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NASA NTRS2017

Synopsis of Precision Landing and Hazard Avoidance (PL&HA) Capabilities for Space Exploration

Until recently, robotic exploration missions to the Moon, Mars, and other solar system bodies relied upon controlled blind landings. Because terrestrial techniques for terrain relative navigation (TRN) had not yet been evolved to support space exploration, landing dispersions were driven by the capabilities of inertial navigation systems combined with surface relative altimetry and velocimetry. Lacking tight control over the actual landing location, mission success depended on the statistical vetting of candidate landing areas within the predicted landing dispersion ellipse based on orbital reconnaissance data, combined with the ability of the spacecraft to execute a controlled landing in terms of touchdown attitude, attitude rates, and velocity. In addition, the sensors, algorithms, and processing technologies required to perform autonomous hazard detection and avoidance in real time during the landing sequence were not yet available. Over the past decade, NASA has invested substantial resources on the development, integration, and testing of autonomous precision landing and hazard avoidance (PL&HA) capabilities. In addition to substantially improving landing accuracy and safety, these autonomous PL&HA functions also offer access to targets of interest located within more rugged and hazardous terrain. Optical TRN systems are baselined on upcoming robotic landing missions to the Moon and Mars, and NASA JPL is investigating the development of a comprehensive PL&HA system for a Europa lander. These robotic missions will demonstrate and mature PL&HA technologies that are considered essential for future human exploration missions. PL&HA technologies also have applications to rendezvous and docking/berthing with other spacecraft, as well as proximity navigation, contact, and retrieval missions to smaller bodies with microgravity environments, such as asteroids.

Robertson, Edward A.↗
NASA NTRS2015

Enhanced Gravity Tractor Technique for Planetary Defense

Given sufficient warning time, Earth-impacting asteroids and comets can be deflected with a variety of different "slow push/pull" techniques. The gravity tractor is one technique that uses the gravitational attraction of a rendezvous spacecraft to the impactor and a low-thrust, high-efficiency propulsion system to provide a gradual velocity change and alter its trajectory. An innovation to this technique, known as the Enhanced Gravity Tractor (EGT), uses mass collected in-situ to augment the mass of the spacecraft, thereby greatly increasing the gravitational force between the objects. The collected material can be a single boulder, multiple boulders, regolith or a combination of different sources. The collected mass would likely range from tens to hundreds of metric tons depending on the size of the impactor and warning time available. Depending on the propulsion system's capability and the mass collected, the EGT approach can reduce the deflection times by a factor of 10 to 50 or more, thus reducing the deflection times of several decades to years or less and overcoming the main criticism of the traditional gravity tractor approach. Additionally, multiple spacecraft can orbit the target in formation to provide the necessary velocity change and further reduce the time needed by the EGT technique to divert hazardous asteroids and comets. The robotic segment of NASA's Asteroid Redirect Mission (ARM) will collect a multi-ton boulder from the surface of a large Near-Earth Asteroid (NEA) and will provide the first ever demonstration of the EGT technique and validate one method of collecting in-situ mass on an asteroid of hazardous size.

Mazanek, Daniel D.↗
NASA NTRS1999

Radar Reconnaissance of Near-Earth Asteroids

Groundbased radar observations of NEAs can help identify space resources with commercial potential and can dramatically reduce the cost and risk of the initial spacecraft missions to those objects. The near-Earth asteroid (NEA) population is thought to contain approximately 1500 objects as large as a kilometer, approximately 300,000 as large as 100 meters, and more than 100,000,000 as large as 10 meters. More than 10% of the NEAs are more accessible in terms of mission delta-V (i.e., fuel required) than the Moon, Mars, or the moons of Mars. Fewer than 1000 NEAs have been found, but the discovery rate is increasing rapidly. Once an asteroid is discovered (necessarily by wide-field optical telescopes), radar can provide otherwise unavailable information about its size, shape, spin state, and surface properties if it approaches within the range of the Goldstone (California) or Arecibo (Puerto Rico) radar telescopes. Asteroids generally appear as unresolved points through groundbased optical telescopes, but radar measurements of the distribution of echo power in time delay (range) and Doppler frequency (radial velocity) can yield images with resolution as fine as a decameter. Image sequences that furnish adequate orientational coverage can be inverted to construct geologically detailed 3-D models, to define the rotation state precisely, and to constrain the object's internal density distribution. Estimates of radar scattering properties characterize the surface's cm-to-m-scale roughness as well as its bulk density, which for asteroids depends primarily on porosity and metal concentration. A useful spin-off of radar detection is orbit refinement that simplifies navigation of flyby and rendezvous spacecraft.

Ostro, S. J.↗
NASA NTRS1999

Radar Reconnaissance of Near-Earth Asteroids

Groundbased radar observations of NEAs can help identify space resources with commercial potential and can dramatically reduce the cost and risk of the initial spacecraft missions to those objects. The near Earth asteroid (NEA) population is thought to contain approx. 1500 objects as large as a kilometer, approx. 300,000 as large as 100 meters, and more than 100,000,000 as large as 10 meters. More than 10% of the NEAs are more accessible in terms of mission delta-V (i.e., fuel required) than the Moon, Mars, or the moons of Mars. Fewer than 1000 NEAs have been found, but the discovery rate is increasing rapidly. Once an asteroid is discovered (necessarily by wide-field optical telescopes), radar can provide otherwise unavailable information about its size, shape, spin state, and surface properties if it approaches within the range of the Goldstone (California) or Arecibo (Puerto Rico) radar telescopes. Asteroids generally appear as unresolved points through groundbased optical telescopes, but radar measurements of the distribution of echo power in time delay (range) and Doppler frequency (radial velocity) can yield images with resolution as fine as a decameter. Image sequences that furnish adequate orientational coverage can be inverted to construct geologically detailed 3-D models, to define the rotation state precisely, and to constrain the object's internal density distribution. Estimates of radar scattering properties characterize the surface's cm-to-m-scale roughness as well as its bulk density, which for asteroids depends primarily on porosity and metal concentration. A useful spin-off of radar detection is orbit refinement that simplifies navigation of flyby and rendezvous spacecraft.

Ostro, S. J.↗
NASA NTRS2017

Characteristics of a high-power ion beam deflection system necessary to deflect the hypothetical asteroid 2017 PD

The July 2027 impact date for the hypothetical asteroid 2017 PDC, that is the subject of an emergency response exercise, leaves just over ten years to implement a deflection approach. The analyses herein allocates four years to the design, fabrication, assembly, test and launch of a notional high-power Ion Beam Deflection (IBD) vehicle to meet a launch readiness date no later than May 2021. Using this launch date along with estimates for the vehicle mass and performance characteristics of the electric propulsion system, low-thrust trajectory analyses indicate a 2.56-year flight time to rendezvous with 2017 PDC. This would leave 3.6 years to execute the actual deflection phase. A 160-kW IBD vehicle could deflect 2017 PDC by at least one Earth radius within this time provided the asteroid’s actual diameter was less than about 140 m and its density was 2 g/cm3 or less. Larger diameters and/or higher densities would require a higher power IBD vehicle, multiple IBD vehicles, or a longer deflection phase. Ion beam deflection is largely independent of the characteristics of the threat object, but its effectiveness, like all deflection approaches, is sensitive to both the asteroid mass and the time available for deflection. The characteristics of IBD, i.e., large standoff distance between the spacecraft and the asteroid surface, as well as ion beam divergence angles of a few degrees, facilitates the possible simultaneous use of multiple IBD vehicles to improve the performance and robustness of the asteroid deflection. The 65-cm diameter, 20-kW NEXIS ion thruster developed in support of the Jupiter Icy Moons Orbiter mission concept is particularly well suited for application to a high-power IBD system. It has demonstrated an ion beam divergence angle of approximately 2 degrees and operation at 20 kW for over 2,000 hours. Completion of the development and flight qualification of this technology would significantly reduce the risk and time necessary to respond to the discovery of potentially hazardous asteroid in the size range of 50- to 100-m diameter.

Reeves, David↗
NASA NTRS2016

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Pinson, Robin M.↗
NASA NTRS2015

BILLIARDS: A Demonstration Mission for Hundred-Meter Class Near-Earth Asteroid Disruption

Collisions from near-Earth asteroids (NEAs) have the potential to cause widespread harm to life on Earth. The hypervelocity nature of these collisions means that a relatively small asteroid (about a quartermile in diameter) could cause a global disaster. Proposed strategies for deflecting or disrupting such a threatening asteroid include detonation of a nuclear explosive device (NED) in close proximity to the asteroid, as well as intercepting the asteroid with a hypervelocity kinetic impactor. NEDs allow for the delivery of large amounts of energy to a NEA for a given mass launched from the Earth, but have not yet been developed or tested for use in deep space. They also present safety and political complications, and therefore may only be used when absolutely necessary. Kinetic impactors require a relatively simple spacecraft compared to NEDs, but also deliver a much lower energy for a given launch mass. To date, no demonstration mission has been conducted for either case, and such a demonstration mission must be conducted prior to the need to utilize them during an actual scenario to ensure that an established, proven system is available for planetary defense when the need arises. One method that has been proposed to deliver a kinetic impactor with impact energy approaching that of an NED is the "billiard-ball" approach. This approach would involve capturing an asteroid approximately ten meters in diameter with a relatively small spacecraft (compared to the launch mass of an equivalent direct kinetic impactor), and redirecting it into the path of an Earth-threatening asteroid. This would cause an impact which would disrupt the Earth-threatening asteroid or deflect it from its Earth-crossing trajectory. The BILLIARDS Project seeks to perform a demonstration of this mission concept in order to establish a protocol that can be used in the event of an impending Earth/asteroid collision. In order to accomplish this objective, the mission must (1) rendezvous with a small (less than 10m), NEA (hereinafter "Alpha"), (2) maneuver Alpha to a collision with a approx. 100 m NEA (hereinafter "Beta"), and (3) produce a detectable deflection or disruption of Beta. In addition to these primary objectives, the BILLIARDS project will contribute to the scientific understanding of the physical properties and collision dynamics of asteroids, and provide opportunities for international collaboration.

Asteroid↗
NASA NTRS2000

The Deep Space 4/Champollion Comet Rendezvous and Lander Technology Demonstration Mission

The Deep Space 4/Champollion mission is designed to test and validate technologies for landing on and anchoring to small bodies, and sample collection and transfer, in preparation for future sample return missions from comets, asteroids, and satellites. in addition, DS-4 will test technologies for advanced, multi-engine solar electric propulsion (SEP) systems, inflatable-rigidizable solar arrays, autonomous navigation and precision guidance for landing, autonomous hazard detection and avoidance, and advanced integrated avionics and packaging concepts. Deep Space-4/Champollion consists of two spacecraft: an orbiter/carrier vehicle which includes the multi-engine SEP stage, and a lander, called Champollion, which will descend to the surface of the 46P/Tempel 1 cometary nucleus. The spacecraft will launch in April, 2003 and land on the comet in September, 2006 Deep Space 4/Champollion is a joint project between NASA and CNES, the French space agency.

Smythe, William D.↗
NASA NTRS2005

The Interstellar Conspiracy

If we were designing a human-carrying starship that could be launched in the not-too-distant future, it would almost certainly not use a warp drive to instantaneously bounce around the universe, as is done in Isaac Asimov's classic Foundation series or in episodes of Star Trek or Star Wars. Sadly, those starships that seem to be within technological reach could not even travel at high relativistic speeds, as does the interstellar ramjet in Poul Anderson's Tau Zero. Warp-speeds seem to be well outside the realm of currently understood physical law; proton-fusing ramjets may never be technologically feasible. Perhaps fortunately in our terrorist-plagued world, the economics of antimatter may never be attractive for large-scale starship propulsion. But interstellar travel will be possible within a few centuries, although it will certainly not be as fast as we might prefer. If humans learn how to hibernate, perhaps we will sleep our way to the stars, as do the crew in A. E. van Vogt's Far Centaurus. However, as discussed in a landmark paper in The Journal of the British Interplanetary Society, the most feasible approach to transporting a small human population to the planets (if any) of Alpha Centauri is the worldship. Such craft have often been featured in science fiction. See for example Arthur C. Clarke's Rendezvous with Rama, and Robert A. Heinlein's Orphans of the Sky. Worldships are essentially mobile versions of the O Neill free-space habitats. Constructed mostly from lunar and/or asteroidal materials, these solar-powered, multi-kilometer-dimension structures could house 10,000 to 100,000 humans in Earth-approximating environments. Artificial gravity would be provided by habitat rotation, and cosmic ray shielding would be provided by passive methods, such as habitat atmosphere and mass shielding, or magnetic fields. A late 21st century space-habitat venture might support itself economically by constructing large solar-powered satellites to beam energy back to Earth.

Johnson, Les↗
NASA NTRS1989

Performance of advanced missions using fusion propulsion

A quantitive evaluation of the premise that nuclear fusion propulsion offers benefits as compared to other propulsion technologies for carrying out a program of advanced exploration of the solar system and beyond is presented. Using a simplified analytical model of trajectory performance, numerical results of mass requirements versus trip time are given for robotic missions beyond the solar system that include flyby and rendezvous with the Oort cloud of comets and with the star system Alpha Centauri. Round trip missions within the solar system, including robotic sample returns from the outer planet moons and multiple asteroid targets, and manned Mars exploration are also described.

Friedlander, Alan↗
NASA NTRS1991

Short-period comets

The spacecraft flybys of Comet Halley in 1986 confirmed Whipple's icy conglomerate hypothesis for cometary nuclei and showed that comets are far richer in volatiles than any other class of solar system bodies. Water is the most abundant volatile, comprising roughly 80 percent of the gas flowing out from the nucleus. Carbon monoxide is next with a content of 15 percent relative to water, though with approximately half of that coming from an extended source in the cometary coma, i.e., hydrocarbon dust grains. The detection of large numbers of hydrocarbon CHON grains was one of the more significant discoveries of the Halley flybys, as was the ground-based observation that CN occurs in jets, again indicating an extended source. Evidence was also found for more complex hydrocarbons. Estimates of the total dust-to-gas ratio for Halley range as high as 2:1, indicating that a substantial fraction of the volatile material may be tied up in solid hydrocarbons rather than ices. The role of clathrates in trapping more volatile ices is not yet understood. If Halley can be taken to be representative of all short-period comets, then the short-period comets may provide a significant source of volatiles in near-earth space. This resource is more difficult to reach dynamically than the near-earth asteriods, but the high volatile content may justify the additional effort necessary. In addition, there is considerable evidence that at least some fraction of the near-earth asteriods are extinct cometary nuclei which have evolved into asteroid orbits, and which may contain significant volatiles buried beneath an insulating lag-deposit crust of nonvolatiles. Knowledge of comets will be greatly enhanced in the near future by the Comet Rendezvous Flyby mission now under development by NASA, and by the proposed Rosetta mission.

Weissman, Paul R.↗
NASA NTRS2003

Space Colonization Using Space-Elevators from Phobos

A novel approach is examined for creating an industrial civilization beyond Earth. The approach would take advantage of the unique configuration of Mars and its moon Phobos to make a transportation system capable of raising mass from the surface of Mars to space at a low cost. Mars would be used as the primary location for support personnel and infrastructure. Phobos would be used as a source of raw materials for space-based activity, and as an anchor for tethered carbon-nanotube-based space-elevators. One space-elevator would terminate at the upper edge of Mars' atmosphere. Small craft would be launched from Mars' surface to rendezvous with the moving elevator tip and their payloads detached and raised with solar powered loop elevators to Phobos. Another space-elevator would be extended outward from Phobos to launch craft toward the Earth/Moon system or the asteroid belt. The outward tip would also be used to catch arriving craft. This approach would allow Mars to be colonized, and allow transportation of people and supplies from Mars to support the space industry. In addition, large quantities of material obtained from Phobos could be used to construct space habitats and also supply propellant and material for space industry in the Earth/Moon system as well as around Mars.

Weinstein, Leonard M.↗
NASA NTRS2013

Asteroid Retrieval Mission Concept - Trailblazing Our Future in Space and Helping to Protect Us from Earth Impactors

The Asteroid Retrieval Mission (ARM) is a robotic mission concept with the goal of returning a small (~7 m diameter) near-Earth asteroid (NEA), or part of a large NEA, to a safe, stable orbit in cislunar space using a 50 kW-class solar electric propulsion (SEP) robotic spacecraft (~40 kW available to the electric propulsion system) and currently available technologies. The mass of the asteroidal material returned from this mission is anticipated to be up to 1,000 metric tons, depending on the orbit of the target NEA and the thrust-to-weight and control authority of the SEP spacecraft. Even larger masses could be returned in the future as technological capability and operational experience improve. The use of high-power solar electric propulsion is the key enabling technology for this mission concept, and is beneficial or enabling for a variety of space missions and architectures where high-efficiency, low-thrust transfers are applicable. Many of the ARM operations and technologies could also be applicable to, or help inform, planetary defense efforts. These include the operational approaches and systems associated with the NEA approach, rendezvous, and station-keeping mission phases utilizing a low-thrust, high-power SEP spacecraft, along with interacting with, capturing, maneuvering, and processing the massive amounts of material associated with this mission. Additionally, the processed materials themselves (e.g., high-specific impulse chemical propellants) could potentially be used for planetary defense efforts. Finally, a ubiquitous asteroid retrieval and resource extraction infrastructure could provide the foundation of an on call planetary defense system, where a SEP fleet capable of propelling large masses could deliver payloads to deflect or disrupt a confirmed impactor in an efficient and timely manner.

Mazanek, Daniel D.↗
NASA NTRS2014

Mars, Phobos, and Deimos Sample Return Enabled by ARRM Alternative Trade Study Spacecraft

The Asteroid Robotic Redirect Mission (ARRM) has been the topic of many mission design studies since 2011. The reference ARRM spacecraft uses a powerful solar electric propulsion (SEP) system and a bag device to capture a small asteroid from an Earth-like orbit and redirect it to a distant retrograde orbit (DRO) around the moon. The ARRM Option B spacecraft uses the same propulsion system and multi-Degree of Freedom (DoF) manipulators device to retrieve a very large sample (thousands of kilograms) from a 100+ meter diameter farther-away Near Earth Asteroid (NEA). This study will demonstrate that the ARRM Option B spacecraft design can also be used to return samples from Mars and its moons - either by acquiring a large rock from the surface of Phobos or Deimos, and/or by rendezvousing with a sample-return spacecraft launched from the surface of Mars.

optimization↗
NASA NTRS1985

Operational implications for path constrained rendezvous

After noting that many large orbiting space structures will be of such magnitude as to require proximity rendezvous guidance targeting in order to accomplish path-constrained approaches in the vicinity of their exterior surfaces, attention is given to the difficulties that inhere in the accomplishment of such rendezvous transfers due to physical constraints imposed by the structures' surfaces. Operationally feasible transfer techniques which circumvent the path constraints inherent in these maneuvers are discussed under the assumption of a number of restrictions. The techniques presented may be important in asteroid exploration and exploitation.

Stern, S. A.↗
NASA NTRS2014

Mars, Phobos, and Deimos Sample Return Enabled by ARRM Alternative Trade Study Spacecraft

The Asteroid Robotic Redirect Mission (ARRM) has been the topic of many mission design studies since 2011. The reference ARRM spacecraft uses a powerful solar electric propulsion (SEP) system and a bag device to capture a small asteroid from an Earth-like orbit and redirect it to a distant retrograde orbit (DRO) around the moon. The ARRM Option B spacecraft uses the same propulsion system and multi-Degree of Freedom (DoF) manipulators device to retrieve a very large sample (thousands of kilograms) from a 100+ meter diameter farther-away Near Earth Asteroid (NEA). This study will demonstrate that the ARRM Option B spacecraft design can also be used to return samples from Mars and its moons - either by acquiring a large rock from the surface of Phobos or Deimos, and or by rendezvousing with a sample-return spacecraft launched from the surface of Mars.

trajectory design↗
NASA NTRS2005

Orbit Modification of Earth-Crossing Asteroids/Comets Using Rendezvous Spacecraft and Laser Ablation

This report describes the approach and results of an end-to-end simulation to deflect a long-period comet (LPC) by using a rapid rendezvous spacecraft and laser ablation system. The laser energy required for providing sufficient deflection DELTA V and an analysis of possible intercept/rendezvous spacecraft trajectories are studied in this analysis. These problems minimize a weighted sum of the flight time and required propellant by using an advanced propulsion system. The optimal thrust-vector history and propellant mass to use are found in order to transfer a spacecraft from the Earth to a targeted celestial object. One goal of this analysis is to formulate an optimization problem for intercept/rendezvous spacecraft trajectories. One approach to alter the trajectory of the object in a highly controlled manner is to use pulsed laser ablative propulsion. A sufficiently intense laser pulse ablates the surface of a near-Earth object (NEO) by causing plasma blowoff. The momentum change from a single laser pulse is very small. However, the cumulative effect is very effective because the laser can interact with the object over long periods of time. The laser ablation technique can overcome the mass penalties associated with other nondisruptive approaches because no propellant is required to generate the DELTA V (the material of the celestial object is the propellant source). Additionally, laser ablation is effective against a wide range of surface materials and does not require any landing or physical attachment to the object. For diverting distant asteroids and comets, the power and optical requirements of a laser ablation system on or near the Earth may be too extreme to contemplate in the next few decades. A hybrid solution would be for a spacecraft to carry a laser as a payload to a particular celestial body. The spacecraft would require an advanced propulsion system capable of rapid rendezvous with the object and an extremely powerful electrical generator, which is likely needed for the propulsion system as well. The spacecraft would station-keep with the object at a small standoff distance while the laser ablation is performed.

Park, Sang-Young↗
NASA NTRS1974

A study of unmanned mission opportunities to comets and asteroids

Several unmanned multiple-target mission opportunities to comets and asteroids were studied. The targets investigated include Grigg-Skjellerup, Giacobini-Zinner, Tuttle-Giacobini-Kresak, Borrelly, Halley, Schaumasse, Geographos, Eros, Icarus, and Toro, and the trajectories consist of purely ballistic flight, except that powered swingbys and deep space burns are employed when necessary. Optimum solar electric rendezvous trajectories to the comets Giacobini-Zinner/85, Borrelly/87, and Temple (2)/83 and /88 employing the 8.67 kw Sert III spacecraft modified for interplanetary flight were also investigated. The problem of optimizing electric propulsion heliocentric trajectories, including the effects of geocentric launch asymptote declination on launch vehicle performance capability, was formulated, and a solution developed using variational calculus techniques. Improvements were made to the HILTOP trajectory optimization computer program. An error analysis of high-thrust maneuvers involving spin-stabilized spacecraft was developed and applied to a synchronous meteorological satellite mission.

Mann, F. I.↗