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Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 2: Analytic manual

The Interplanetary Program to Optimize Space Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization is performed using the Stanford NPSOL algorithm. IPOST structure allows subproblems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Hong, P. E.↗

Lunar Navigation with Libration Point Orbiters and GPS

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Carpenter, J. Russell↗

Orbital flux integrations: Parameter values for effective computer time reductions

To improve computer utilization and to reduce the cost of orbital flux integrations, the effects of integration parameters 'duration' (T) and 'stepsize' (delta t) on integration results were investigated. Over given ranges of T and delta t, and within specified acceptable accuracy restraints, optimal values of these parameters were established for circular subsynchronous trajectories, in terms of the variables altitude (H) and inclination (i). It is shown that (1) above a certain statistically important value, duration is independent of both h and i; (2) stepsize has a relative altitude dependence; and (3) stepsize is not a function of inclination. The substantial savings in computer time are discussed along with the possibility of greater savings by relaxing accuracy restrictions while not exceeding the minimum model-associated uncertainty factors of the environments.

Stassinopoulos, E. G.↗

Safety Related Considerations in Autonomy

In this talk I will describe NASA strategy and research efforts to provide safety assurance for increasingly autonomous systems used in aviation. In the near future, autonomy will play an important role in civil aviation, and its applications will range from vehicles and platforms (UAVs, transport-class, including supersonic to hypersonic, aircraft) to airspace operations, or health management systems. This infusion of autonomy is driven by a need for optimizing airspace operations to accommodate increasing traffic density (e.g., adaptive trajectory-based operations, autonomous tugs, close parallel runways, and dynamic separation assurance), reducing operation costs to ensure that US operators can compete with emergent countries, and enabling new business models (e.g., fire fighting, UAS-based package delivery and precise aerial photography). In essence virtually every component of the National Airspace System will become increasingly autonomous. Yet we need to do so in a safe manner and have techniques and processes in place to ensure the safety of the public. This talk describes NASA plans to address this problem

Air Traffic Management↗

Quantifying the challenge of reaching a 100% renewable energy power system for the United States

We simulate pathways for achieving up to 100% renewable energy (RE) electric power systems for the contiguous United States. Under base conditions, the least-cost buildout has RE penetration growing up to 57% in 2050. Relative to this base scenario, average CO2 abatement costs of achieving 80%, 90%, 95%, and 100% RE are $25, $33, $40, and $61/ton, respectively, with system costs growing from $30 to $36/MWh at 95% (achieved in 2040) and $39/MWh at 100%. Incremental abatement costs from 99% to 100% RE reach $930/ton, driven primarily by the need for firm RE capacity. In addition to the base conditions, we also examined 22 alternative conditions for a buildout of up to 100%. These sensitivities capture different technology trajectories, compliance requirements, requirement timing, electrification, and transmission availability. Nonlinear marginal costs for the last few percent approaching 100% RE were found for all sensitivities, which might motivate alternative nonelectric-sector abatement opportunities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA's Near Earth Asteroid Scout Mission

NASA is developing solar sail propulsion for a near-term Near Earth Asteroid (NEA) reconnaissance mission and laying the groundwork for their future use in deep space science and exploration missions. The NEA Scout mission, funded by NASA's Advanced Exploration Systems Program and managed by NASA MSFC, will use the sail as primary propulsion allowing it to survey and image one or more NEA's of interest for possible future human exploration. NEA Scout uses a 6U cubesat (to be provided by NASA's Jet Propulsion Laboratory), an 86 m2 solar sail and will weigh less than 14 kilograms. The solar sail for NEA Scout will be based on the technology developed and flown by the NASA NanoSail-D and The Planetary Society's Lightsail-A. Four ~7 m stainless steel booms wrapped on two spools (two overlapping booms per spool) will be motor deployed and pull the sail from its stowed volume. The sail material is an aluminized polyimide approximately 3 microns thick. NEA Scout will launch on the Space Launch System (SLS) first mission in 2018 and deploy from the SLS after the Orion spacecraft is separated from the SLS upper stage. The NEA Scout spacecraft will stabilize its orientation after ejection using an onboard cold-gas thruster system. The same system provides the vehicle Delta-V sufficient for a lunar flyby. After its first encounter with the moon, the 86 m2 sail will deploy, and the sail characterization phase will begin. A mechanical Active Mass Translation (AMT) system, combined with the remaining ACS propellant, will be used for sail momentum management. Once the system is checked out, the spacecraft will perform a series of lunar flybys until it achieves optimum departure trajectory to the target asteroid. The spacecraft will then begin its two year-long cruise. About one month before the asteroid flyby, NEA Scout will pause to search for the target and start its approach phase using a combination of radio tracking and optical navigation. The solar sail will provide continuous low thrust to enable a relatively slow flyby of the target asteroid under lighting conditions favorable to geological imaging. Once complete, NASA will have demonstrated the capability to fly low-cost, high Delta-V cubesats to perform interplanetary missions.

Johnson, Les↗

Improvement of Automated POST Case Success Rate Using Support Vector Machines

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases.3 As noted in [4] work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points.

Zwack, Mathew R.↗

Improvement of Automated POST Case Success Rate Using Support Vector Machines

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal [1]. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases [2]. Additional work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points [3]. The conclusion of the previous work illustrated the utility of the graph theory approach for completing a DOE through POST. However, this approach was still dependent upon the use of random repetitions to generate seed points for the graph. As noted in [3], only 8% of these random repetitions resulted in converged trajectories. This ultimately affects the ability of the random reps method to confidently approach the global optima for a given vehicle case in a reasonable amount of time. With only an 8% pass rate, tens or hundreds of thousands of reps may be needed to be confident that the best repetition is at least close to the global optima. However, typical design study time constraints require that fewer repetitions be attempted, sometimes resulting in seed points that have only a handful of successful completions. If a small number of successful repetitions are used to generate a seed point, the graph method may inherit some inaccuracies as it chains DOE cases from the non-global-optimal seed points. This creates inherent noise in the graph data, which can limit the accuracy of the resulting surrogate models. For this reason, the goal of this work is to improve the seed point generation method and ultimately the accuracy of the resulting POST surrogate model. The work focuses on increasing the case pass rate for seed point generation.

Zwack, Matthew R.↗

Pterodactyl: Non-propulsive Control Systems for Future Planetary Missions

This white paper presents an assessment of control systems as it relates to state-of-the-art hypersonic entry vehicles and addresses technological advances that enable new control systems for future hypersonic entry vehicles. Advancements in deployable entry vehicle (DEV) technology, entry guidance, woven thermal protection systems, and affordable launch services make it possible to conceive of entry vehicles that optimize entry loads, maneuverability, usable payload mass and volume, and operational costs. NASA’s Space Technology Mission Directorate (STMD) is currently funding the authors on a project, Pterodactyl, that is using on-the-fly trajectory design and integrated software and hardware development to investigate non-propulsive entry control systems for precision targeting of mechanical DEVs. The authors recently reported key findings of these control systems for an asymmetric DEV to track bank commands for a lunar sample return entry.

Sarah D'Souza↗

Should We Enhance the Observing Systems or Improve Coordination Among the Operating Agencies: What is Needed the Most for Security--A Philosophical Discussion

As an integrated observing strategy, the concept of sensorweb for Earth observations is appealing in many aspects. For instance, by increasing the spatial and temporal coverage of observations from space and other vantage points, one can eventually aid in increasing the accuracy of the atmospheric models which are precursor to hurricane track prediction, volcanic eruption forecast, and trajectory path of transcontinental transport of dust, harmful nuclear and chemical plumes. In reality, there is little analysis available in terms of benefits, costs and optimized set of sensors needed to make these necessary observations. This is a complex problem that must be carefully studied and balanced over many boundaries such as science, defense, early warning, security, and surveillance. Simplistically, the sensorweb concept from the technological point of view alone has a great appeal in the defense, early warning and security applications. In fact, it can be relatively less expensive in per unit cost as opposed to building and deploying it for the scientific use. However, overall observing approach should not be singled out and aligned somewhat orthogonally to serve a particular need. On the other hand, the sensorweb should be designed and deployed to serve multiple subject areas and customers simultaneously; and can behave as directed measuring systems for both science and operational entities. Sensorweb can be designed to act as expert systems, and/or also provide a dedicated integrated surveillance network. Today, there is no system in the world that is fully integrated in terms of reporting timely multiple hazards warnings, computing the loss of life and property damage estimates, and is also designed to cater to everyone's needs. It is not an easier problem to undertake and more so is not practically solvable. At this time due to some recent events in the world, the scientific community, social scientists, and operational agencies are more cognizant and getting together to address such colossal problems. Increasing our knowledge of the home planet, via amplified set of observations, is certainly a right step in a right direction. Furthermore, this is a pre-requisite in understanding multiple hazard phenomenas. This paper examines various sensorweb options and observing architectures that can be useful specifically in addressing some of these complex issues. The ultimate goal is to serve the society by providing potential natural hazards information to the decision makers in the most expeditious manner so they can prepare themselves to mitigate potential risks to human life, livestock and property.

Habib, Shahid↗

Applying Advanced and Existing Sensors in Dealing with Potential Natural Disasters

As an integrated observing strategy, the concept of sensorweb for Earth observations is appealing in many aspects. For instance, by increasing the spatial and temporal coverage of observations from space and other vantage points, one can eventually aid in increasing the accuracy of the atmospheric models which are precursor to hurricane track prediction, volcanic eruption forecast, and trajectory path of transcontinental transport of dust, harmful nuclear and chemical plumes. In reality, there is little analysis available in terms of benefits, costs and optimized set of sensors needed to make these necessary observations. This is a complex problem that must be carefully studied and balanced over many boundaries such as science, defense, early warning, security, and surveillance. Simplistically, the sensorweb concept from the technological point of view alone has a great appeal in the defense, early warning and security applications. In fact, it can be relatively less expensive in per unit cost as opposed to building and deploying it for the scientific use. However, overall observing approach should not be singled out and aligned somewhat orthogonally to serve a particular need. On the other hand, the sensorweb should be designed and deployed to serve multiple subject areas and customers simultaneously; and can behave as directed measuring systems for both science and operational entities. Sensorweb can be designed to act as expert systems, and/or also provide a dedicated integrated surveillance network. Today, there is no system in the world that is fully integrated in terms of reporting timely multiple hazards warnings, computing the loss of life and property damage estimates, and is also designed to cater to everyone s needs. It is not an easier problem to undertake and more so is not practically solvable. At this time due to some recent events in the world, the scientific community, social scientists, and operational agencies are more cognizant and getting together to address such colossal problems. Increasing our knowledge of the home planet, via amplified set of observations, is certainly a right step in a right direction. Furthermore, this is a prerequisite in understanding multiple hazard phenomena's. This paper examines various sensorweb options and observing architectures that can be useful specifically in addressing some of these complex issues. The ultimate goal is to serve the society by providing potential natural hazards information to the decision makers in the most expeditious manner so they can prepare themselves to mitigate potential risks to human life, livestock and property.

Habib, Shahid↗

Acquiring Comprehensive Observations using an Integrated Sensorweb for Early Warning

As an integrated observing strategy, the concept of sensorweb for Earth observations is appealing in many aspects. For instance, by increasing the spatial and temporal coverage of observations from space and other vantage points, one can eventually aid in increasing the accuracy of the atmospheric models which are precursor to hurricane track prediction, volcanic eruption forecast, and trajectory path of transcontinental transport of dust, harmful nuclear and chemical plumes. In reality, there is little analysis'available in terms of benefits, costs and optimized set of sensors needed to make these necessary observations. This is a complex problem that must be carefully studied and balanced over many boundaries such as science, defense, early warning security, and surveillance. Simplistically, the sensorweb concept from the technological point of view alone has a great appeal in the defense, early warning and security applications. In fact, it can be relatively less expensive in per unit cost as opposed to building and deploying it for the scientific use. However, overall observing approach should not be singled out and aligned somewhat . orthogonally to serve a particular need. On the other hand, the sensorweb should be designed and deployed to serve multiple subject areas and customers simultaneously; and can behave as directed measuring systems for both science and operational entities. Sensorweb can be designed to act as expert systems, and/or also provide a dedicated integrated surveillance network. Today, there is no system in the world that is fully integrated in terms of reporting timely multiple hazards warnings, computing the lass of life and property damage estimates, and is also designed to cater to everyone's needs. It is not an easier problem to undertake and more so is not practically solvable. At this time due to some recent events in the world, the scientific community, social scientists, and operational agencies are more cognizant and getting together to address such colossal problems. Increasing our knowledge of the home planet, via amplified set of observations, is certainly a right step in a right direction. Furthermore, this is a pre-requisite in understanding multiple hazard phenomena's. This paper examines various sensorweb options and observing architectures that can be useful specifically in addressing some of these complex issues. The ultimate goal is to serve the society by providing potential natural hazards information to the decision makers in the most expeditious manner so they can prepare themselves to mitigate potential risks to human life, livestock and property.

Habib, Shahid↗

Acquiring Comprehensive Observations using an integrated Sensorweb for Early Warning

As an integrated observing strategy, the concept of sensorweb for Earth observations is appealing in many aspects. For instance, by increasing the spatial and temporal coverage of observations from space and other vantage points, one can eventually aid in increasing the accuracy of the atmospheric models which are precursor to hurricane track prediction, volcanic eruption forecast, and trajectory path of transcontinental transport of dust, harmful nuclear and chemical plumes. In reality, there is little analysis'available in terms of benefits, costs and optimized set of sensors needed to make these necessary observations. This is a complex problem that must be carefully studied and balanced over many boundaries such as science, defense, early warning, security, and surveillance. Simplistically, the sensorweb concept from the technological point of view alone has a great appeal in the defense, early warning and security applications. In fact, it can be relatively less expensive in per unit cost as opposed to building and deploying it for the scientific use. However, overall observing approach should not be singled out and aligned somewhat orthogonally to serve a particular need. On the other hand, the sensorweb should be designed and deployed to serve multiple subject areas and customers simultaneously; and can behave as directed measuring systems for both science and operational entities. Sensorweb can be designed to act as expert systems, and/or also provide a dedicated integrated surveillance network. Today, there is no system in the world that is fully integrated in terms of reporting timely multiple hazards warnings, computing the loss of life and property damage estimates, and is also designed to cater to everyone's needs. It is not an easier problem to undertake and more so is not practically solvable. At this time due to some recent events in the world, the scientific community, social scientists, and operational agencies are more cognizant and getting together to address such colossal problems. Increasing our knowledge of the home planet, via amplified set of observations, is certainly a right step in a right direction. Furthermore, this is a pre-requisite in understanding multiple hazard phenomena's. This paper examines various sensorweb options and observing architectures that can be useful specifically in addressing some of these complex issues. The ultimate goal is to serve the society by providing potential natural hazards information to the decision makers in the most expeditious manner so they can prepare themselves to mitigate potential risks to human life, livestock and property.

Habib, Shahid↗

Addition of Electrostatic Forces to EDEM with Applications to Triboelectrically Charged Particles

Tribocharging of particles is common in many processes including fine powder handling and mixing, printer toner transport and dust extraction. In a lunar environment with its high vacuum and lack of water, electrostatic forces are an important factor to consider when designing and operating equipment. Dust mitigation and management is critical to safe and predictable performance of people and equipment. The extreme nature of lunar conditions makes it difficult and costly to carryout experiments on earth which are necessary to better understand how particles gather and transfer charge between each other and with equipment surfaces. DEM (Discrete Element Modeling) provides an excellent virtual laboratory for studying tribocharging of particles as well as for design of devices for dust mitigation and for other purposes related to handling and processing of lunar regolith. Theoretical and experimental work has been performed pursuant to incorporating screened Coulombic electrostatic forces into EDEM Tm, a commercial DEM software package. The DEM software is used to model the trajectories of large numbers of particles for industrial particulate handling and processing applications and can be coupled with other solvers and numerical models to calculate particle interaction with surrounding media and force fields. In this paper we will present overview of the theoretical calculations and experimental data and their comparison to the results of the DEM simulations. We will also discuss current plans to revise the DEM software with advanced electrodynamic and mechanical algorithms.

Hogue, Michael D.↗

Discrete Element Modeling of Triboelectrically Charged Particles

Tribocharging of particles is common in many processes including fine powder handling and mixing, printer toner transport and dust extraction. In a lunar environment with its high vacuum and lack of water, electrostatic forces are an important factor to consider when designing and operating equipment. Dust mitigation and management is critical to safe and predictable performance of people and equipment. The extreme nature of lunar conditions makes it difficult and costly to carry out experiments on earth which are necessary to better understand how particles gather and transfer charge between each other and with equipment surfaces. DEM (Discrete Element Modeling) provides an excellent virtual laboratory for studying tribocharging of particles as well as for design of devices for dust mitigation and for other purposes related to handling and processing of lunar regolith. Theoretical and experimental work has been performed pursuant to incorporating screened Coulombic electrostatic forces into EDEM, a commercial DEM software package. The DEM software is used to model the trajectories of large numbers of particles for industrial particulate handling and processing applications and can be coupled with other solvers and numerical models to calculate particle interaction with surrounding media and force fields. While simple Coulombic force between two particles is well understood, its operation in an ensemble of particles is more complex. When the tribocharging of particles and surfaces due to frictional contact is also considered, it is necessary to consider longer range of interaction of particles in response to electrostatic charging. The standard DEM algorithm accounts for particle mechanical properties and inertia as a function of particle shape and mass. If fluid drag is neglected, then particle dynamics are governed by contact between particles, between particles and equipment surfaces and gravity forces. Consideration of particle charge and any tribocharging and electric field effects requires calculation of the forces due to these effects.

Hogue, Michael D.↗

Low-cost unmanned lunar lander

Two student groups designed unmanned landers to deliver 200 kilogram payloads to the lunar surface. Payloads could include astronomical telescopes, small lunar rovers, and experiments related to future human exploration. Requirements include the use of existing hardware where possible, use of a medium-class launch vehicle, an unobstructed view of the sky for the payload, and access to the lunar surface for the payload. The projects were modeled after Artemis, a project that the NASA Office of Exploration is pursuing with a planned first launch in 1996. The Lunar Scout design uses a Delta 2 launch vehicle with a Star 48 motor for insertion into the trans-lunar trajectory. During the transfer, the solar panels will be folded inward and the spacecraft will be powered by rechargeable nickel-cadmium batteries. The lander will use a combination of a solid rocket motor and hydrazine thrusters for the descent to the lunar surface. The solar arrays will be deployed after landing. The lander will provide power for operations to the payload during the lunar day; batteries will provide 'stay-alive' power during the lunar night. A horn antenna on the lander will provide communications between the payload and the earth.

Daniel, Walter K.↗

(abstract) Cassini MLI Balnkets High-Temperature Exposure Tests

The trajectory required for the Cassini spacecraft to reach Saturn will subject the spacecraft to a 0.61 AU temperature environment at perihelion. Temperatures on some sunlit blanket surfaces at 0.61 AU can reach levels that are beyond the service capability of the conventional Mylar/Dacron net MLI. The majority of the blanket surfaces, however, will experience temperatures with an upper bound of 250(deg) C. The maximum allowable temperature for Mylar/Dacron net is determined to be 220(deg)C. Kapton can withstand temperatures in excess of 400(deg) C; however, the high cost of embossed Kapton relative to Mylar/Dacron net requires a baseline design which includes a standard layup and a high-temperature layup. The high-temperature layup is utilized at a limited number of locations, while at least 90% of the blankets are of the standard layup. The verification of both layups' capability to meet all temperature requirements has been accomplished by a comprehensive test program which addressed their high-temperature survivability, effective emittance, and optical and electrical properties. This paper focuses on the high-temperature exposure tests which helped define the hybrid standard layup, and which demonstrated the adequacy of both layups in withstanding their respective thermal environments.

temperature control insulation Cassini↗

Launching Payloads Into Orbit at Relatively Low Cost

A report proposes the development of a system for launching payloads into orbit at about one-fifth the cost per unit payload weight of current systems. The PILOT system was a solid-fuel, aerodynamically spun and spin-stabilized, five-stage rocket with onboard controls including little more than an optoelectronic horizon sensor and a timer for triggering the second and fifth stages, respectively. The proposal calls for four improvements over the PILOT system to enable control of orbital parameters: (1) the aerodynamic tipover of the rocket at the top of the atmosphere could be modeled as a nonuniform gyroscopic precession and could be controlled by selection of the initial rocket configuration and launch conditions; (2) the attitude of the rocket at the top of the first-stage trajectory could be measured by use of radar tracking or differential Global Positioning System receivers to determine when to trigger the second stage; (3) the final-stage engines could be configured around the payload to enhance spin stabilization during a half-orbit coast up to apoapsis where the final stage would be triggered; and (4) the final payload stage could be equipped with a "beltline" of small thrusters for correcting small errors in the trajectory as measured by an off-board tracking subsystem.

Wilcox, Brian↗