

The problem of synthesizing stable feedback control is considered based on solving the problem of time minimization for a multiorbit transfer between noncoplanar elliptic and circular orbits in a Newtonian gravitational field. The problem is solved using asymptotic properties and symmetries of optimal control in the unperturbed problem. Stability of the obtained control against external perturbations, deviations of initial conditions, and errors in thrust vector realizations is demonstrated. The obtained quasioptimal control with feedback can be used as an onboard algorithm of spacecraft control and when performing design and ballistic analysis.