Showing papers in "Journal of Spacecraft and Rockets in 2007"

Nonlinear Longitudinal Dynamical Model of an Air-Breathing Hypersonic Vehicle

Abstract: A nonlinear, physics-based model of the longitudinal dynamics for an air-breathing hypersonic vehicle is developed. The model is derived from first principles and captures a number of complex interactions between the propulsion system, aerodynamics, and structural dynamics. Unlike conventional aircraft, air-breathing hypersonic vehicles require that the propulsion system be highly integrated into the airframe. Furthermore, full-scale hypersonic aircraft tend to have very lightweight, flexible structures that have low natural frequencies. Therefore, the first bending mode of the fuselage is important, as its deflection affects the amount of airflow entering the engine, thus influencing the performance of the propulsion system. The equations of motion for the flexible aircraft are derivedusingLagrange’sequations.Theequationsof motioncaptureinertial couplingeffectsbetween thepitch and normal accelerations of the aircraft and the structural dynamics. The linearized aircraft dynamics are found to be unstableand,inmostcases,exhibitnonminimumphasebehavior.Thelinearizedmodelalsoindicatesthatthereisan aeroelastic mode that has a natural frequency more than twice the frequency of the fuselage bending mode, and the short-period mode is very strongly coupled with the bending mode of the fuselage.

Mars Exploration Entry, Descent, and Landing Challenges

Abstract: The United States has successfully landed five robotic systems on the surface of Mars. These systems all had landed mass below 0.6 metric tons (t), had landed footprints on the order of hundreds of km and landed at sites below -1 km MOLA elevation due the need to perform entry, descent and landing operations in an environment with sufficient atmospheric density. Current plans for human exploration of Mars call for the landing of 40-80 t surface elements at scientifically interesting locations within close proximity (10's of m) of pre-positioned robotic assets. This paper summarizes past successful entry, descent and landing systems and approaches being developed by the robotic Mars exploration program to increased landed performance (mass, accuracy and surface elevation). In addition, the entry, descent and landing sequence for a human exploration system will be reviewed, highlighting the technology and systems advances required.

Navigating the Road to Autonomous Orbital Rendezvous

Abstract: The fundamental techniques and approaches to orbital rendezvous have predominantly been defined by the United States and Russian space programs. Although both programs were initially pursuing the same goal, they chose two very distinct paths. Themanualmethod pursued by theUnited States has given it the capability to handle a variety of complex rendezvous and docking missions, whereas the Russians’ automated approach has come to symbolize efficiency and reliability. What is the reason that these two storied programs chose such different paths? How have these pioneering decisions affected the course of orbital rendezvous?Where is orbital rendezvous heading in the future? This paper provides a comprehensive overview of the programs,missions, and techniques that have set the standards for orbital rendezvous. In particular, it reveals the rationale and events behind the early engineering decisions regarding orbital rendezvous navigation systems, how they have come to influence ensuing programs, and why these traditional methods are beginning to be replaced by new autonomous approaches for current and future missions.

Density and Winds in the Thermosphere Deduced from Accelerometer Data

Abstract: With the emergence and increased use of highly accurate accelerometers for geodetic satellite missions, a new opportunity has arisen to study nonconservative forces acting on a number of satellites with high temporal resolution. As the number of these satellite missions increases, so does our ability to determine the spatial characteristics and time response of total density and winds in the thermosphere. This paper focuses on the derivation and methodology of inferring density and winds from along-track and cross-track accelerometer measurements, with themain goal of determining the feasibility of this data set. The principal sources of error such as solar radiation pressure, the unknown coefficients of drag and lift, instrument precision and biases, and unaccounted-for winds are discussed in the context of both density and winds. In the context of our treatment of errors, density errors are generally less than 15%, whereas wind-speed errors are more substantial. Finally, comparisons of results to existing empirical models (i.e., horizontal wind model 93) and to self-consistent numerical models (i.e., thermosphere–ionosphere electrodynamic general circulation model) are provided. Comparisons of results to ion drift velocities (as measured by Defense Meteorological Satellite Program) are also provided.

Very-Small-Satellite Design for Distributed Space Missions

Abstract: A new class of remote sensing and scientific distributed space missions is emerging that requires hundreds to thousands of satellites for simultaneous multipoint sensing. These missions, stymied by the lack of a low-cost mass-producible sensor node, can become reality by merging the concepts of distributed satellite systems and terrestrial wireless sensor networks. A novel, subkilogram, very-small-satellite design can potentially enable these missions. Existing technologies are first investigated, such as standardized picosatellites and microengineered aerospace systems. Two new alternatives are then presented that focus on a low-cost approach by leveraging existing commercial mass-production capabilities: a satellite on a chip (SpaceChip) and a satellite on a printed circuit board. Preliminary results indicate that SpaceChip and a satellite on a printed circuit board offer an order of magnitude of cost savings over existing approaches.

Advanced Self-Deployable Structures for Space Applications

Abstract: Cold-hibernated elastic memory structures technology is one of the most recent results of the quest for simple, reliable, and low-cost self-deployable structures. The cold-hibernated elastic memory technology uses shapememory polymers in open-cell foam structures or sandwich structures made of shape-memory-polymer foam cores and polymeric laminated-composite skins. It takes advantage of a polymer’s shape memory and the corresponding internal elastic recovery forces to self-deploy a compacted structure. This paper describes these structures and their major advantages over other expandable and deployable structures presently used. Previous experimental and analytical results indicate that the cold-hibernated elastic memory foam technology can perform robustly in the Earth’s environment as well as in space. Further improvements in cold-hibernated elastic memory technology that can widen potential space applications, including advanced solar-sail structural concepts, are revealed and described.

Autonomous Formation Flying for the PRISMA Mission

Abstract: PRISMA is a technology demonstration mission for satellite formation flying and in-orbit servicing. The space segment comprises the fully maneuverable Main minisatellite and the smaller Target satellite in a low Earth orbit at 700-km altitude. A key mission objective is to demonstrate onboard, fully autonomous, robust, safe, and precise formation flying of spacecraft. This is accomplished by spaceborne global positioning system navigation, guidance, and control functionalities for the maintenance of the relative motion between the two spacecraft. An innovative estimation approach employs a common Kalman filter for the absolute states of Main and Target, which accounts for the interdependency of absolute and relative navigation without the need for an explicit relative state. As a result, the onboard navigation system provides absolute and relative orbit information in real time with a position accuracy of 2 and 0.1 m, respectively. The formation control achieves accuracies of a few tenths of meters with minimum usage of thrusters. The guidance and control concept is detailed with emphasis on a relative eccentricity and inclination vector separation strategy. The paper derives estimates of the expected relative orbit control performances based upon realworld simulations using typical global positioning system receiver and propulsion system characteristics.

Laboratory Experimentation of Autonomous Spacecraft Approach and Docking to a Collaborative Target

Abstract: A new laboratory test bed i s introduced, which enables the hardware -in -the -loop simulation of the autonomous approach and docking of a chaser spacecraft to a target spacecraft of similar mass. The test bed consists of a chaser spacecraft and a target spacecraft simulator s floating via air pads on a flat floor. The prototype docking interface mechanism of Defense Advanced Research Projec ts Agency’s (DARPA’s) Orbital Express mission is integrated on the spacecraft simulators. Relative navigation of the chaser spacecraft is obtained by fusing the measurements from a single -camera vision sensor and an inertial measurement unit , through Kalma n filters . The target is collaborative in the sense that a pattern of three infrared Light Emitting Diodes is mounted on it as reference for the relative navigation. Eight cold -gas on -off thrusters are used for the t ranslation of the chaser vehicle . They a re commanded using a non -linear control algorithm based on S ch mit t triggers. Furthermore, a reaction wheel is used for the vehicle rotation with a proportional derivative linear control. Experimental results are presented of both autonomous proximity maneu ver a nd autonomous docking of the chaser simulator to the non -floating target . The presented results validate the proposed estimation and control methods and demonstrate the capability of the test bed.

On-Orbit Servicing: A New Value Proposition for Satellite Design and Operation

Abstract: The use of humans to service satellites designed for servicing has been adequately demonstrated on the Hubble Space Telescope and International Space Station. Currently, robotic on-orbit servicing technology is maturing with risk reduction programs such asOrbital Express. Robotic servicing appears to be technically feasible and provides a set of capabilities which range from satellite inspection to physical upgrade of components. However, given the current design and operation paradigms of satellite architectures, it appears that on-orbit servicing will not be heavily used, and, as a result, is not likely to be economically viable. To achieve the vision of on-orbit servicing, the development of a newvalue proposition for satellite architectures is necessary. This new value proposition is oriented around rapid response to technological or market change and design of satellites with less redundancy.

Calculation of Stagnation-Point Heating Rates Associated with Stardust Vehicle

Abstract: Stagnation-point heating rate is calculated for the Stardust entry vehicle and for its heat-shieldmodels tested in an arcjetwind tunnel. The calculations aremade for the convective component for both the laminar and turbulent cases, the radiative component produced by the gas flow, and the radiative component produced by solid particles. A onedimensional viscous shock layer method is used with an up-to-date thermochemical, gas–surface interaction, radiation, turbulence, and particulate models. For the flight cases, radiation absorption in the boundary layer is found to increase the convective heating rate by a factor of up to two. The calculated sums of all heating rates for the flight cases are nearly the same as those obtained by Olynick et al., and are substantially larger than those by Gupta. The calculated sums of all heating rates for the arcjet test cases are smaller than those calculated by the formula of Fay and Riddell, and are nearly the same as those experimentally determined using copper calorimeters.

Evaluation of Solar Electric Propulsion Technologies for Discovery Class Missions

Abstract: A detailed study examines the potential benefits that advanced electric propulsion technologies offer to costcapped missions in NASA’s Discovery program. The study looks at potential cost and performance benefits provided by three electric propulsion technologies that are currently in development: NASA’s evolutionary xenon thruster, an enhanced NSTAR system, and a low-power Hall effect thruster. These systems are analyzed on three potential Discovery-class missions and their performance is compared with a state-of-the-art system using the NSTAR ion thruster. An electric propulsion subsystem cost model is used to conduct a cost–benefit analysis for each option. The results show that each proposed technology offers a different degree of performance and/or cost benefit for Discovery-class missions. However, lower subsystem costs (particularly, power processing and digital control interface unit costs) are needed for ion thruster systems, to make them more competitive for cost-capped missions. It is observed that the best mass performance generally comes from electric propulsion systems that best use available solar array power during the mission. Finally, first-flight qualification costs are identified as a significant barrier to the implementation of new electric propulsion technologies on costcapped missions.

GeoSail: an elegant solar sail demonstration mission

Abstract: In this paper a solar sail magnetotail mission concept was examined. The 43-m square solar sail is used to providethe required propulsion for continuous sun-synchronous apse-line precession. The main driver in this mission was found to be the reduction of launch mass and mission cost while enabling a nominal duration of 2 years within the framework of a demonstration mission. It was found that the mission concept provided an excellent solar sail technology demonstration option. The baseline science objectives and engineering goals were addressed, and mission analysis for solar sail, electric, and chemical propulsion performed. Detailed subsystems were defined for each propulsion system and it was found that the optimum propulsion system is solar sailing. A detailed tradeoff as to the effect of spacecraft and sail technology levels, and requirements, on sail size is presented for the first time. The effect of, for example, data acquisition rate and RF output power on sail size is presented, in which it is found that neither have a significant effect. The key sail technology requirements have been identified through a parametric analysis.

Impact of Optical Degradation on Solar Sail Mission Performance

Abstract: The optical properties of the thin metalized polymer films that are projected for solar sails are likely to be affected by the damaging effects of the space environment, but their real degradation behavior is to a great extent unknown. The standard solar sail force models that are currently used for solar sail mission analysis and design do not take these effects into account. In this paper we use a parametric model to describe the sail film's optical degradation with its environmental history to estimate the impact of different degradation behaviors on solar sail mission performance for some example interplanetary missions: Mercury rendezvous missions, fast missions to Neptune and to the heliopause, and artificial Lagrange-point missions.

Interplanetary Mission Design Using Differential Evolution

Abstract: Global optimization methods have been increasingly under consideration for preliminary interplanetary mission design. One promising global method, differential evolution, has been identified as being particularly well suited to high-thrust trajectory optimization. Differential evolution is a stochastic direct search optimization method which uses parameter vectors that interact in a manner motivated by the evolution of living species. To improve the performance of differential evolution for this application, the effect of the tuning parameters is investigated over a diverse group of trajectory optimization problems. The quality of solutions obtained with differential evolution is found to be very sensitive to the selection of the routine’s tuning parameters. A set of tuning parameter values is found that results in the rapid global optimization of an array of typical ballistic interplanetary missions. The fine-tuned differential evolution routine is implemented in a new tool, the mission-direct trajectory optimization program, and the effectiveness of this tool is demonstrated by the rapid solution of interplanetary trajectory optimization problems that involve complex features such as multiple gravity assists and parking orbit considerations.

Survey of Ballute Technology for Aerocapture

Abstract: Ballute aerodynamic decelerators have been studied since early in the space age (1960’s), being proposed for aerocapture in the early 1980’s. Significant technology advances in fabric and polymer materials as well as analysis capabilities lend credibility to the potential of ballute aerocapture. The concept of the thin-film ballute for aerocapture shows the potential for large mass savings over propulsive orbit insertion or rigid aeroshell aerocapture. The mass savings of this concept enables a number of high value science missions. Current studies of ballute aerocapture at Titan and Earth may lead to flight test of one or more ballute concepts within the next five years. This paper provides a survey of the literature with application to ballute aerocapture. Special attention is paid to advances in trajectory analysis, hypersonic aerothermodynamics, structural analysis, coupled analysis, and flight tests. Advances anticipated over the next 5 years are summarized.

Minimum-Fuel Powered Descent for Mars Pinpoint Landing

Abstract: Motivated by the requirement for pinpoint landing in futureMarsmissions, we consider the problemofminimumfuel powered terminal descent to a prescribed landing site. The first-order necessary conditions are derived and interpreted for a point-mass model with throttle and thrust angle control and for rigid-bodymodel with throttle and angular velocity control, clarifying the characteristics of the minimum-fuel solution in each case. The optimal thrust magnitude profile is bang–bang for bothmodels; for the point-mass, the most general thrust magnitude profile has a maximum–minimum–maximum structure. The optimal thrust direction law for the point-mass model (alignment with the primer vector) corresponds to a singular solution for the rigid-bodymodel.Whether the point-mass solution accurately approximates the rigid-body solution depends on the thrust direction boundary conditions imposed for the rigid-body model. Minimum-fuel solutions, obtained numerically, illustrate the optimal strategies.

Solar-Sail Attitude Control Design for a Flight Validation Mission

Abstract: This paper presents the solar-sail attitude control system design for a solar-sail flight validation mission proposed in a dawn–dusk sun-synchronous orbit. The proposed solar-sail attitude control system architecture consists of a propellantless primary attitude control system and a microthruster-based secondary attitude control system. The primary attitude control system employs two ballast masses running alongmast lanyards for pitch/yaw trim control and roll stabilizer bars at themast tips for roll control. The secondary attitude control system uses lightweight pulsed plasma thruster modules mounted at the mast tips. Such a microthruster-based secondary attitude control system can be employed for attitude recovery maneuvers from various off-nominal conditions, including tumbling, that cannot be handled by the propellantless primary attitude control system. The overall simplicity, effectiveness, and robustness of the proposed solar-sail attitude control system architecture are demonstrated for a sailflight validation mission employing a 40-m, 150-kg sailcraft in a 1600-kmdawn–dusk sun-synchronous orbit. The proposed solar-sail attitude control systemwill be applicable with minimal modifications to a wide range of future solar-sailing missions with varying requirements and mission complexity.

Improved Corrections Process for Constrained Trajectory Design in the n-Body Problem

Abstract: The general objective is the development of efficient techniques for preliminary design of trajectory arcs in nonlinear autonomous dynamic systems in which the desired solution is subject to algebraic interior and/or exterior constraints. For application to then-body problem, trajectoriesmust satisfy specific requirements, e.g., periodicity in terms of the states, interior or boundary constraints, and specified coverage. Thus, a strategy is formulated in a sequence of increasingly complex steps: 1) a trajectory isfirstmodeled as a series of arcs (analytical or numerical) and general trajectory characteristics and timing requirements are established; 2) the specific constraints and associated partials are formulated; 3) a corrections process ensures position and velocity continuity while satisfying the constraints; and finally, 4) the solution is transitioned to a full model employing ephemerides. Though the examples pertain to spacecraft mission design, the methodology is generally applicable to autonomous systems subject to algebraic constraints. For spacecraft mission design applications, an immediate advantage of this approach, particularly for the identification of periodic orbits, is that the startup solution need not exhibit any symmetry to achieve the objectives.

N-Impulse Orbit Transfer Using Genetic Algorithms

Abstract: T HE orbit transfer problems using impulsive thrusters have attracted researchers for a long time [1]. One of the objectives in these problems is to find the optimal fuel orbit transfer between two orbits, generally inclined eccentric orbits. The optimal two-impulse orbit transfer problem poses multiple local optima, and classical optimization methods find only local optimum solution. McCue [2] solved the problem of optimal two-impulse orbit transfer using a combination between numerical search and steepest descent optimization procedures. Jezewaski and Rozendall [3] developed an iterative method to calculate local minima solutions for the nimpulse fixed time rendezvous problems. Genetic algorithms (GAs) have been used in the literature to search for the global optimal orbit maneuver. Reichert [4] addressed the optimum two-impulse orbit transfer problem for coplanar orbits only. The accuracy obtained using this formulation is not good unless a narrow range, around the optimal value, for each design variable is known in advance [4]. Given narrow ranges for the design variables, the solution obtained using this formulation does not guarantee that the satellite will be inserted exactly into final orbit, but rather there is a small error unless the GA finds exactly the global optimal solution. Kim and Spencer [5] introduced a different formulation to the two-impulse orbit transfer problem by using six design variables for coplanar orbits. This formulation also does not guarantee the satellite is placed exactly in the final orbit. In this note, a new formulation to the problem is introduced. This formulation is general for noncoplanar elliptical orbits. It can also implement any number of thrust impulses. For the case of twoimpulse maneuver, this formulation requires only three design variables for any noncoplanar orbit transfer. The solution obtained by this formulation is guaranteed to insert the satellite in the final orbit exactly, even if the GAs did not converge to the global optimal solution. This formulation requires solving Lambert’s problem to find the parameters of the transfer orbit for a given set of the three design variables. The next section describes the orbit maneuver algorithm. The two-impulse transfer is considered a special case and is presented separately. Validation to this formulation is performed by solving several case studies to which the optimal solution is known.

Radiative Heating Methodology for the Huygens Probe

Abstract: The radiative heating environment for the Huygens probe near peak heating conditions for Titan entry is investigated in this paper. The task of calculating the radiation-coupled flowfield, accounting for non-Boltzmann and non-optically thin radiation, is simplified to a rapid yet accurate calculation. This is achieved by using the viscous-shock layer (VSL) technique for the stagnation-line flowfield calculation and a modified smeared rotational band (SRB) model for the radiation calculation. These two methods provide a computationally efficient alternative to a Navier-Stokes flowfield and line-by-line radiation calculation. The results of the VSL technique are shown to provide an excellent comparison with the Navier-Stokes results of previous studies. It is shown that a conventional SRB approach is inadequate for the partially optically-thick conditions present in the Huygens shock-layer around the peak heating trajectory points. A simple modification is proposed to the SRB model that improves its accuracy in these partially optically-thick conditions. This modified approach, labeled herein as SRBC, is compared throughout this study with a detailed line-by-line (LBL) calculation and is shown to compare within 5% in all cases. The SRBC method requires many orders-of-magnitude less computational time than the LBL method, which makes it ideal for coupling to the flowfield. The application of a collisional-radiative (CR) model for determining the population of the CN electronic states, which govern the radiation for Huygens entry, is discussed and applied. The non-local absorption term in the CR model is formulated in terms of an escape factor, which is then curve-fit with temperature. Although the curve-fit is an approximation, it is shown to compare well with the exact escape factor calculation, which requires a computationally intensive iteration procedure.

Application of Acclerometer Data to Atmospheric Modeling During Mars Aerobraking Operations

Abstract: R. H. Tolson∗ North Carolina State University, Hampton, Virginia 23666-6147 G. M. Keating George Washington University, Newport News, Virginia 23602 R. W. Zurek Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109-8099 S. W. Bougher University of Michigan, Ann Arbor, Michigan 48109-2143 C. G. Justus Morgan Research Corporation, Huntsville, Alabama 35805-1948 and D. C. Fritts∗∗ NorthWest Research Associates, Inc., Boulder, Colorado 80301

Solar Sail Kinetic Energy Impactor Trajectory Optimization for an Asteroid-Deflection Mission

Abstract: A fictional asteroid-mitigation problem created by AIAA assumes that a 200-m near-Earth asteroid, detected on 04 July 2004 and designated as 2004 WR, will impact the Earth on 14 January 2015. Adopting this example scenario, we show that solar-sail spacecraft that impact the asteroid with a very high relative velocity are a realistic near-term option for mitigating the impact threat from near-Earth asteroids. The proposed mission requires several kinetic energy impactor solar-sail spacecraft. Each kinetic energy impactor consists of a 160 x 160 m, 168-kg solar sail and a 150-kg impactor. Because of their large ΔV capability, solar sailcraft with a relatively modest characteristic acceleration of 0.5 mm/s 2 can achieve an orbit that is retrograde to the target orbit within less than about 4.5 years. Before impacting 2004 WR at its perihelion of about 0.75 AU, each impactor is to be separated from its solar sail. With a relative impact velocity of about 81 km/s, each impactor will cause a conservatively estimated Δv of about 0.35 cm/s in the trajectory of the target asteroid, largely due to the impulsive effect of material ejected from the newly formed crater. The deflection caused by a single impactor will increase the Earth-miss distance by about 0.7 Earth radii. Several sailcraft will therefore be required for consecutive impacts, to increase the total Earth-miss distance to a safe value. In this paper, we elaborate on a potential mission scenario and investigate trade-offs between different mission parameters; for example, characteristic acceleration, sail temperature limit, hyperbolic excess energy for interplanetary insertion, and optical solar-sail degradation.

Drag Sail for End-of-Life Disposal from Low Earth Orbit

Abstract: International standards are moving toward the requirement that spacecraft should be removed from orbit at the end of their operational lives. The feasibility of a deployable aerodynamically stable drag-enhancement structure is considered for the end-of-life disposal of low-Earth-orbit spacecraft, and how this structure could fulfil NASA deorbit guidelines is demonstrated. The concept is a thin membrane supported by deployed struts. A shuttlecock like geometry is chosen to take advantage of the small stabilising effect caused by oscillatory motion in, and descent through, the free molecular flow during deorbit. The shuttlecock is approximated to a cone, and the aerodynamic loads due to orbital and rotational motion are calculated and used to model the stabilisation and descent of a deployed system toward final reentry. Finally it is is shown that this system can provide an effective and mass-efficient deorbit solution for future missions.

Heliocentric Solar Sail Orbit Transfers with Locally Optimal Control Laws

Abstract: Solar sailing is increasingly being considered by space agencies for future science missions. With the absence of reaction mass from the primary propulsion system arises the potential for new high-energy mission concepts in the mid to far term, such as a Solar Polar Orbiter or an Interstellar Heliopause Probe [1,2]. One of the most time consuming tasks of mission analysis is trajectory generation and optimization. Optimal trajectory generation is a complex field and many schemes exist; however, these are typically characterized as being computationally intensive systems requiring a good degree of engineering judgment [3-6].

Neutral density measurements from the gravity recovery and climate experiment accelerometers

Abstract: Predicting the orbits of space objects in low-altitude orbits requires an accuratemodel for the atmospheric neutral density. The current accuracy of semi-empirical models limits the prediction accuracy and impacts a number of operational decisions. The currentmodels are based on sparsemeasurements of the neutral density, collected over an extended period. One of the problems is observing the thermosphere density changes in response to the solar and geomagnetic variability on short temporal scales, such as those characterized by geomagnetic storms. The stochastic behavior of the solar forcing represents one of the major challenges in predicting satellite orbits. In situ measurements of thedensity canplay a significant role in improving the structure of the neutral densitymodels and in providing a timelymeasurement for enhancing the accuracy of the satellite predictions.Measurements fromorbiting accelerometers carried by the twin Gravity Recovery and Climate Experiment satellites have the potential for providing accurate and timelymeasurements to improve the satellite prediction accuracy. The objective of this paper is to describe the procedure for using the Gravity Recovery and Climate Experiment accelerometer measurements for determining accurate density measurements.

Collisionless Gas Expanding into Vacuum

Abstract: H IGH-SPEED collisionless, or free-molecular, gas flows passing through small circular or annular holes are fundamental problems with many real applications such as neutral gas expansion out of electric propulsion (EP) devices Usually, the cold plume flow out of an EP device is modeled by assuming freemolecular flows with a nonzero uniform average exit velocity U0 Even when the average bulk velocity of gas near the orifice is zero, the average velocity at the orifice exit plane is not zero, it corresponds to an outflow with a half-Maxwellian distribution In the past, analytical studies of similar problems were concentrated on true effusion problems with a zero average exit speed For example, Liepmann [1] reported the efflux of gases through circular apertures, which is an example of a transition from the gas-dynamic to the gaskinetic regime; Narasimha [2] obtained the exact solutions of density and velocity distributions for a free-molecular effusion flow and the results for a nearly free-molecular effusion flow expanding into vacuum through a circular orifice; and Brook [3] reported the density field of free-molecular flow from an annulus, to study the gas leakage effect from a spacecraft hatch Other researchers reported many approximate methods or numerical simulations to study rarefied flows through a slit; for example, Rotenberg and Weitzner [4], Hasegawa and Sone [5], Cercignani and Sharipov [6], and Sharipov [7] Recently, Lilly et al [8] reported their work onmeasurement and computation ofmass flow andmomentum flux through short tubes in rarefied gas For the case of free-molecular flows with a nonzero average velocity, the problems are usually very complicated and approximations are often made, such as neglecting the details of the exit geometry or assuming that free-molecular flow are emitted from a point source [9] In our previous study [10,11], we adopted a relation between velocity directions and geometry locations to investigate freemolecular plume flow problems This treatment is more general than the solid angle treatment [2] which was widely used in studying true collisionless effusion flows with a zero average exit speed, but is not applicable to collisionless flows with a nonzero average exit speed In this study, we further investigate collisionless flows out of a circular or an annular exit with a nonzero average speed These two cases are very important, not only because of their mathematical significance, but also because of their many direct applications, including spacecraft propulsion This Note is organized as follows: Section II describes the problems, the corresponding complex exact solutions, and also approximate far-field solutions, which are simpler andmore accurate than existing formulas in the literature; Sec III compares the analytical results with particle simulation results; and Sec IV summarizes this study

Formation and Attitude Control for Rotational Tethered Satellite Clusters

Abstract: A tethered satellite cluster system, which consists of a cluster of satellites connected by tethers and which can maintain and change formation via active control of tether tension and length to save thruster fuel and improve control accuracy is proposed. The concept can be applied to tethered multisatellites for in-orbit servicing, which can perform various missions, including inspection, casting, capture, recovery, moorage, and deorbiting of an uncontrolled satellite. The rotational motion of such a system that the satellites in formation flying are required to rotate about the center of mass of the system on the same desired plane is considered. The equilibrium conditions that the tether tension imposes on the rotational motion are given, and a coordinated control method for the thrusters, the reaction wheels, and the tether tension/torque is proposed. Numerical simulations and ground experiments show that the control of the tether tension and torque not only saves thruster fuel, but also improves the position and attitude accuracy of formation flying.