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Follow That Satellite: EO-1 Maneuvers into Closed Formation With Landsat-7

As the Landsat-7 spacecraft continued NASA's historic program of earth imaging, begun over three decades ago, NASA launched the Earth Observing-1 (EO-1) spacecraft carrying examples of the next generation of Landsat-7 instruments. The validation method for these instruments was to have EO-1 fly in a close formation behind Landsat-7 on the same World Reference System path. From that formation hundreds of near coincident images would be taken by each spacecraft and compared to evaluate improvements in the EO-1 instruments. This paper will address the mission analysis required to launch and maneuver EO-1 into the formation with Landsat-7 where instrument validation was to occur plus a summary of completing the formation acquisition. EO-1 is required to operate one minute +/- 6 seconds behind Landsat-7 during the period of co-fly imaging with a cross track separation of within + 3 kilometers. This separation time can also be stated as a one minute +/- 6 seconds time difference in the Mean Local Time (MLT) at the descending nodes. Achieving the required MLT is heavily dependent on the time of launch. The EO-1 launch window, which had to accommodate the dual payloads of EO-1 and SAC-C, was very limited ranging from 0 to 22 seconds over the 16 day Landsat-7 WRS repeat cycle during which EO-1 was launched. Each EO-1 launch opportunity that occurred on a different day of a Landsat-7 16 day repeat cycle required a separate and distinct maneuver profile. These profiles varied significantly in duration and amount of onboard propellant required to achieve them. EO-1 launched on a day judged to have "medium" resource requirements for achieving the formation with Landsat-7. To phase EO-1 one minute behind Landsat-7 in the along track direction, a series of altitude adjusts separated by specific drift intervals were executed. Additional maneuvers slightly changed the EO-1 inclination to maintain the MLT requirements. Orbit maneuvers were planned and executed within errors of less than 1.5 percent and propellant usage was near nominal consuming 3.4 kilograms out of a launch and early orbit budget of 11 kilograms. The pre-launch 3 -sigma propellant budget allowed for 1+ years of EO-1 mission life. The success of the EO-1 launch and early orbit operations provided sufficient propellant for nearly 4 years of on orbit operations. Special action taken during the EO-1 maneuver period involved some maneuver re-planning to reduce concerns about a potential close approach between EO-1 and Landsat-7. The result of this re-planning was a safer close approach and improvement in future formation acquisition planning.

DeFazio, Robert↗

The Integration, Testing and Flight of the EO-1 GPS

The Global Positioning System has long been hailed as the wave of the future for autonomous on-board navigation of low Earth orbiting spacecraft despite the fact that relatively few spacecraft have actually employed it for this purpose. While several missions operated out of the Goddard Space Flight Center have flown GPS receivers on board, the New Millenium Program (NMP) Earth Orbiting-1 (EO-1) spacecraft is the first to employ GPS for active, autonomous on-board navigation. Since EO-1 was designed to employ GPS as its primary source of the navigation ephemeris, special care had to be taken during the integration phase of spacecraft construction to assure proper performance. This paper is a discussion of that process: a brief overview of how the GPS works, how it fits into the design of the EO-1 Attitude Control System (ACS), the steps taken to integrate the system into the EO-1 spacecraft, the ultimate on-orbit performance during launch and early operations of the EO-1 mission and the performance of the on-board GPS ephemeris versus the ground based ephemeris. Conclusions will include a discussion of the lessons learned.

Quinn, David A.↗

Follow That Satellite: EO-1 Maneuvers Into Close Formation With Landsat-7

As the Landsat-7 (LS-7) spacecraft continued NASA's historic program of earth imaging begun over three decades ago, NASA launched the Earth Observing-1 (EO-1) spacecraft carrying examples of the next generation of LS instruments. The validation method for these instruments was to have EO-1 fly in a close formation behind LS-7 on the same World Reference System (WRS) path. From that formation hundreds of near-coincident images would be taken by each spacecraft and compared to evaluate improvements in the EO-1 instruments. This paper will address the mission analysis required to launch and maneuver EO-1 into the formation with LS-7 where instrument validation was to occur plus a summary of completing the formation acquisition. Each EO-1 launch opportunity that occurred on a different day of a LS-7 16-day repeat cycle required a separate and distinct maneuver profile.

DeFazio, Robert L.↗

Enhanced Formation Flying for the Earth Observing-1 (EO-1) New Millennium Mission

With scientific objectives for Earth observation programs becoming more ambitious and spacecraft becoming more autonomous, the need for new technical approaches on the feasibility of achieving and maintaining formations of spacecraft has come to the forefront. The trend to develop small low cost spacecraft has led many scientists to recognize the advantage of flying several spacecraft in formation, an example of which is shown in the figure below, to achieve the correlated instrument measurements formerly possible only by flying many instruments on a single large platform. Yet, formation flying imposes additional complications on orbit maintenance, especially when each spacecraft has its own orbit requirements. However, advances in automation proposed by GSFC Codes 550 and 712 allow more of the burden in maneuver planning and execution to be placed onboard the spacecraft, mitigating some of the associated operational concerns. The purpose of this analysis is to develop the fundamentals of formation flying mechanics, concepts for understanding the relative motion of free flying spacecraft, and an operational control theory for formation maintenance of the Earth Observing-1 (EO-l) spacecraft that is part of the New Millennium. Results of this development can be used to determine the appropriateness of formation flying for a particular case as well as the operational impacts. Applications to the Mission to Planet Earth (MTPE) Earth Observing System (EOS) and New Millennium (NM) were highly considered in analysis and applications. This paper presents the proposed methods for the guidance and control of the EO-1 spacecraft to formation fly with the Landsat-7 spacecraft using an autonomous closed loop three axis navigation control, GPS, and Cross link navigation support. Simulation results using various fidelity levels of modeling, algorithms developed and implemented in MATLAB, and autonomous 'fuzzy logic' control using AutoCon will be presented. The results of these analysis on the ability to meet mission and formation flying requirements will be presented.

Folta, David↗

Lessons Learned on Operating and Preparing Operations for a Technology Mission from the Perspective of the Earth Observing-1 Mission

The New Millennium Program's first Earth-observing mission (EO-1) is a technology validation mission. It is managed by the NASA Goddard Space Flight Center in Greenbelt, Maryland and is scheduled for launch in the summer of 2000. The purpose of this mission is to flight-validate revolutionary technologies that will contribute to the reduction of cost and increase of capabilities for future land imaging missions. In the EO-1 mission, there are five instrument, five spacecraft, and three supporting technologies to flight-validate during a year of operations. EO-1 operations and the accompanying ground system were intended to be simple in order to maintain low operational costs. For purposes of formulating operations, it was initially modeled as a small science mission. However, it quickly evolved into a more complex mission due to the difficulties in effectively integrating all of the validation plans of the individual technologies. As a consequence, more operational support was required to confidently complete the on-orbit validation of the new technologies. This paper will outline the issues and lessons learned applicable to future technology validation missions. Examples of some of these include the following: (1) operational complexity encountered in integrating all of the validation plans into a coherent operational plan, (2) initial desire to run single shift operations subsequently growing to 6 "around-the-clock" operations, (3) managing changes in the technologies that ultimately affected operations, (4) necessity for better team communications within the project to offset the effects of change on the Ground System Developers, Operations Engineers, Integration and Test Engineers, S/C Subsystem Engineers, and Scientists, and (5) the need for a more experienced Flight Operations Team to achieve the necessary operational flexibility. The discussion will conclude by providing several cost comparisons for developing operations from previous missions to EO-1 and discuss some details that might be done differently for future technology validation missions.

Mandl, Dan↗

Global Positioning System Simulator Field Operational Procedures

Global Positioning System (GPS) simulation is an important activity in the development or qualification of GPS signal receivers for space flight. Because a GPS simulator is a critical resource it is highly desirable to develop a set of field operational procedures to supplement the basic procedures provided by most simulator vendors. Validated field procedures allow better utilization of the GPS simulator in the development of new test scenarios and simulation operations. These procedures expedite simulation scenario development while resulting in scenarios that are more representative of the true design, as well as enabling construction of more complex simulations than previously possible, for example, spacecraft maneuvers. One difficulty in the development of a simulation scenario is specifying various modes of test vehicle motion and associated maneuvers requiring that a user specify some (but not all) of a few closely related simulation parameters. Currently this can only be done by trial and error. A stand-alone procedure that implements the simulator maneuver motion equations and solves for the motion profile transient times, jerk and acceleration would be of considerable value. Another procedure would permit the specification of some configuration parameters that would determine the simulated GPS signal composition. The resulting signal navigation message, for example, would force the receiver under test to use only the intended C-code component of the simulated GPS signal. A representative class of GPS simulation-related field operational procedures is described in this paper. These procedures were developed and used in support of GPS integration and testing for many successful spacecraft missions such as SAC-A, EO-1, AMSAT, VCL, SeaStar, sounding rockets, and by using the industry standard Spirent Global Simulation Systems Incorporated (GSSI) STR series simulators.

Kizhner, Semion↗

Earth Orbiter 1 (EO-1): Wideband Advanced Recorder and Processor (WARP)

An overview of the Earth Orbitor 1 (EO1) Wideband Advanced Recorder and Processor (WARP) is presented in viewgraph form. The WARP is a spacecraft component that receives, stores, and processes high rate science data and its associated ancillary data from multispectral detectors, hyperspectral detectors, and an atmospheric corrector, and then transmits the data via an X-band or S-band transmitter to the ground station. The WARP project goals are: (1) Pathfinder for next generation LANDSAT mission; (2) Flight prove architectures and technologies; and (3) Identify future technology needs.

Smith, Terry↗

An Overview of Future NASA Missions, Concepts, and Technologies Related to Imaging of the World's Land Areas

In the near term NASA is entering into the peak activity period of the Earth Observing System (EOS). The EOS AM-1 /"Terra" spacecraft is nearing launch and operation to be followed soon by the New Millennium Program (NMP) Earth Observing (EO-1) mission. Other missions related to land imaging and studies include EOS PM-1 mission, the Earth System Sciences Program (ESSP) Vegetation Canopy Lidar (VCL) mission, the EOS/IceSat mission. These missions involve clear advances in technologies and observational capability including improvements in multispectral imaging and other observing strategies, for example, "formation flying". Plans are underway to define the next era of EOS missions, commonly called "EOS Follow-on" or EOS II. The programmatic planning includes concepts that represent advances over the present Landsat-7 mission that concomitantly recognize the advances being made in land imaging within the private sector. The National Polar Orbiting Environmental Satellite Series (NPOESS) Preparatory Project (NPP) is an effort that will help to transition EOS medium resolution (herein meaning spatial resolutions near 500 meters), multispectral measurement capabilities such as represented by the EOS Moderate Resolution Imaging Spectroradiometer (MODIS) into the NPOESS operational series of satellites. Developments in Synthetic Aperture Radar (SAR) and passive microwave land observing capabilities are also proceeding. Beyond these efforts the Earth Science Enterprise Technology Strategy is embarking efforts to advance technologies in several basic areas: instruments, flight systems and operational capability, and information systems. In the case of instruments architectures will be examined that offer significant reductions in mass, volume, power and observational flexibility. For flight systems and operational capability, formation flying including calibration and data fusion, systems operation autonomy, and mechanical and electronic innovations that can reduce spacecraft and subsystem resource requirements. The efforts in information systems will include better approaches for linking multiple data sets, extracting and visualizing information, and improvements in collecting, compressing, transmitting, processing, distributing and archiving data from multiple platforms. Overall concepts such as sensor webs, constellations of observing systems, and rapid and tailored data availability and delivery to multiple users comprise and notions Earth Science Vision for the future.

Salomonson, Vincent V.↗

Implementation of Autonomous GPS Guidance and Control for Spacecraft Formation Flying

This paper presents the general relative orbit dynamics equations and GPS (Global Positioning System) orbit observational equations that have been developed for on-board control of spacecraft flying in formation. The approach to the implementation of the autonomous control for orbit acquisition and maintenance of spacecraft formation using GPS code pseudoranges are presented. As a practical application of the models and method provided in this paper, the orbit control of the Earth-Orbiter 1(EO-1) / Landsat 7 system has been designed, using the discrete-time linear optimal output feedback control. For the actuator of the on/off type reaction jets, the implementation problem of the pulse-amplitude modulation is also studied. Simulation results of autonomous orbit control and maintenance, for 3-dimensional initial orbit error, using optimal output feedback control are shown. These simulation results certified the feasibility of the implementation of the autonomous maintenance control for EO-1/Landsat 7 formation flying by means of the discrete-time linear optimal output feedback control.

Xing, Guang Q.↗

Relative navigation for spacecraft formation flying

The Goddard Space Flight Center Guidance, Navigation, and Control Center (GNCC) is currently developing and implementing advanced satellite systems to provide autonomous control of formation flyers. The initial formation maintenance capability will be flight-demonstrated on the Earth-Orbiter-1 (EO-1) satellite, which is planned under the National Aeronautics and Space Administration New Millennium Program to be a coflight with the Landsat-7 (L-7) satellite. Formation flying imposes relative navigation accuracy requirements in addition to the orbit accuracy requirements for the individual satellites. In the case of EO-1 and L-7, the two satellites are in nearly coplanar orbits, with a small difference in the longitude of the ascending node to compensate for the Earth's rotation. The GNCC has performed trajectory error analysis for the relative navigation of the EO-1/L-7 formation, as well as for a more advanced tracking configuration using cross-link satellite communications. This paper discusses the orbit determination and prediction accuracy achievable for EO-1 and L-7 under various tracking and orbit determination scenarios and discusses the expected relative separation errors in their formation flying configuration.

Hartman, Kate R.↗

Onboard Processor for Compressing HSI Data

With EO-1 Hyperion and MightySat in orbit NASA and the DoD are showing their continued commitment to hyperspectral imaging (HSI). As HSI sensor technology continues to mature, the ever-increasing amounts of sensor data generated will result in a need for more cost effective communication and data handling systems. Lockheed Martin, with considerable experience in spacecraft design and developing special purpose onboard processors, has teamed with Applied Signal & Image Technology (ASIT), who has an extensive heritage in HSI, to develop a real-time and intelligent onboard processing (OBP) system to reduce HSI sensor downlink requirements. Our goal is to reduce the downlink requirement by a factor greater than 100, while retaining the necessary spectral fidelity of the sensor data needed to satisfy the many science, military, and intelligence goals of these systems. Our initial spectral compression experiments leverage commercial-off-the-shelf (COTS) spectral exploitation algorithms for segmentation, material identification and spectral compression that ASIT has developed. ASIT will also support the modification and integration of this COTS software into the OBP. Other commercially available COTS software for spatial compression will also be employed as part of the overall compression processing sequence. Over the next year elements of a high-performance reconfigurable OBP will be developed to implement proven preprocessing steps that distill the HSI data stream in both spectral and spatial dimensions. The system will intelligently reduce the volume of data that must be stored, transmitted to the ground, and processed while minimizing the loss of information.

Cook, Sid↗

Autonomous Formation Flying from Ground to Flight

The cost of on-orbit operations remains a significant and increasingly visible concern in the support of satellite missions. Headway has been made in automating some ground operations; however, increased mission complexity and more precise orbital constraints have compelled continuing human involvement in mission design and maneuver planning operations. AI Solutions, Inc. in cooperation with the National Aeronautics and Space Administration's (NASA) Goddard Space Flight Center (GSFC) has tackled these more complex problems through the development of AutoCon as a tool for an automated solution. NASA is using AutoCon to automate the maneuver planning for the Earth Orbiter-1 (EO-1) mission. AutoCon was developed originally as a ground system tool. The EO-1 mission will be using a scaled version of AutoCon on-board the EO-1 satellite to command orbit adjustment maneuvers. The flight version of AutoCon plans maneuvers based on formation flying algorithms developed by GSFC, JPL, and other industry partners. In its fully autonomous mode, an AutoCon planned maneuver will be executed on-board the satellite without intervention from the ground. This paper describes how AutoCon automates maneuver planning for the formation flying constraints of the EO-1 mission. AutoCon was modified in a number of ways to automate the maneuver planning on-board the satellite. This paper describes how the interface and functionality of AutoCon were modified to support the on-board system. A significant component of this modification was the implementation of a data smoother, based on a Kalman filter, that ensures that the spacecraft states estimated by an on-board GPS receiver are as accurate as possible for maneuver planning. This paper also presents the methodology use to scale the AutoCon functionality to fit and execute on the flight hardware. This paper also presents the modes built that allow the incremental phasing in of autonomy. New technologies for autonomous operations are usually received with significant, and probably appropriate trepidation. A number of safeguards have been designed in both AutoCon and the interfacing systems to alleviate the potential of mission-impacting anomalies from the on-board autonomous system. This paper describes the error checking, input data integrity validation and limits set on maneuvers in AutoCon and the on-board system.

Chapman, Keith B.↗

Autonomous Formation Flying from the Ground to Flight

The cost of on-orbit operations remains a significant and increasingly visible concern in the support of satellite missions. Headway has been made in automating some ground operations; however, increased mission complexity and more precise orbital constraints have compelled continuing human involvement in mission design and maneuver planning operations. AI Solutions, Inc. in cooperation with the National Aeronautics and Space Administration's (NASA) Goddard Space Flight Center (GSFC) has tackled these more complex problems through the development of AutoCon(TM) as a tool for an automated solution. NASA is using AutoCon(TM) to automate the maneuver planning for the Earth Orbiter-1 (EO-1) mission. AutoCon(TM) was developed originally as a ground system tool. The EO-1 mission will be using a scaled version of AutoCon(TM) on-board the EO-1 satellite to command orbit adjustment maneuvers. The flight version of AutoCon(TM) plans maneuvers based on formation flying algorithms developed by GSFC, JPL, and other industry partners. In its fully autonomous mode, an AutoCon(TM) planned maneuver will be executed on-board the satellite without intervention from the ground. This paper describes how AutoCon(TM) automates maneuver planning for the formation flying constraints of the EO-1 mission. AutoCon(TM) was modified in a number of ways to automate the maneuver planning on-board the satellite. This paper describes how the interface and functionality of AutoCon(TM) were modified to support the on-board system. A significant component of this modification was the implementation of a data smoother, based on a Kalman filter, that ensures that the spacecraft states estimated by an on-board GPS receiver are as accurate as possible for maneuver planning. This paper also presents the methodology used to scale the AutoCon(TM) functionality to fit and execute on the flight hardware. This paper also presents the modes built into the system that allow the incremental phasing in of autonomy. New technologies for autonomous operations are usually received with significant, and probably appropriate, trepidation. A number of safeguards have been designed in both AutoCon(TM) and the interfacing systems to alleviate the potential of mission-impacting anomalies from the on-board autonomous system. This paper describes the error checking, input data integrity validation, and limits set on maneuvers in AutoCon(TM) and the on-board system.

Chapman, Keith B.↗

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗

LIDAR Remote Sensing Concepts

The primary goal of the NASA New Millennium Program (NMP) is to develop technology for use on future operational missions. The Program consists of two thrust areas, one oriented towards developing technologies for Deep Space Probes and one oriented towards developing technology for Earth Observing Probes. Each thrust area intends to fly several technology demonstrator spacecraft designated DS-X and EO-X respectively where X is the mission number. Each mission has an approximately $100 million cap on total mission cost. The EO-1 mission has been selected and is under development. The instrument discussed here was submitted by NASA MSFC as a potential candidate for the EO-2 or EO-3 missions due to launch in 2001 and late 2002 or early 2003 respectively. This report summarizes and follows the format of the material provided to NMP.

Spiers, Gary D.↗

Relative Navigation for Spacecraft Formation Flying

The Goddard Space Flight Center Guidance, Navigation, and Control Center (GNCC) is currently developing and implementing advanced satellite systems to provide autonomous control of formation flyers. The initial formation maintenance capability will be flight-demonstrated on the Earth-Orbiter-1 (EO-l) satellite, which is planned under the National Aeronautics and Space Administration New Millennium Program to be a coflight with the Landsat-7 (L-7) satellite. Formation flying imposes relative navigation accuracy requirements in addition to the orbit accuracy requirements for the individual satellites. In the case of EO-1 and L-7, the two satellites are in nearly coplanar orbits, with a small difference in the longitude of the ascending node to compensate for the Earth's rotation. The GNCC has performed trajectory error analysis for the relative navigation of the EO-1/L-7 formation, as well as for a more advanced tracking configuration using cross- link satellite communications. This paper discusses the orbit determination and prediction accuracy achievable for EO-1 and L-7 under various tracking and orbit determination scenarios and discusses the expected relative separation errors in their formation flying configuration.

Hartman, Kate R.↗

Overview of the Landsat-7 Mission

Landsat-7 is scheduled for launch on April 15 from the Western Test Range at Vandenberg Air Force Base, Calif., on a Delta-H expendable launch vehicle. The Landsat 7 satellite consists of a spacecraft bus being provided by Lockheed Martin Missiles and Space (Valley Forge, Pa.) and the Enhanced Thematic Mapper Plus instrument built by Raytheon (formerly Hughes) Santa Barbara Remote Sensing (Santa Barbara, Calif.). The instrument on board Landsat 7 is the Enhanced Thematic Mapper Plus (ETM+). ETM+ improves upon the previous Thematic Mapper (TM) instruments on Landsat's 4 and 5 (Fig. la and lb). It includes the previous 7 spectral bands measuring reflected solar radiation and emitted thermal emissions but, in addition, includes a new 15 in panchromatic (visible-near infrared) band. The spatial resolution of the thermal infrared band has also been improved to 60 m. Both the radiometric precision and accuracy of the sensor are also improved from the previous TM sensors. After being launched into a sun-synchronous polar orbit, the satellite will use on-board propulsion to adjust its orbit to a circular altitude of 438 miles (705 kilometers) crossing the equator at approximately 10 a.m. on its southward track. This orbit will place Landsat 7 along the same ground track as previous Landsat satellites. The orbit will be maintained with periodic adjustments for the life of the mission. A three-axis attitude control subsystem will stabilize the satellite and keep the instrument pointed toward the Earth to within 0.05 degrees. Later this year, plans call for the NASA Earth Observation System (EOS) Terra (AM-1) observatory and the experimental EO-1 mission to closely follow Landsat-7's orbit to support synergistic research and applications from this new suite of terrestrial sensor systems. Landsat is the United States' oldest land-surface observation satellite system, with satellites continuously operating since 1972. Although the program has scored numerous successes in scientific and resource-management applications, Landsat has had a tumultuous history of management and funding changes over its nearly 27-year history. Landsat-7 marks a new direction in the program to reduce the cost of data and increase systematic global coverage for use in global change research as well as commercial and regional applications. With the passage of the Land Remote Sensing Policy Act in 1992, oversight of the Landsat program began to shift from the commercial sector to the federal government. NASA integrated Landsat-7 into its EOS science program in 1994. Landsat-7 is managed and operated jointly by NASA and U.S. Geological Survey (USGS). As a result, the costs of acquiring observations from

Williams, Darrel↗