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.
As scientific knowledge of orbiting objects has progressed, simplicity and order have thus given way to complexity and chaos. 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. As a unified Combatant Command, the U. The AOC provides ready space forces and capabilities to the JSpOC in order to execute theater and global operations with a priority on warfighter support.
These command relationships 2 are shown in Figure 1. To protect vital U. These standardized astrodynamics algorithms are used to measure and describe satellite motion. The JSpOC currently uses the algorithms found in AFSPC standardized astrodynamics algorithms for a significant portion of its daily space operations, in which it must detect and track space events and maintain a catalog of more than 20, space objects.
A typical day at the JSpOC using the standardized astrodynamics algorithms includes:. On February 10, , the Iridium 33 satellite maneuvered into the path of the inactive Russian communications satellite Cosmos , resulting in a collision that destroyed both satellites and left a debris cloud in a densely populated orbit regime.
After this event the JSpOC began screening about 1, active satellites for conjunctions with other satellites and debris, including commercial and foreign satellites. 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. The U. Navy developed, deployed in , and funded until 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 receivers 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. The concept of standardized astrodynamics algorithms within the DOD was developed in the early s by.
By that time, various branches of the U. Each satellite system developed its own control station and often its own control and processing software quite independent of Space Command or its predecessors. 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. Either NASA or the universities themselves developed the necessary control and orbit determination software, again tuned to the specific application and type of data.
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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. 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 s, a member of the user community wanted to update to the newer and improved WGS Earth gravity model. The user reverted to using the WGS gravity model and was able to successfully meet the requirements for accuracy. The y-axis depicts the root-mean-square position error. The red line at 1, 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 meters or less show the result using the compatible WGS gravity model, and the taller bars all greater than the requirement show the results of using an incompatible WGS gravity model in the prediction interval. Finding: AFSPC has recognized the importance of maintaining interoperability to support the community of operational users. Because of the requirements of the NRO and NASA for a more complete 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.
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. They were developed as closed systems on proprietary hardware with customized software and operating systems.
The systems all took many years to implement, and frequently new systems were implemented over time while older systems were phased out. Today, leading-edge organizations adopt a service-oriented architecture SOA approach for major computing 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. Enough information regarding current systems was available and reviewed without evaluating ITAR-restricted algorithms. The orbit propagator uses a special perturbations numerical integration technique with high-order geopotential modeling, 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 astrodynamics 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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BOX 1. SP Special Perturbations — An algorithm that uses numerical integration to generate ephemerides for satellites in Earth-centered orbits. LAMOD— Computes sensor ground-based or space-based viewing opportunities so-called look angles for Earth-centered satellites. 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.
These differential corrections are computed in a sequential mode, which uses one or more observations or tracks while retrieving former covariance information from a prior differential correction. The GP method uses much less computer time than the SP method, but provides less accurate results because of its truncated modeling. High Frontier: The U. An Astronaut's Guide to Life on Earth. Chris Hadfield. Strike Warfare.
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