1

Meeting the Mission

The scientific field of celestial mechanics began when Johannes Kepler analyzed the astronomical data of Tycho Brahe and discovered that the orbits of the planets are ellipses, overthrowing the complicated Ptolemaic system that had been used for more than a millennium. Kepler sought to find harmony and order in the motion of the planets around the Sun, even describing planetary motion in terms of music. Kepler’s method was inductive and provided no reason why the ellipse was the preferred shape of planetary orbits. Using his newly discovered calculus, Isaac Newton was able to deduce the elliptical motion from his universal law of gravitation, which applied to orbiting celestial objects as well as on Earth. In Newton’s theory, an exact elliptical orbit is only obtained in the idealized case of two spherically symmetric objects (the two-body problem). The elliptic orbit is perturbed by nonsphericity of the objects’ gravitational fields, and by the presence of a third body. Using just Newtonian mechanics and the universal law of gravitation, astronomers were able to derive the perturbed orbits of all the planets with great precision. This has been the great triumph of celestial mechanics.

Astrodynamics, a subfield of celestial mechanics, is concerned with the orbits of manmade objects around Earth and other celestial bodies. Newtonian mechanics can still be applied to derive these orbits, but the perturbing forces acting on these objects—including atmospheric drag, solar radiation pressure, and Earth tides—are much more complicated than for celestial objects, To account for the uncertainty in these perturbing forces and the uncertainty in the observational measurements, statistical methods for orbit determination have been developed. Chaotic motion was first observed in celestial mechanics by Henri Poincaré in the three-body problem, and the modern theory of dynamical systems studies such chaotic behavior. As scientific knowledge of orbiting objects has progressed, simplicity and order have thus given way to complexity and chaos. The term “chaos” here and throughout the report is used in the technical sense to mean that small perturbations can, in some circumstances, result in large changes in orbits. The dynamics are complicated and difficult to model, in part because the system exhibits all the mathematical traits of a chaotic dynamical system. The problem is further exacerbated by interactions between sensor data and object dynamics. This is the challenge that the Air Force faces in using astrodynamics algorithms to maintain a catalog of Earth-orbiting space objects and to provide space situational awareness to its many customers.

The President of the United States develops the National Space Policy that establishes goals to strengthen stability in space and promote safe and responsible operations in space.1 The Secretary of Defense (SECDEF)

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1 National Space Policy of the United States of America, June 28, 2010, available at http://www.whitehouse.gov/sites/default/files/national_space_policy_6-28-10.pdf.



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1 Meeting the Mission The scientific field of celestial mechanics began when Johannes Kepler analyzed the astronomical data of Tycho Brahe and discovered that the orbits of the planets are ellipses, overthrowing the complicated Ptolemaic system that had been used for more than a millennium. Kepler sought to find harmony and order in the motion of the planets around the Sun, even describing planetary motion in terms of music. Kepler’s method was inductive and provided no reason why the ellipse was the preferred shape of planetary orbits. Using his newly discovered calculus, Isaac Newton was able to deduce the elliptical motion from his universal law of gravitation, which applied to orbiting celestial objects as well as on Earth. In Newton’s theory, an exact elliptical orbit is only obtained in the idealized case of two spherically symmetric objects (the two-body problem). The elliptic orbit is perturbed by nonsphericity of the objects’ gravitational fields, and by the presence of a third body. Using just Newtonian mechanics and the universal law of gravitation, astronomers were able to derive the perturbed orbits of all the planets with great precision. This has been the great triumph of celestial mechanics. Astrodynamics, a subfield of celestial mechanics, is concerned with the orbits of manmade objects around Earth and other celestial bodies. Newtonian mechanics can still be applied to derive these orbits, but the perturbing forces acting on these objects—including atmospheric drag, solar radiation pressure, and Earth tides—are much more complicated than for celestial objects, To account for the uncertainty in these perturbing forces and the uncertainty in the observational measurements, statistical methods for orbit determination have been developed. Chaotic motion was first observed in celestial mechanics by Henri Poincaré in the three-body problem, and the modern theory of dynamical systems studies such chaotic behavior. As scientific knowledge of orbiting objects has progressed, simplicity and order have thus given way to complexity and chaos. The term “chaos” here and throughout the report is used in the technical sense to mean that small perturbations can, in some circumstances, result in large changes in orbits. The dynamics are complicated and difficult to model, in part because the system exhibits all the mathematical traits of a chaotic dynamical system. The problem is further exacerbated by interac- tions between sensor data and object dynamics. This is the challenge that the Air Force faces in using astrodynamics algorithms to maintain a catalog of Earth-orbiting space objects and to provide space situational awareness to its many customers. The President of the United States develops the National Space Policy that establishes goals to strengthen stability in space and promote safe and responsible operations in space. 1 The Secretary of Defense (SECDEF) 1 National Space Policy of the United States of America, June 28, 2010, available at http://www.whitehouse.gov/sites/default/files/ national_space_policy_6-28-10.pdf. 7

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8 CONTINUING KEPLER’S QUEST—ASSESSING AIR FORCE SPACE COMMAND’S ASTRODYNAMICS STANDARDS assigns missions to the unified and specified Combatant Commands in the Unified Command Plans (UCPs). As a unified Combatant Command, the U.S. Stratetic Command (USSTRATCOM) has been assigned the space control mission in its UCP. USSTRATCOM has delegated its space control mission to the Joint Functional Component Command for Space (JFCC SPACE) at Vandenberg Air Force Base. The Joint Space Operations Center (JSpOC) is the Command and Control (C2) center where the Commander JFCC SPACE exercises Space Coordinating Authority and C2 of assigned and attached forces. The Commander JFCC SPACE is dual hatted, also being the Commander of the 14th Air Force, headquartered at Vandenberg Air Force Base in California. The 14th Air Force reports administratively to Air Force Space Command (AFSPC) but operationally supports USSTRATCOM through JFCC SPACE. The 614th Air and Space Operations Center (614 AOC) is a subordinate unit of the 14th Air Force and is the primary force provider to the JSpOC. The 614 AOC provides ready space forces and capabilities to the JSpOC in order to execute theater and global operations with a priority on warfighter support. The 614th AOC Detachment 1 is located in Dahlgren, Virginia, at the Distributive Space Command and Control–Dahlgren (DSC2-D) center, which is the backup facility to the JSpOC. These command relationships2 are shown in Figure 1.1. To protect vital U.S. national security and other interests, the Commander JFCC SPACE must conduct near- real-time space situational awareness (SSA), assess threats, and plan courses of action. 3 Joint Publication 3-14, “Space Operations,” defines SSA as the requisite current and predictive knowledge of the space environment and the operational environment on which space operations depend—including physical, virtual, and human domains—as well as all factors, activities, and events of friendly and adversary space forces across the spectrum of conflict. 4 AFSPC standardized astrodynamics algorithms are used at the JSpOC, and the distributed software containing these algorithms is used by its customers. These standardized astrodynamics algorithms are used to measure and describe satellite motion. The distributed software sent to the user community is maintained by AFSPC. Within the Headquarters AFSPC Space Analysis Directorate, designated AFSPC/A9, is a small office that maintains and distributes the software modules. The JSpOC currently uses the algorithms found in AFSPC standardized astrodynamics algorithms for a sig - nificant portion of its daily space operations, in which it must detect and track space events and maintain a catalog of more than 20,000 space objects. A typical day at the JSpOC using the standardized astrodynamics algorithms includes: • Collecting and processing 400,000 satellite observations; • Updating at least three times a special perturbations precision catalog on more than 20,000 objects; • Preparing and transmitting 200,000 Space Surveillance Network (SSN) sensor taskings; and • Processing 30 detailed conjunction assessments as a result of screening more than 1,000 active payloads against the special perturbations catalog of 20,000 objects. On February 10, 2009, the Iridium 33 satellite maneuvered into the path of the inactive Russian communica - tions satellite Cosmos 2251, resulting in a collision that destroyed both satellites and left a debris cloud in a densely populated orbit regime. Before the collision, the JSpOC was screening only about 300 Department of Defense (DOD) and National Aeronautics and Space Administration (NASA) satellites for conjunctions. After this event the JSpOC began screening about 1,000 active satellites for conjunctions with other satellites and debris, including commercial and foreign satellites. USSTRATCOM also initiated the Space Situational Awareness Data Sharing program to further develop products that can be shared with commercial and foreign entities. AFSPC is a major command (MAJCOM; i.e., it reports administratively to Headquarters Air Force) whose responsibility is to organize, train, and equip for the space mission. Like JFCC, AFSPC is operationally under USSTRATCOM. The JSpOC is supported in its mission by AFSPC, which develops requirements, advocates for budgets at a national level, funds the SSN sensors, and provides other MAJCOM Headquarters level support. The 2 U.S. Air Force, Space Operations, Air Force Doctrine Document 3-14, June 19, 2012, available at http://www.e-publishing.af.mil. 3 Colonel Mike Wasson, Joint Space Operations Center, U.S. Air Force, “JSpOC SSA Processing,” presentation to the Committee for the Assessment of the U.S. Air Force’s Astrodynamic Standards on December 12, 2011. 4 U.S. Air Force, Space Operations, Air Force Doctrine Document 3-14, June 19, 2012, available at http://www.e-publishing.af.mil.

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9 MEETING THE MISSION FIGURE 1.1 Command relationships. SOURCE: U.S. Air Force, Space Operations, Air Force Doctrine Document 3-14, June 19, 2012, available at http://www.e-publishing.af.mil. Electronic Systems Center (ESC) acquires and maintains some SSN sensor sites as well as maintains the current Space Defense Operations Center (SPADOC) C2 system. Space and Missiles Systems Center (SMC) acquires Figure 1-1 satellites and is also acquiring the new JSpOC Mission System (JMS), which will replace SPADOC. Prior to 2001 Bitmapped SMC was part of Air Force Materiel Command (AFMC) but is now part of AFSPC. ESC remains part of AFMC and, although it receives requirements from AFSPC, ESC does not report to AFSPC. The global network of SSN sensors includes dedicated sensors that are operated and controlled by AFSPC, contributing (1) sensors that are funded by the Command or, in some cases, other governments and provide data to the Command and (2) collateral sensors that are operated by other agencies such as the Missile Defense Agency but do provide data to the Command. This sensor network has broader coverage than that currently available to any other country. (See Figure 1.2.) HISTORY OF STANDARDS IN ASTRODYNAMICS The U.S. Navy developed, deployed in 1961, and funded until 2004 the first sensor capable of the large-scale detection of satellites. Known in the past as the Navy Space Surveillance System, and now as the Air Force Space Surveillance System (AFSSS), this sensor is a set of bistatic radars consisting of three transmitters and six receiv - ers located along a great circle on the 33rd parallel north across the southern United States. Because the Navy had its own sensor, it developed its own software and processing techniques, specifically tuned to the type of data generated by the Navy Space Surveillance System. A major customer of the products developed from the Space Surveillance System was the U.S. Navy’s fleet. The concept of standardized astrodynamics algorithms within the DOD was developed in the early 1980s by

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10 CONTINUING KEPLER’S QUEST—ASSESSING AIR FORCE SPACE COMMAND’S ASTRODYNAMICS STANDARDS MSX / SBV THULE GLOBUS II CLEAR FYLINGDALES LSSC CAVALIER COBRA DANE MOSS CAPE COD BEALE SCC ASCC KAENA PT SOCORRO EGLIN Maui MSSS RTS AFSSS ASCENSION DIEGO GARCIA LSSC = Lincoln Space Surveillance Complex Tracking Radar Dedicated Millstone, Haystack, HAX Detection Radar Collateral MSSS = Maui Space Surveillance System Imaging Radar Contributing (former AMOS/MOTIF site) Optical Telescope AFSSS = Air Force Space Surveillance System SSN C2 SSN C2 RTS = Reagan Test Site 3 FIGURE 1.2 The Space Surveillance Network. SOURCE: Courtesy of the Air Force Space Command. the Air Force Space Command Directorate of Operations and has evolved since then. By that time, various branches of the U.S. government (the Navy, SMC, the National Reconnaissance Office [NRO], NASA, and the National Figure 1-2 Oceanic and Atmospheric Administration [NOAA]) as well as various commercial entities (RCA, Hughes, etc.) had launched satellites into space for a variety of users and uses. Each satellite system developed its own control station and often its own control and processing software quite independent of Space Command or its predeces - sors. They generally relied on their own transponder data for determining orbits and assessing the status of their satellites and made very little use of the data from the sensors operated by Space Command. The same was true of satellites launched by allied governments. Several universities, with funding mostly from NASA and the National Science Foundation (NSF), developed satellites for specific scientific studies. Either NASA or the universities themselves developed the necessary control and orbit determination software, again tuned to the specific application and type of data. Standardized astrodynamics algorithms were originally developed within Air Force Space Command to pro - vide software for the user community to ensure the interoperability of military space surveillance systems with the C2 Space Surveillance Center within the North American Aerospace Defense Command (NORAD) located at Cheyenne Mountain Air Force Station. The orbital products distributed by the C2 center needed to be used in a compatible manner by the users (for example, unless an orbit is propagated in the same manner it was derived, the best possible result will not be obtained). A historical example of the problem that can occur if interoperability is not maintained is found in the selection of the Earth gravity model for propagating the precision orbits distributed for the Defense Meteorological Support Program (DMSP) satellites. The program originated in the 1970s, and the available WGS-72 Earth gravity model was used by AFSPC during the orbit determination process. It was able to successfully meet the DMSP accuracy requirement of predicting the position of the satellite within 1 kilometer, 3 days in the future. In the 1980s, a member of the user community wanted to update to the newer and improved WGS-84 Earth gravity model. When it used the “better” model to propagate the WGS-72-determined state vectors obtained from the Air Force C2 center, the user had worse results and could no longer meet its requirements. (See Figure 1.3.) The user reverted to using the WGS-72 gravity model and was able to successfully meet the requirements for accuracy. (Note that AFSPC has been unable to get the DMSP legacy user community to upgrade to newer gravity models—e.g., the Earth Gravitational Model 1996—because upgrading would involve significant cost and because the existing WGS-72 model embedded in the legacy software meets the user requirements.)

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11 MEETING THE MISSION 3500 3237 72 with 72 3000 72 with 84 2799 2500 Position Rms (m) 2000 1500 1265 3 Day DMSP 1000 requirement 500 350 276 178 0 1 2 3 Days Since Epoch FIGURE 1.3 DMSP interoperability. The y-axis depicts the root-mean-square position error. The red line at 1,000 meters is the mission requirement. The shaded pairs of bars show results for predictions of 1, 2, and 3 days into the future. The shorter bars (all 350 meters or less) show the result using the compatible WGS-72 gravity model, and the taller bars (all greater than the requirement) show the results of using an incompatible WGS-84 gravity model in the prediction interval. SOURCE: Figure 1-3 Denise Kaya, A9AC, Air Force Space Command, presentation to the Committee for the Assessment of the U.S. Air Force’s Astrodyamic Standards on October 11, 2011. Finding: AFSPC has recognized the importance of maintaining interoperability to support the community of operational users. AFSPC standardized astrodynamics algorithms have been implemented in various mainframe-based computer systems at the C2 Space Surveillance Center (renamed the Space Control Center; SCC) at Cheyenne Mountain Air Force Station in Colorado Springs, Colorado, including the Delta computer system, the 427M computer system, and the SPADOC system. (See Figure 1.4.) Because of the requirements of the NRO and NASA for a more com - plete high-accuracy catalog to support conjunction assessments and collision avoidance of high-value assets with other orbiting objects, a contractor-developed prototype of a high-accuracy catalog was implemented about 10 years ago in the astrodynamics support workstation (ASW), using the Special Perturbations (SP) least-squares differential correction algorithm from the AFSPC standardized astrodynamics algorithms, and then deployed on the off-line Command, Analysis, Verification and Ephemeris Network (CAVENet) as an operational prototype. In 2007, SPADOC and CAVENet were moved from Cheyenne Mountain in Colorado to Vandenberg Air Force Base in California. There has been a perception that the ASW contains unchanging legacy algorithms; however, the contractor has made substantial improvements to the ASW over the past 10 years to improve prediction accuracy and propagated covariance realism (e.g., integrating the High Accuracy Satellite Drag Model (HASDM) developed by AFSPC, and integrating a drag/radiation segmentation solution, as well as track weighting and a drag-consider parameter for improved propagated covariance realism). The Delta, 427M, and SPADOC systems were traditional Air Force acquisitions that took decades to develop and to deploy operationally. They were developed as closed systems on proprietary hardware with customized software and operating systems. Because of the difficulty of making changes to SPADOC, the ASW was deployed

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12 CONTINUING KEPLER’S QUEST—ASSESSING AIR FORCE SPACE COMMAND’S ASTRODYNAMICS STANDARDS ‘67 ‘72 ‘77 ‘79 ‘83 ‘87 ‘95 ‘97 ‘98 ‘07 ‘10 C MAF S VAF B “DELTA” Philco 2000 Computers ‘89 CMAFS ‘91 Opens ‘93 427M Development Test- integration ‘95 Honeywell Computers 427M Contract Award A ‘72 Development SPADOC B SPADOC Development Contract Award C1 ‘83 Development IBM Computers “Turn Key” C2 Development Delivery ASW Phased Prototyping ASW Acquisition Silicon Graphics Servers (CAVENet) Delivery Operational Prototype No Ops Acceptance FIGURE 1.4 History of C2 Space Surveillance System. The systems all took many years to implement, and frequently new systems were implemented over time while older systems were phased out. SOURCE: Colonel Mike Wasson, Joint Space Operations Center, U.S. Air Force, “JSpOC SSA Processing,” presentation to the Committee for the Assessment of the U.S. Air Force’s Astrodynamic Standards on December 12, 2011. Figure 1-4 as an operational prototype on the off-line system CAVENet, consisting of Silicon Graphics Incorporated servers and workstations. Today, leading-edge organizations adopt a service-oriented architecture (SOA) approach for major comput - ing applications. The development time of such modern systems is potentially greatly reduced compared to the traditional acquisition approach, with the added advantage of providing a more flexible and extensible system. Products and services can be more loosely coupled in an SOA, making it easier to provide advanced products to some users while still supporting legacy products for those who do not need a change and may have no funds to adapt their organic systems to the advanced products. DESCRIPTION OF THE CURRENT “STANDARDS” The standardized astrodynamics algorithms were originally documented in Air Force Space Command Instruction AFSPCI 60-102, Space Surveillance Astrodynamics Standards, and included standards for coordinate systems and time, physical constants, physical models (e.g., neutral atmospheric density models), and astrody - namics algorithms. Enough information regarding current systems was available and reviewed without evaluating ITAR-restricted algorithms. In general, the special perturbations precision orbit determination process is a weighted batch least-squares solution with segmented drag/radiation pressure, with the duration of the segments being on the order of hours. The orbit propagator uses a special perturbations numerical integration technique with high-order geopotential model - ing, Earth and ocean tide modeling, gravity of the Sun and Moon modeling, dynamic atmospheric drag modeling, radiation pressure modeling, and covariance propagation for estimation of prediction error. In addition to the numerical methods used in the special perturbations processing, AFSPC standardized astro - dynamics algorithms include an analytic method using a general perturbations (GP) technique; the Simplified General Perturbations 4 (SGP4) propagator is the core algorithm in this method. This is the orbital theory used to

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13 MEETING THE MISSION BOX 1.1 AFSPC Standardized Astrodynamics Algorithms SGP4 (Simplified General Perturbations 4)—An analytic method of generating ephemerides for satellites in Earth-centered orbits. SP (Special Perturbations)—An algorithm that uses numerical integration to generate ephemerides for satellites in Earth-centered orbits. BATCHDC (Batch Differential Correction)—Performs a least-squares batch differential correction of orbital elements using tracking data and either the SGP4 or the SP propagator. LAMOD—Computes sensor (ground-based or space-based) viewing opportunities (so-called look angles) for Earth-centered satellites. LAMOD uses either SGP4 or SP for generating ephemerides. IOMOD—Computes an initial set of orbital elements from three observations. AOF (Area Overflight)—Computes when overhead satellites can see a particular location on Earth. AOF uses either SGP4 or SP for generating ephemerides. FOV (field of view)—Determines times in which orbiting satellites fly through a ground-based observer’s conical field of view. The field of view can be defined by a constant azimuth and elevation, a constant right ascension and declination, or as a line-of-site to another orbiting satellite. FOV uses either SGP4 or SP for generating ephemerides. COMBO (Computation of Miss Between Orbits)—Computes close approaches between satellites using either SGP4 or SP for generating ephemerides. ROTAS (Report/Observation Association)—Associates observations against satellite element sets. SEQDC (Sequential Differential Correction)—Performs a series of least-squares differential corrections. These differential corrections are computed in a sequential mode, which uses one or more obser- vations or tracks while retrieving former covariance information from a prior differential correction. SEQDC uses either SGP4 or SP for generating ephemerides. SOURCE: Denise Kaya, A9AC, Air Force Space Command, presentation to the Committee for the Assess- ment of the U.S. Air Force’s Astrodynamic Standards on October 11, 2011. propagate the two-line orbital element sets of the space catalog that are widely distributed. The GP method uses much less computer time than the SP method, but provides less accurate results because of its truncated modeling. Software implementations of the astrodynamics algorithms with accompanying test cases are maintained by Air Force Space Command and distributed to authorized users who need to interface with the JSpOC. Besides the goal of interoperability, the standardized astrodynamics algorithms have the goal of reducing cost by eliminating the need for independent software implementations of astrodynamics algorithms and maintaining separate software baselines across multiple space surveillance systems. The standardized astrodynamics algorithms are currently maintained by AFSPC/A9 as dynamic link librar- ies, shared objects, or executable code on various computer platforms. However, not all operating systems or computer platforms are supported by AFSPC/A9 and the source code is rarely distributed, making it difficult for some users, such as those possessing unique computers, to obtain a useful product. The fact that the standardized astrodynamics algorithms are under the ITAR restrictions limits the distribution of the software. Box 1.1 describes the 10 applications currently available. (Note that the operational C2 system contains more algorithms than these 10, which have been packaged by AFSPC for outside distribution to authorized users.)

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14 CONTINUING KEPLER’S QUEST—ASSESSING AIR FORCE SPACE COMMAND’S ASTRODYNAMICS STANDARDS How Standardized Astrodynamics Algorithms Are Meeting Requirements for Accuracy and Interoperability The committee received presentations from three general groups in the JSpOC standardized astrodynamics algorithms customer community: the DOD users, the civilian government users (e.g., NASA), and the commercial community (e.g., Iridium, Intelsat, etc.). The DOD users are more interested in catalog maintenance, new launch processing, precision orbit prediction in support of various DOD missions, and conjunction assessment. The other two groups focus almost entirely on conjunction assessment for orbit safety. There is also some interest from NASA and the commercial community in JSpOC assistance for anomaly resolution (e.g., when a satellite is injected into the wrong orbit and must be located). Since the Iridium/Cosmos collision in February 2009, there has been heightened interest by the commercial community in orbit safety. NASA has always been interested because of human spaceflight, and the JSpOC and its predecessor organizations have a long history of supporting human spaceflight with conjunction assessment analysis. The newly involved commercial community has varying capabilities to process and evaluate JSpOC prod - ucts such as the Conjunction Summary Message (CSM), which contains the SP orbit information for two satellites at the time of conjunction along with an estimate of the error based on standardized astrodynamics algorithms covariance propagation (this error is usually an ellipsoidal shaped volume). However, it is difficult to characterize the accuracy of the uncertainty (i.e., the covariance) of the estimated position. It is important to users of the data to know the “uncertainty in the uncertainty” of the estimated position in order for the information to be actionable (i.e., to allow a decision about whether the risk is so high that a maneuver is truly needed). For example, during conjunction assessment risk analysis (see Chapter 2), the probability of collision (PC) is used to decide whether to make an evasive maneuver to avoid a collision, and this probability is highly sensitive to the covariance propa - gated to the time of closest approach because the PC is the product of two intersecting ellipsoidal volumes (when considering a debris avoidance maneuver NASA uses a collision probability of 10 –4, 1 chance in 10,000 for a “red alert”). Without knowledge of the accuracy of the covariance, users cannot calculate a reliable risk and make informed decisions about when to perform evasive maneuvers to avoid potential collisions. To make meaningful decisions on whether to expend limited fuel for an evasive maneuver, the owner/operator of a maneuverable satellite needs some knowledge of the uncertainty in the covariance propagated to the time of closest approach from which the owner/operator can calculate a PC. Established users such as NASA have devel - oped procedures and devote significant manpower to computing the PC and tracking the evolution of the PC over time to gain confidence in the trend being seen. Some of the newer commercial users have difficulty computing the PC and developing insight into the confidence of the data. For these users, having the JSpOC include a PC in its alert messages would be helpful, but the JSpOC historically has been reluctant to include a PC in its alerts. Its position has been that the owner/operator should assess the risk to the spacecraft and determine whether a maneuver is truly needed. Unfortunately, the problems of sparse tracking of very small debris objects, the unmodeled errors in the tracking sensor data, and uncertainties in atmospheric density variations combine to make the calculation of an unvarying, highly trusted PC an elusive goal. STANDARDIZED ASTRODYNAMICS ALGORITHMS—THE VIEW OF THE USER COMMUNITY The committee sought input from a variety of users of the data produced by Space Command. During the course of its deliberations the committee heard from representatives from DOD, NASA, and commercial users. DOD Users During the course of the committee’s deliberations it became apparent that it would be difficult to evaluate the performance of standardized astrodynamics algorithms against specific DOD requirements because many requirements were classified and out of the scope of this unclassified effort. In addition, there are multiple Air Force requirements documents with sometimes conflicting accuracy requirements such as the 2000 USSPACECOM Space Control Capstone Requirements Document (CRD), the 2006 USSPACECOM Space Control Joint Capabili -

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15 MEETING THE MISSION ties Document (JCD), the 2010 Capability Development Document (CDD) for the JSpOC Mission System (JMS), the 2011 Functional Requirements Document (FRD) for JMS, and the 2011 draft Initial Capabilities Document (ICD) for Space Situational Awareness (SSA). The committee was informed that the only unclassified DOD accu - racy requirement (DMSP orbit prediction within 1,000 meters over 3 days) is currently being met. Traditionally, accuracy requirements have been classified by the Air Force because they reveal system limitations and capabilities. The legacy systems, SPADOC, the astrodynamics support workstation, and CAVENet are meeting current operational needs but are rapidly approaching their end of life and are not easily extensible to meet increased capacity and future space situational awareness needs. However, the DOD presentations to the committee generally expressed satisfaction with the performance of the current algorithms. Indeed, the positional accuracy require - ments in the CDD for the new JMS program are derived from the performance of the standardized astrodynamics algorithms in the current operational system. Because there is widespread use of the standardized astrodynamics algorithms within the DOD community, there are few interoperability issues. AFSPC presented some accuracy results that showed that when evaluating the performance of an algorithm against requirements, one must consider the tracking data available as well as the algorithm itself. A specific example was the significant improvement seen from 2000 to 2004 in geosynchronous and highly elliptical orbit fit accuracy without changing the standard precision astrodynamics algorithm used for orbit determination and propagation. A six-fold improvement in median SP orbital accuracy at epoch time was achieved by improving Ground-based Electro-Optical Deep-Space Surveillance (GEODSS) telescope sensor performance to achieve better metric quality and an increased number of tracks per night. Another example of data-induced accuracy variation can be seen in the results obtained for SP orbit predictions for the Topex/Poseidon satellite in a 1340-km circular orbit. The accuracy was improved by a factor of three by increasing the number of tracks from the Space Surveillance Network radars; however, the biggest improvement 100 90 80 70 Position RMS (meters) Moderate SSN Data 60 Heavy SSN Data 50 Precision SLR Data 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Time since Epoch (hours) FIGURE 1.5 Topex/Poseidon Astrodynamics Support Workstation special perturbations prediction errors. The observed posi - tion error relative to an external, high-precision reference orbit is shown for a 12-hour prediction. Note that increasing the amount of SSN radar tracking passes improves the prediction quality, but using the much more accurate and complete orbit coverage of the laser tracking data results in the best prediction 1-5 lowest of the three lines that stays under 10 meters for the Figure (the 12-hour prediction). Changing the quality and orbit coverage of the data yielded an almost 10-fold improvement in prediction accuracy without changing the astrodynamics modeling. SOURCE: Denise Kaya, A9AC, Air Force Space Command, presenta- tion to the Committee for the Assessment of the U.S. Air Force’s Astrodyamic Standards on October 11, 2011.

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16 CONTINUING KEPLER’S QUEST—ASSESSING AIR FORCE SPACE COMMAND’S ASTRODYNAMICS STANDARDS FIGURE 1.6A European Space Agency (ESA) and Joint Space Operations Center (JSpOC) fit comparison. This plot shows the difference between ESA and JSpOC orbits staying within 50 meters over a 72-hour fitting period. ESA used onboard Global Positioning System (GPS) data while JSpOC used Space Surveillance Network (SSN) radar data. SOURCE: Denise Kaya, A9AC, Air Force Space Command, presentation to the Committee for the Assessment of the U.S. Air Force’s Astrodyamic Figure 1-6a Standards on October 11, 2011. Bitmapped (almost a factor of 10) came when the JSpOC astrodynamics support workstation SP orbit determination algorithm was given access to the precision laser tracking data available for this satellite. Figure 1.5 illustrates the results. All of these examples are for satellites that experience little or no atmospheric drag. In the case of high-drag satel - lites, the results are not as good because of the uncertainties in modeling the neutral atmospheric density and the frontal area of the satellite. Finding: For satellites not experiencing significant atmospheric drag, the current orbital coverage and quality of the Space Surveillance Network sensor data are more of a limitation on precision orbit accuracy than the standardized astrodynamics SP algorithms. Civilian Government Users Both NASA Houston human spaceflight and NASA Goddard robotics made presentations on their use of JSpOC conjunction products. Both NASA groups have a long history of working with the JSpOC and were gener- ally satisfied with the results obtained using AFSPC standardized astrodynamics algorithms. They did ask for more documentation and better covariance information. The NASA Goddard representatives asserted that the “quality of numerical results [is] satisfactory for our mission and analytical needs, the only exception being covariance.” 5 The performance of the current astrodynamics orbit determination and orbit propagation algorithms has been compared by AFSPC to results achieved by various outside agencies, including the European Space Agency (ESA). One such comparison was for the ESA controlled Rapid Eye 2 spacecraft (catalog number 33312). Rapid Eye 2 is in a 97.9 degree inclination, 620 × 640 km orbit. AFSPC compared both the precision SP orbit fit and predic - tion results from the JSpOC using SSN radars with that from ESA fitting and predicting the orbit with onboard 5Navigation and Mission Design Branch, NASA Goddard Space Flight Center, “The General Mission Analysis Tool,” presentation to the Committee for the Assessment of the U.S. Air Force’s Astrodynamic Standards on February 7, 2012.

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17 MEETING THE MISSION FIGURE 1.6B ESA and JSpOC prediction comparison. This plot shows the difference between ESA and JSpOC orbits staying within 300 meters over a 7-day prediction period. ESA used onboard GPS data while JSpOC used SSN radar data to fit the orbit prior to the prediction. SOURCE: Denise Kaya, A9AC, 1-6b Figure Air Force Space Command, presentation to the Committee for the Assessment of the U.S. Air Force’s Astrodyamic Standards on October 11, 2011. Bitmapped GPS-based tracking data. The two orbits were within about 50 meters of each other over the fit interval, and the 7-day predictions were within 300 meters (with the JSpOC prediction being more accurate, probably because of the more complex atmosphere density modeling in HASDM, although one test is not enough to assess overall performance differences). Figures 1.6A and 1.6B illustrate these results. Commercial Users The committee received presentations from the Iridium and Intelsat operators. The Iridium community seemed satisfied with the data they are receiving from JSpOC and looked forward to more detailed interaction. Since the collision of Iridium 33 with Cosmos 2251 in February 2009, the Iridium program has developed a more robust interface with the JSpOC. The Iridium representatives asserted that: The Iridium Space Network Operations Center receives regular conjunction updates from the JSpOC and when neces- sary, we maneuver our satellites based on this information to avoid potential collisions. We believe this is a substantial first step in better information sharing between the government and industry and support even more robust interaction which can provide better and more efficient constellation operation. We continue to work with the government on an ongoing basis across a variety of fronts and forums, including ongoing efforts to exchange additional data that will help us to make even better-informed decisions in the future.6 The Intelsat representatives expressed some frustration with the lack of a close relationship with the JSpOC such as that of Iridium. They also cited some examples of interoperability problems involving differences with JSpOC on the computed position of an Intelsat object. Geostationary orbit communication satellites such as Intelsat 6 Joe Pizzicaroli, Iridium Communications, Inc., “Panel Discussion,” presentation to the Committee for the Assessment of the U.S. Air Force’s Astrodynamic Standards on February 7, 2012.

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18 CONTINUING KEPLER’S QUEST—ASSESSING AIR FORCE SPACE COMMAND’S ASTRODYNAMICS STANDARDS that maneuver frequently have a special problem in that their future position for conjunction avoidance analysis must include the effects of a planned maneuver. Unfortunately JSpOC currently can include this effect only by manually loading a predicted ephemeris file sent by a satellite owner who is aware of the planned delta-v. All this requires close interagency cooperation. There seems to be a pattern that organizations with a close relationship with the JSpOC for conjunction assessment are satisfied whereas those without such a relationship are not. Finding: The community that is interested in conjunction assessments needs further improvements in the quality of the characterization of uncertainty (covariance) realism in the predicted ephemerides. Anticipated Future Needs The space catalog has been growing dramatically in recent years with the breakup of the Fengyun 1C satel - lite from the Chinese anti-satellite test and the collision of the Iridium and Cosmos satellites. These events have placed a greater emphasis on predicting satellite conjunctions and providing warning to satellite owner/operators of potential collisions. Conjunction assessments and launch screenings have greatly increased the workload at the JSpOC. The space catalog lost list (objects whose element set epoch age exceeds 30 days) is currently at an all- time high. The cataloging of satellite breakup pieces and the recovering of lost satellites from uncorrelated tracks are manually intensive and require the talents of subject-matter experts who are often in short supply. The space catalog will grow even more dramatically with additions to the Space Surveillance Network of new and future sensors such as the space fence radar and the Space Surveillance Telescope, which because of their increased sensitivity will discover small debris objects in space that have never been tracked before. In addition, because of changes in the U.S. National Space Policy there is an increased emphasis on sharing of space situational awareness data with mission partners and commercial and foreign entities. New standardized astrodynamics algorithms will be required for the exchange of space situational awareness data. Besides the tra - ditional Space Surveillance Network sensors, nontraditional sensors (e.g., Missile Defense Agency sensors) may become additional contributors to the space situational awareness mission. Each of these changes will make the space situational awareness mission more complex and will require improved algorithms to fuse and exploit the information generated by this increase in diverse data types. Subsequent chapters of this report will describe some of the possibilities for modernization to deal with these changes.