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NASA NTRS1994

Venusian atmospheric and Magellan properties from attitude control data

Results are presented of the study of the Venusian atmosphere, Magellan aerodynamic moment coefficients, moments of inertia, and solar moment coefficients. This investigation is based upon the use of attitude control data in the form of reaction wheel speeds from the Magellan spacecraft. As the spacecraft enters the upper atmosphere of Venus, measurable torques are experienced due to aerodynamic effects. Solar and gravity gradient effects also cause additional torques throughout the orbit. In order to maintain an inertially fixed attitude, the control system counteracts these torques by changing the angular rates of three reaction wheels. Model reaction wheel speeds are compared to observed Magellan reaction wheel speeds through a differential correction procedure. This method determines aerodynamic, atmospheric, solar pressure, and mass moment of inertia parameters. Atmospheric measurements include both base densities and scale heights. Atmospheric base density results confirm natural variability as measured by the standard orbital decay method. Potential inconsistencies in free molecular aerodynamic moment coefficients are identified. Moments of inertia are determined with a precision better than 1 percent of the largest principal moment of inertia.

Croom, Christopher A.↗

NASA NTRS2013

Estimation of Gravitation Parameters of Saturnian Moons Using Cassini Attitude Control Flight Data

A major science objective of the Cassini mission is to study Saturnian satellites. The gravitational properties of each Saturnian moon is of interest not only to scientists but also to attitude control engineers. When the Cassini spacecraft flies close to a moon, a gravity gradient torque is exerted on the spacecraft due to the mass of the moon. The gravity gradient torque will alter the spin rates of the reaction wheels (RWA). The change of each reaction wheel's spin rate might lead to overspeed issues or operating the wheel bearings in an undesirable boundary lubrication condition. Hence, it is imperative to understand how the gravity gradient torque caused by a moon will affect the reaction wheels in order to protect the health of the hardware. The attitude control telemetry from low-altitude flybys of Saturn's moons can be used to estimate the gravitational parameter of the moon or the distance between the centers of mass of Cassini and the moon. Flight data from several low altitude flybys of three Saturnian moons, Dione, Rhea, and Enceladus, were used to estimate the gravitational parameters of these moons. Results are compared with values given in the literature.

angular momentum↗

NASA NTRS1988

Spacecraft redesign to reduce microphonic response of a VCO component

Reaction wheel vibration was found to induce out of specification sidebands on the carrier frequencies of some spacecraft components containing mechanical voltage control oscillators (VCOs). Concurrent investigations were performed to redesign the VCOs to reduce their response to the wheel vibration, and to design a reaction wheel isolation system to reduce the vibration input to the affected components. Component level tests indicated that both efforts provided viable solutions. The redesigned VCO will be incorporated into future spacecraft in the series, while affected spacecraft already in production will be retrofitted with the reaction wheel isolation system.

Strain, J. C.↗

NASA NTRS2008

Pointing Stability Performance of the Cassini Spacecraft

Twelve scientific instruments onboard the Cassini spacecraft depend on the accurate pointing capabilities of the spacecraft to return data critical to the success of the mission and to improving our understanding of Saturn. Throughout the seven year interplanetary cruise to Saturn and the four year prime mission, the control of the Cassini spacecraft is achieved by employing either the Reaction Control System (RCS) composed of a set of eight thrusters or the Reaction Wheel Assembly (RWA) made up of four reaction wheels, only three of which are active at a given time. The operations of Cassini imaging instruments (such as the Narrow Angle Camera) require a high level of spacecraft pointing stability in order to minimize the distortion and smearing of the image during the exposure time. In designing the Cassini attitude control system, a pointing stability performance metric that considered the frequency contents of the disturbance sources was employed. The flight performance of the Cassini pointing stability, achieved with a set of three reaction wheels or RCS thrusters, is summarized in this paper.

Lee, Allan Y.↗

NASA NTRS1991

Wheel speed management control system for spacecraft

A spacecraft attitude control system uses at least four reaction wheels. In order to minimize reaction wheel speed and therefore power, a wheel speed management system is provided. The management system monitors the wheel speeds and generates a wheel speed error vector. The error vector is integrated, and the error vector and its integral are combined to form a correction vector. The correction vector is summed with the attitude control torque command signals for driving the reaction wheels.

Goodzeit, Neil E.↗

NASA NTRS2007

Contingency Operations during Failure of Inertial Attitude Acquisition Due to Star Tracker Blinding for Three-Axes-Stabilized Interplanetary Spacecraft

The three interplanetary ESA missions Mars-Express, Rosetta and Venus-Express (launched 2003, 2004 and 2005 resp.) are three-axes stabilized spacecraft (s/c) that estimate their inertial attitude (i.e. the attitude of the s/c w.r.t. the inertial frame) using measurements from a redundant set of star trackers (STR). Each s/c is equipped with four reaction wheels, a reaction control system based on thrusters and a redundant set of ring laser gyroscopes (gyros). The STR h/w layout of the three s/c is identical whereas there is a difference in the star pattern recognition algorithm of Rosetta which uses five neighbouring stars around a central star instead of star triads. The Rosetta algorithm has been implemented to cope with the presence of false stars which are expected to be seen during operations around the comet. The attitude acquisition capability from lost in space is different also in terms of AOCMS: The survival mode of Rosetta which is entered upon STR failure is presented. The AOCMS of Mars- and Venus-Express manages temporary STR outages during sky occultation by the planet not even by using redundancy. Though, a blinding of both STR during cruise lasting for the order of days confronts the ground operators with the limits of the AOCMS design. The operations and analyses that have been planned and partially been performed to compensate for the outage of the STR are demonstrated for Mars-Express. The caution measures taken before Venus orbit insertion of Venus-Express are detailed.

Keil, Joachim↗

NASA NTRS2017

Momentum Management for the NASA Near Earth Asteroid Scout Solar Sail Mission

The Momentum Management (MM) system is described for the NASA Near Earth Asteroid Scout (NEA Scout) cubesat solar sail mission. Unlike many solar sail mission proposals that used solar torque as the primary or only attitude control system, NEA Scout uses small reaction wheels (RW) and a reaction control system (RCS) with cold gas thrusters, as described in the abstract "Solar Sail Attitude Control System for Near Earth Asteroid Scout Cubesat Mission." The reaction wheels allow fine pointing and higher rates with low mass actuators to meet the science, communication, and trajectory guidance requirements. The MM system keeps the speed of the wheels within their operating margins using a combination of solar torque and the RCS.

Heaton, Andrew↗

NASA NTRS2010

Lunar Reconnaissance Orbiter (LRO) Thruster Control Mode Design and Flight Experience

National Aeronautics and Space Administration s (NASA) Goddard Space Flight Center (GSFC) in Greenbelt, MD, designed, built, tested, and launched the Lunar Reconnaissance Orbiter (LRO) from Cape Canaveral Air Force Station on June 18, 2009. The LRO spacecraft is the first operational spacecraft designed to support NASA s return to the Moon, as part of the Vision for Space Exploration. LRO was launched aboard an Atlas V 401 launch vehicle into a direct insertion trajectory to the Moon. Twenty-four hours after separation the propulsion system was used to perform a mid-course correction maneuver. Four days after the mid-course correction a series of propulsion maneuvers were executed to insert LRO into its commissioning orbit. The commission period lasted eighty days and this followed by a second set of thruster maneuvers that inserted LRO into its mission orbit. To date, the spacecraft has been gathering invaluable data in support of human s future return to the moon. The LRO Attitude Control Systems (ACS) contains two thruster based control modes: Delta-H and Delta-V. The design of the two controllers are similar in that they are both used for 3-axis control of the spacecraft with the Delta-H controller used for momentum management and the Delta-V controller used for orbit adjust and maintenance maneuvers. In addition to the nominal purpose of the thruster modes, the Delta-H controller also has the added capability of performing a large angle slew maneuver. A suite of ACS components are used by the thruster based control modes, for both initialization and control. For initialization purposes, a star tracker or the Kalman Filter solution is used for providing attitude knowledge and upon entrance into the thruster based control modes attitude knowledge is provided via rate propagation using a inertial reference unit (IRU). Rate information for the controller is also supplied by the IRU. Three-axis control of the spacecraft in the thruster modes is provided by eight 5-lbf class attitude control thrusters configured in two sets of four thrusters for redundancy purposes. Four additional 20-lbf class thrusters configured in two sets of two thrusters are used for Lunar Orbit Insertion maneuvers. The propulsion system is one the few systems on-board the LRO spacecraft that has built in redundancy. The Delta-H controller consists of a Proportional-Derivative (PD) controller with a structural filter on the thrusters and a Proportional controller on the reaction wheels. The PD control that employs the thrusters is used for attitude and rate control. The Proportional controller on the reaction wheels is used for commanding the wheels to a new momentum state. The ground commands used for the Delta-H controller are the system momentum vector, reaction wheel momentum, maximum expected command time, and which set of attitude control thrusters to use. The ability to command both the system momentum vector and reaction wheel momentum in the Delta-H controller provides both a capability and an additional source of operator error. Large angle slews via the Delta-H controller is achievable via this commands because these commands are used for the exit mode criteria. Setting these commands to non-consistent values prevents the mode from exiting nominally.

Hsu, Oscar C.↗

NASA NTRS2021

Validation of Small Satellite Dynamics Simulation Modules using ASTERIA Flight Data

ASTERIA (Arcsecond Space Telescope Enabling Research in Astrophysics) was a CubeSat space telescope that operated in low-Earth orbit, having been deployed from the International Space Station in 2017. The spacecraft has achieved sub-arcsecond pointing stability and millikelvin thermal stability over 20-minute observations. A key enabling feature of the ASTERIA mission is the low level of pointing error that has been demonstrated under ASTERIA’s fine pointing control mode. Prior to launch, the ASTERIA mission performed analysis and simulations to estimate the in-flight pointing performance. This analysis used reaction wheel models provided by JPL’s Small Satellite Dynamics Testbed (SSDT), which had performed Kistler table testing to characterize the jitter caused by the reaction wheels of the Blue Canyon Technologies XACT attitude control unit within ASTERIA. These models were subsequently incorporated into the SSDT simulation. The main source of jitter, the high-frequency attitude disturbance over the camera exposure time, on ASTERIA is the set of rotating reaction wheels that are used for maintaining fine pointing during observations. The reaction wheels impart disturbance forces and torques continuously that cause unwanted motion during imaging. Increased jitter consequently leads to blurring of the image. Therefore, to benefit all SmallSat missions devoted to photometric or spectroscopic astrophysics applications, an on-orbit flight data acquisition and jitter testing campaign was performed in an attempt to help validate the SSDT’s simulation models. This paper describes the process used to validate several simulation models and attempt to characterize the ASTERIA jitter by analyzing the size of the resulting spot size for the target stars as a function of wheel speed, having commanded four wheel speeds for each of three stars of known brightness. After summarizing the on-orbit observation and jitter level measurement process, this paper compares the results obtained from the flight operational environment to the corresponding set of simulation jitter levels. Though the flight data obtained during this experiment was not sufficient to validate the simulation’s jitter model, other models have been validated with flight data, including the magnetic field, orbit propagation, sun position, and long-duration orbit decay models, which may be used by all other projects that use the SSDT’s simulation to increase system capability knowledge.

Mohan, Swati↗

NASA NTRS2005

Line of Sight Stabilization of James Webb Space Telescope

The James Webb Space Telescope (JWST) builds upon the successful flight experience of the Chandra Xray Telescope by incorporating an additional LOS pointing servo to meet the more stringent pointing requirements. The LOS pointing servo, referred to in JWST as the Fine Guidance Control System (FGCS), will utilize a Fine Guidance Sensor (FGS) as the sensor, and a Fine Steering Mirror (FSM) as the actuator. The FSM is a part of the Optical Telescope Element (OTE) and is in the optical path between the tertiary mirror and the instrument focal plane, while the FGS is part of the Integrated Science Instrument Module (ISIM). The basic Chandra spacecraft bus attitude control and determination architecture, utilizing gyros, star trackers/aspect camera, and reaction wheels, is retained for JWST. This system has achieved pointing stability of better than 0.5 arcseconds. To reach the JWST requirements of milli-arcsecond pointing stability with this ACS hardware, the local FGCS loop is added to the optical path. The FGCS bandwidth is about 2.0 Hz and will therefore attenuate much of the spacecraft ACS induced low frequency jitter. In order to attenuate the higher frequency (greatet than 2.0 Hz) disturbances associated with reaction wheel static and dynamic imbalances, as well as bearing run-out, JWST will employ a two-stage passive vibration isolation system consisting of (1) 7.0 Hz reaction wheel isolators between each reaction wheel and the spacecraft bus, and (2) a 1.0 Hz tower isolator between the spacecraft bus and the Optical Telescope Element (OTE). In order to sense and measure the LOS, the FGS behaves much like an autonomous star tracker that has a very small field of view and uses the optics of the telescope. It performs the functions of acquisition, identification and tracking of stars in its 2.5 x 2.5 arcminute field of view (FOV), and provides the centroid and magnitude of the selected star for use in LOS control. However, since only a single star is being tracked at any time within the FGS FOV there is only tip and tilt information; rotation about the FGS LOS will not be sensed. The FGCS uses the FSM to move the guide star within the FGS FOV and place the centroid of the guide star at any desired position within the FGS focal plane. Using this architecture allows the FGCS to correct the low frequency LOS jitter that is induced by the spacecraft ACS in pitch and yaw, and achieve the milli-arcsecond pointing stability required by JWST. The less stringent ISIM FOV roll performance will be provided solely by the ACS, using the spacecraft gyros and star trackers. Since the FSM is in the optical path, the pointing stabilrty of a science object in any of the instruments will be similar to that of the guide star LOS.

Meza, Luis↗

NASA NTRS1986

Emitted vibration measurement device and method

This invention is directed to a method and apparatus for measuring emitted vibrational forces produced by a reaction wheel assembly due to imbalances, misalignment, bearing defects and the like. The apparatus includes a low mass carriage supported on a large mass base. The carriage is in the form of an octagonal frame having an opening which is adapted for receiving the reaction wheel assembly supported thereon by means of a mounting ring. The carriage is supported on the base by means of air bearings which support the carriage in a generally frictionless manner when supplied with compressed air from a source. A plurality of carriage brackets and a plurality of base blocks provided for physical coupling of the base and carriage. The sensing axes of the load cells are arranged generally parallel to the base and connected between the base and carriage such that all of the vibrational forces emitted by the reaction wheel assembly are effectively transmitted through the sensing axes of the load cells. In this manner, a highly reliable and accurate measurment of the vibrational forces of the reaction wheel assembly can be had. The output signals from the load cells are subjected to a dynamical analyzer which analyzes and identifies the rotor and spin bearing components which are causing the vibrational forces.

Gisler, G. L.↗

NASA NTRS2016

GOES-16 On-Orbit Dual Isolation Performance Characterization Results

The Geostationary Operational Environmental Satellite-R Series (GOES-R) is the first of the next generation geostationary weather satellites. GOES-R successfully launched on November19, 2016 and renamed GOES-16 upon entering geostationary orbit. Subsequently, GOES-16post-launch testing began. This paper presents the GOES-16 Satellite Dynamic Interaction Characterization results for the Earth Pointed Platform (EPP) stowed, referred to as the Reaction Wheel Assembly (RWA) Isolation Only configuration, and deployed, referred to as the Dual Isolation configuration. GOES-R represents a quantum increase in Earth and solar weather observation capabilities, with 4 times the resolution, 5 times the observation rate, and 3 times the number of spectral bands for Earth observations. With the improved resolution, comes the instrument suites increased sensitivity to disturbances over a broad spectrum 0-512Hz. Sources of disturbance include reaction wheels, thruster firings for station keeping and momentum management, gimbal motion, and internal instrument disturbances. To minimize the impact of these disturbances, the baseline design included an EPP, a stiff optical bench to which the two nadir pointed instruments are collocated together with the Guidance Navigation Control (GNC) star trackers and Inertial Measurement Units (IMUs). The EPP is passively isolated from the spacecraft bus with Honeywell D-Strut isolators providing attenuation for frequencies above 5 Hz in all six degrees-of-freedom. To reduce the risk of wheel disturbances impacting performance, a secondary passive isolation system manufactured by Moog CSA Engineering was incorporated under each of the six 160 Nms reaction wheels, tuned to provide attenuation at frequencies above 50 Hz. Integrated wheel and isolator testing was performed on a Kistler table at NASA Goddard Space Flight Center. Pre-launch Satellite Dynamic Interaction Characterization high-fidelity simulations and ground testing were conducted to evaluate jitter performance for two cases: 1) deployed EPP and reaction wheel (Dual Isolation) and 2) EPP hard mounted (RWA Isolation Only) to the spacecraft. A comparison of pre-launch to post-launch Satellite Dynamic Interaction Characterization results are also presented in this paper.

Carter, Delano↗

NASA NTRS2017

Solar Sail Attitude Control System for the NASA Near Earth Asteroid Scout Mission

An Attitude Control System (ACS) has been developed for the NASA Near Earth Asteroid (NEA) Scout mission. The NEA Scout spacecraft is a 6U cubesat with an eighty-six square meter solar sail for primary propulsion that will launch as a secondary payload on the Space Launch System (SLS) Exploration Mission 1 (EM-1) and rendezvous with a target asteroid after a two year journey, and will conduct science imagery. The spacecraft ACS consists of three major actuating subsystems: a Reaction Wheel (RW) control system, a Reaction Control System (RCS), and an Active Mass Translator (AMT) system. The reaction wheels allow fine pointing and higher rates with low mass actuators to meet the science, communication, and trajectory guidance requirements. The Momentum Management System (MMS) keeps the speed of the wheels within their operating margins using a combination of solar torque and the RCS. The AMT is used to adjust the sign and magnitude of the solar torque to manage pitch and yaw momentum. The RCS is used for initial de-tumble, performing a Trajectory Correction Maneuver (TCM), and performing momentum management about the roll axis. The NEA Scout ACS is able to meet all mission requirements including attitude hold, slews, pointing for optical navigation and pointing for science with margin and including flexible body effects. Here we discuss the challenges and solutions of meeting NEA Scout mission requirements for the ACS design, and present a novel implementation of managing the spacecraft Center of Mass (CM) to trim the solar sail disturbance torque. The ACS we have developed has an applicability to a range of potential missions and does so in a much smaller volume than is traditional for deep space missions beyond Earth.

Orphee, Juan↗

NASA NTRS2017

Flex Dynamics Avoidance Control of the NEA Scout Solar Sail Spacecraft's Reaction Control System

The Attitude Control System (ACS) is developed for a Near Earth Asteroid (NEA) Scout mission using a solar sail. The NEA-Scout spacecraft is a 6U cubesat with an 86 square-meter solar sail. NEA Scout will launch on Space Launch System (SLS) Exploration Mission 1 (EM-1), currently scheduled to launch in 2018. The spacecraft will rendezvous with a target asteroid after a two year journey, and will conduct science imagery. The solar sail spacecraft ACS consists of three major actuating subsystems: a Reaction Wheel (RW) control system, a Reaction Control System (RCS), and an Adjustable Mass Translator (AMT) system. The three subsystems allow for a wide range of spacecraft attitude control capabilities, needed for the different phases of the NEA-Scout mission. Because the sail is a flexible structure, care must be taken in designing a control system to avoid exciting the structural modes of the sail. This is especially true for the RCS, which uses pulse actuated, cold-gas jets to control the spacecraft's attitude. While the reaction wheels can be commanded smoothly, the RCS jets are simple on-off actuators. Long duration firing of the RCS jets - firings greater than one second - can be thought of as step inputs to the spacecraft's torque. On the other hand, short duration firings - pulses on the order of 0.1 seconds - can be thought of as impulses in the spacecraft's torque. These types of inputs will excite the structural modes of the spacecraft, causing the sail to oscillate. Sail oscillations are undesirable for many reasons. Mainly, these oscillations will feed into the spacecraft attitude sensors and pointing accuracy, and long term oscillations may be undesirable over the lifetime of the solar sail. In order to limit the sail oscillations, an RCS control scheme is being developed to minimize sail excitations. Specifically, an input shaping scheme similar to the method described in Reference 1 will be employed. A detailed description of the RCS control scheme will be provided with particular emphasis on flexible body excitation. The RCS performance will be provided to show that sail and boom excitation is minimized.

Heaton Andrew↗

NASA NTRS2022

Microthruster-Based Control for Precision Pointing of Next-Generation Space Telescopes

The next generation of space telescopes, such as the Habitable Exoplanet Observatory mission concept (HabEx), are expected to have milli-arcsecond-level pointing requirements at the spacecraft level. The pointing performance of such telescopes tends to be driven by internal rather than external disturbances, in particular reaction wheel jitter. This paper considers an architecture that relies on microthrusters instead of reaction wheels for spacecraft fine pointing, focusing on the HabEx mission concept as a case study. The proposed implementation uses micro-Newton-class colloidal thrusters that were tested in orbit as part of the ST7 payload on the LISA Pathfinder mission to reach Technical Readiness Level (TRL) 7. Key characteristics of these thrusters and the associated system trade-offs are first discussed. The resulting pointing control loop design is then described. Its ability to meet applicable pointing requirements is shown using three-degree-of-freedom simulations, where relevant disturbances are modelled. The control system is shown to reduce the pointing error by several orders of magnitude in about two hours, starting from coarse reaction control system (RCS) handover conditions. Once settled, the system meets the steady-state milli-arcsecond-level performance requirements with significant margin. Overall, the results show that microthruster-based pointing control architectures offer a promising alternative to traditional reaction-wheel-based designs for space telescope applications.

Ziemer, John↗

NASA NTRS2011

Estimation of Enceladus Plume Density Using Cassini Flight Data

The Cassini spacecraft was launched on October 15, 1997 by a Titan 4B launch vehicle. After an interplanetary cruise of almost seven years, it arrived at Saturn on June 30, 2004. In 2005, Cassini completed three flybys of Enceladus, a small, icy satellite of Saturn. Observations made during these flybys confirmed the existence of water vapor plumes in the south polar region of Enceladus. Five additional low-altitude flybys of Enceladus were successfully executed in 2008-9 to better characterize these watery plumes. During some of these Enceladus flybys, the spacecraft attitude was controlled by a set of three reaction wheels. When the disturbance torque imparted on the spacecraft was predicted to exceed the control authority of the reaction wheels, thrusters were used to control the spacecraft attitude. Using telemetry data of reaction wheel rates or thruster on-times collected from four low-altitude Enceladus flybys (in 2008-10), one can reconstruct the time histories of the Enceladus plume jet density. The 1 sigma uncertainty of the estimated density is 5.9-6.7% (depending on the density estimation methodology employed). These plume density estimates could be used to confirm measurements made by other onboard science instruments and to support the modeling of Enceladus plume jets.

Wang, Eric K.↗

NASA NTRS1997

STS-82 Flight Day 08 Highlights

The eighth day of the STS-82 mission begins with the crew, Commander Kenneth D. Bowersox, Pilot Scott J. Horowitz, Payload Commander Mark C. Lee, and Mission Specialists Gregory J. Harbaugh, Steven L. Smith, Joseph R. Tanner, and Steven A. Hawley performing the final spacewalk of the mission. Lee and Smith attach several thermal insulation blankets to three equipment compartments at the top of the Support Systems Module section of Hubble which contain key data processing, electronics and scientific instrument telemetry packages. Following the completion of that work, Lee and Smith briefly return to the airlock while flight controllers evaluated a possible glitch with one of four Reaction Wheel Assembly units in Hubble used to maneuver the telescope for its scientific observations. A spare Reaction Wheel Assembly was available aboard Discovery for a swap out during an additional spacewalk had it been necessary, but a few hours later, after further analysis, payload controllers reported that the Reaction Wheel Assembly was in excellent shape and operating at the proper speed.

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NASA NTRS2021

Application of Micro-thrusters for Space Observatory Precision Attitude Control

This paper describes the results of a NASA investigation into the benefits of micro-thrusters compared to reaction wheels on future observatory-class missions with tight pointing stability requirements. Pointing repeatability and stability (i.e., jitter) requirements are key for space telescope missions of the future. For example, managing jitter is essential to being able to “image” planets orbiting distant stars. Jitter requirements for missions in this class are difficult to meet with current reaction wheel-based architectures. The reaction wheels are typically the largest pointing disturbance on the spacecraft. Disturbances from reaction wheels can be mitigated, typically by mechanically isolating the wheels, which imposes system complexity and cost. Thrusters capable of thrust forces in the micronewton (μN) range (referred to as micro-thrusters or micronewton thrusters) have been developed to support the Laser Interferometer Space Antenna (LISA) mission, which requires drag-free control to place a test mass in near-perfect free-fall Beyond the drag-free control application, micro-thrusters could be used as a substitute for reaction wheels or as a supplement to wheels for fine pointing control. Used in this fashion, micro-thrusters have potential for reducing the cost and technical risks of achieving demanding pointing stability performance on observatory-class missions.

Chiang, Richard Y.↗