木星探测轨道分析与设计

研究了与木星探测相关的轨道设计问题.重点关注木星探测轨道与火星、金星等类地行星探测轨道的不同及由此带来的轨道设计难点.首先分析了绕木星探测任务轨道的选择.建立近似模型讨论了向木星飞行需要借助多颗行星的多次引力辅助,对地木转移的多种行星引力辅助序列,使用粒子群算法搜索了2020年至2025年之间的燃料最省飞行方案并对比得到了向木星飞行较好的引力辅助方式为金星-地球-地球引力辅助.结合多任务探测,研究了航天器在飞向木星途中穿越主小行星带飞越探测小行星的轨道设计.最后,给出2023年发射完整的结合引力辅助与小行星多次飞越的木星探测轨道设计算例.     

Trajectory Analysis and Design for A Jupiter Exploration Mission

The trajectory design for a Jupiter exploration mission is investigated in this paper. The differences between the Jupiter exploration trajectory and the Mars or Venus exploration trajectory are mainly concerned about. Firstly, the selection of the Jupiter-centered orbit is analyzed based on the Galileo Jupiter mission. As for the Earth-Jupiter transfer orbit, the fuel consumption of the direct transfer is too large. So the energy-saving technologies such as the planetary gravity assist should be used for the trajectory to the Jupiter. The different sequences of planetary gravity assists are examined by applying the Particle Swarm Optimization (PSO). According to the searched result, the Venus-Earth-Earth sequence (VEEGA) is the most effective one for the Jupiter mission. During the Jupiter mission, the spacecraft will pass though the main asteroid belt between the orbits of Mars and Jupiter, and may encounter multiple asteroids. Therefore the Jupiter mission is able to combine with the main-belt asteroid flyby mission. The design method of the intermediate asteroid flyby trajectory is also considered. At last, an entire trajectory for the Jupiter mission launched in 2023 is presented.     

The flyby of Rosetta at asteroid Šteins - mission and science operations

The international Rosetta mission, a cornerstone mission of the european space agency scientific Programme, was launched on 2nd March 2004 on its 10 years journey towards a rendezvous with comet Churyumov-Gerasimenko (Gardini et al., 1999). During its interplanetary flight towards its target Rosetta crosses the asteroid belt twice with the opportunity to observe at close quarters two asteroids: (2867)-Šteins in 2008 and (21)-Lutetia in 2010. The spacecraft design was such that these opportunities could be fully exploited to deliver valuable data to the scientific community. The mission trajectory was controlled such that Rosetta would fly next to asteroid Šteins on the 5th of September 2008 with a relative speed of 8.6 km/s at a minimum distance of 800 km. Mission operations have been carefully planned to achieve the best possible flyby scenario and scientific outcome. The flyby scenario, the optical navigation campaign, and the planning of the scientific observations had to be adapted by the Mission and the Science Operations Centres to the demanding requirements expressed by the scientific community. The flyby was conducted as planned with a large number of successful observations.     

Accessibility of Main-belt Asteroids and Trajectory Design for Multi-target Exploration

The mission designed to explore asteroids has nowadays become a hot spot of deep space exploration, and the accessibility of the explored objects is the most important problem to make clear. The number of asteroids is large, and it needs an enormous quantity of calculations to evaluate the accessibility for all asteroids. In this paper, based on the direct transfer strategy, we have calculated the accessibility for the different regions of the solar system and compared it with the distribution of asteroids. It is found that most main-belt asteroids are accessible by the direct transfer orbit with the launch energy of C₃ = 50 km²/s², and that with an additional small velocity correction, the designed trajectory is able to realize the multi-target flyby mission. Such a kind of multi-target flyby can reach the same effect of the orbit manoeuvre in the ΔV-EGA trajectory scheme^[1,2]. Being assisted by the earth's gravity, the accompanying flight with asteroids or the exploration of more distant asteroids can be realized with a lower energy. In the end, as an example, a trajectory scheme is given, in which the probe flies by multiple main-belt asteroids at first, then with the assistance of the earth's gravity, it makes the accompanying flight to a more distant asteroid.     

Multi-rendezvous low-thrust trajectory optimization using costate transforming and homotopic approach

This paper investigates a method for optimizing multi-rendezvous low-thrust trajectories using indirect methods. An efficient technique, labeled costate transforming, is proposed to optimize multiple trajectory legs simultaneously rather than optimizing each trajectory leg individually. Complex inner-point constraints and a large number of free variables are one main challenge in optimizing multi-leg transfers via shooting algorithms. Such a difficulty is reduced by first optimizing each trajectory leg individually. The results may be, next, utilized as an initial guess in the simultaneous optimization of multiple trajectory legs. In this paper, the limitations of similar techniques in previous research is surpassed and a homotopic approach is employed to improve the convergence efficiency of the shooting process in multi-rendezvous low-thrust trajectory optimization. Numerical examples demonstrate that newly introduced techniques are valid and efficient.     

Mission opportunities for human exploration of Mars

An indirect optimization procedure is applied to find the mission opportunities for a manned or round-trip mission to Mars. Both the conjunction-class and opposition-class high-thrust trajectories are considered, taking into account simple legs (with only departure and arrival impulses), three-impulse legs (departure, midcourse and arrival impulses) and flyby legs, where the non-propelled flyby of the planet Venus is used instead of the midcourse impulse to reduce the propellant consumption. The absolute positions of all the relevant planets repeat almost perfectly after 32 years: therefore, only the mission opportunities in a 32-year syzygistic cycle are analyzed. The two-body problem formulation is sufficient for preliminary analyses of interplanetary missions and the trajectory is approximated by heliocentric conic orbits passing through the centres of the planets. The mission opportunities correspond to the local minima of the characteristic velocity, that is, the sum of the actual velocity changes obtained by expending the propellant. Numerical results are presented to show that the same mathematical approach can be applied to different classes of missions, to emphasize the indications suggested by Pontryagin's Maximum Principle, to point out some periodicities in the solutions and to discuss the problem of providing initial guesses at the solutions.     

Simulation and analysis of the revised Huygens probe entry and descent trajectory and radio link modelling

The Cassini spacecraft will arrive at Saturn in 2004 carrying the Huygens probe. The beginning of the Cassini tour at Saturn has been redesigned to achieve a different relative orbiter/probe geometry in order to compensate for the probe relay receiver design flaw that was discovered during tests in February 2000. This paper presents a numerical simulation of the Huygens atmospheric entry and descent trajectory and the Cassini flyby trajectory during the probe mission. A variety of parameters that are crucial for the probe system and its scientific payload have been calculated and analyzed together with an assessment of their uncertainties. Furthermore the orbiter/probe relay link was simulated in order to assess any potential data loss on the basis of an analytical model of the actual Huygens receiver onboard the Cassini spacecraft. The redesigned Cassini/Huygens mission satisfies all science and engineering requirements and assures the best possible radio link for the entire nominal mission duration.     

Evolutionary principles applied to mission planning problems

The space mission planning process is considered as a hybrid optimal control problem. Hybrid optimal control problems are problems that include categorical variables in the problem formulation. For example, an interplanetary trajectory may consist of a sequence of low thrust arcs, impulses and planetary flybys. However, for each choice of the structure of the mission, for example, for a particular choice of the number of planetary flybys to be used, there is a corresponding optimal trajectory. It is not a priori clear which structure will yield the most efficient mission. In this work we present a mathematical framework for describing such problems and solution methods for the hybrid optimal control problem based on evolutionary principles that have the potential for being a robust solver of such problems. As an example, the methods are used to find the optimal choice of three asteroids to visit in sequence, out of a set of eight candidate asteroids, in order to minimize the fuel required.     

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).     

Broad search for unstable resonant orbits in the planar circular restricted three-body problem

Unstable resonant orbits in the circular restricted three-body problem have increasingly been used for trajectory design using optimization and invariant manifold techniques. In this study, several methods for computing these unstable resonant orbits are explored including grid searches, flyby maps, and continuation. Families of orbits are computed focusing on orbits with multiple loops near the secondary in the Jupiter–Europa system, and their characteristics are explored. Different parameters such as period and stability are examined for each set of resonant orbits, and the continuation of several specific orbits is explored in more detail.     

Earth–Mars transfers with ballistic escape and low-thrust capture

In this paper novel Earth–Mars transfers are presented. These transfers exploit the natural dynamics of n-body models as well as the high specific impulse typical of low-thrust systems. The Moon-perturbed version of the Sun–Earth problem is introduced to design ballistic escape orbits performing lunar gravity assists. The ballistic capture is designed in the Sun–Mars system where special attainable sets are defined and used to handle the low-thrust control. The complete trajectory is optimized in the full n-body problem which takes into account planets’ orbital inclinations and eccentricities. Accurate, efficient solutions with reasonable flight times are presented and compared with known results.     

Finding KBO Flyby Targets for New Horizons

Development of the New Horizons mission to Pluto and the Kuiper Belt is now fully funded by NASA (Stern and Spencer, this volume). If all goes well, New Horizons will be launched in January 2006, followed by a Jupiter gravity assist in 2007, with Pluto arrival expected in either 2015 or 2016, depending on the launch vehicle chosen. A backup launch date of early 2007, without a Jupiter flyby, would give a Pluto arrival in 2019 or 2020. In either case, a flyby of at least one Kuiper Belt object (KBO) is planned following the Pluto encounter, sometime before the spacecraft reaches a heliocentric distance of 50 AU, in 2021 or 2023 for the 2006 launch, and 2027 or 2029 for the 2007 launch. However, none of the almost 1000 currently-known KBOs will pass close enough to the spacecraft trajectory to be targeted by New Horizons, so the KBO flyby depends on finding a suitable target among the estimated 500,000 KBOs larger than 40 km in diameter. This paper discusses the issues involved in finding one or more KBO targets for New Horizons. The New Horizons team plans its own searches for mission KBOs but will welcome other U.S, or international team who wish to become involved in exchange for mission participation at the KBO.     

A new probability-one homotopy method for solving minimum-time low-thrust orbital transfer problems

Homotopy methods have been widely utilized to solve low-thrust orbital transfer problems, however, it is not guaranteed that the optimal solution can be obtained by the existing homotopy methods. In this paper, a new homotopy method is presented, by which the optimal solution can be found with probability one. Generalized sufficient conditions, which are derived from the parametrized Sard’s theorem, are first developed. A new type of probability-one homotopy formulation, which is custom-designed for solving minimum-time low-thrust trajectory optimization problems and satisfies all these sufficient conditions, is then constructed. By tracking the continuous zero curve initiated by an initial problem with known solution, the optimal solution of the original problem is guaranteed to be solved with probability one. Numerical demonstrations in a three-dimensional time-optimal low-thrust orbital transfer problem with 43 revolutions is presented to illustrate the applications of the method.     

A greedy global search algorithm for connecting unstable periodic orbits with low energy cost.

A method for space mission trajectory design is presented in the form of a greedy global search algorithm. It uses invariant manifolds of unstable periodic orbits and its main advantage is that it performs a global search for the suitable legs of the invariant manifolds to be connected for a preliminary transfer design, as well as the appropriate points of the legs for maneuver application. The designed indirect algorithm bases the greedy choice on the optimality conditions that are assumed for the theoretical minimum transfer cost of a spacecraft when using invariant manifolds. The method is applied to a test case space mission design project in the Earth–Moon system and is found to compare favorably with previous techniques applied to the same project.     

Optimal low-thrust takeoff from an orbit about an oblate planet

Future space missions to the outer planets may depend upon the use of low-thrust propulsion systems. As these planets are decidedly oblate, the question of the effect of that oblateness on a low-thrust trajectory is of some interest. In this paper the problem of optimal energy increase is attacked under the assumption that the coefficients for the second zonal harmonic, i.e.,J ₂, and the nondimensional thrust acceleration are the same order of magnitude. Using a two variable asymptotic expansion technique, a near optimal control program is generated and the first order uniformly valid approximation for the corresponding trajectory is obtained. Tangential thrust is shown to be a good near-optimal thrust program even in the presence of oblateness effects. The optimal control program is found to be oscillatory and quite similar to the optimal control for energy increase in an inverse square gravitational field.This research was supported by the National Aeronautics and Space Administration under Grant NGR-23-005-329.     

Trojans’ Odyssey: Unveiling the early history of the Solar System

In our present understanding of the Solar System, small bodies (asteroids, Jupiter Trojans, comets and TNOs) are the most direct remnants of the original building blocks that formed the planets. Jupiter Trojan and Hilda asteroids are small primitive bodies located beyond the ‘snow line’, around respectively the L₄ and L₅ Lagrange points of Jupiter at ～5.2?AU (Trojans) and in the 2:3 mean-motion resonance with Jupiter near 3.9?AU (Hildas). They are at the crux of several outstanding and still conflicting issues regarding the formation and evolution of the Solar System. They hold the potential to unlock the answers to fundamental questions about planetary migration, the late heavy bombardment, the formation of the Jovian system, the origin and evolution of trans-neptunian objects, and the delivery of water and organics to the inner planets. The proposed Trojans’ Odyssey mission is envisioned as a reconnaissance, multiple flyby mission aimed at visiting several objects, typically five Trojans and one Hilda. It will attempt exploring both large and small objects and sampling those with any known differences in photometric properties. The orbital strategy consists in a direct trajectory to one of the Trojan swarms. By carefully choosing the aphelion of the orbit (typically 5.3?AU), the trajectory will offer a long arc in the swarm thus maximizing the number of flybys. Initial gravity assists from Venus and Earth will help reducing the cruise time as well as the ΔV needed for injection thus offering enough capacity to navigate among Trojans. This solution further opens the unique possibility to flyby a Hilda asteroid when leaving the Trojan swarm. During the cruise phase, a Main Belt Asteroid could be targeted if requiring a modest ΔV. The specific science objectives of the mission will be best achieved with a payload that will perform high-resolution panchromatic and multispectral imaging, thermal-infrared imaging/ radiometry, near- and mid-infrared spectroscopy, and radio science/mass determination. The total mass of the payload amounts to 50?kg (including margins). The spacecraft is in the class of Mars-Express or a down-scaled version of Jupiter Ganymede Orbiter. It will have a dry mass of 1200?kg, a total mass at launch of 3070?kg and a ΔV capability of 700?m/s (after having reached the first Trojan) and can be launched by a Soyuz rocket. The mission operations concept (ground segment) and science operations are typical of a planetary mission as successfully implemented by ESA during, for instance, the recent flybys of Main Belt asteroids Steins and Lutetia.     

Flybys in the planar, circular, restricted, three-body problem

An analysis is presented of gravity assisted flybys in the planar, circular, restricted three-body problem (pcr3bp) that is inspired by the Keplerian map and by the Tisserand- Poincaré graph. The new Flyby map is defined and used to give insight on the flyby dynamics and on the accuracy of the linked-conics model. The first main result of this work is using the Flyby map to extend the functionality of the Tisserand graph to low energies beyond the validity of linked conics. Two families of flybys are identified: Type I (direct) flybys and Type II (retrograde) flybys. The second main result of this work shows that Type I flybys exist at all energies and are more efficient than Type II flybys, when both exist. The third main result of this work is the introduction of a new model, called ??Conics, When I Can??, which mixes numerical integration and patched conics formulas, and has applications beyond the scope of this work. The last main result is an example trajectory with multiple flybys at Ganymede, all outside the linked-conics domain of applicability. The trajectory is computed with the pcr3bp, and connects an initial orbit around Jupiter intersecting the Callisto orbit, to an approach transfer to Europa. Although the trajectory presented has similar time of flight and radiation dose of other solutions found in literature, the orbit insertion ??v is 150 m/s lower. For this reason, the transfer is included in the lander option of the Europa Habitability Mission Study.     

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.     

Feasibility study for near-earth-object tracking by a piggybacked micro-satellite with penetrators

As of August 2007, over 5000 near-earth-objects (NEO) have been discovered. Some already represent a potential danger to the Earth while others might become hazards in the future. The Planetary Society organised in 2007 the “Apophis Mission Design Competition” in response to this potential threat with the objective to identify promising concepts to track NEOs; the asteroid 99942 Apophis was taken as the study case. This paper describes the “Houyi” proposal which was evaluated by the competition jury as an innovative approach to this problem. Instead of launching a large satellite for NEO tracking, this novel concept proposes a miniaturized satellite that is piggybacked onto a larger (scientific) mission. Such mission design would drastically reduce the costs for NEO surveillance. The presented scenario uses the ESA’s SOLO mission as a design baseline for the piggyback option. This paper summarizes the architecture of this CubeSat towards Apophis and extends the previous study by focusing on the feasibility of a piggybacked mission in terms of propulsion requirements.