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Feasibility study of using a two-plate model to approximate the TDRSS solar pressure effects

An investigation was performed to determine the feasibility of using a two plate model to approximate the Tracking and Data Relay Satellite (TDRS) in orbit propagation, taking into account the effects of solar radiation pressure. The two plate model comprises one plate which always points to the Earth, and the other which is hinged to an axis normal to the orbital plane and is always rotated so that its normal makes a minimum angle with the direction of the sun. The results indicate that it is sufficient to take three parameters, the areas of the two plates and the reflectivity of the Earth pointing plate, to achieve an accuracy of one meter during a 24 hour orbit propagation.

Chan, F. K.

Geosynchronous Environment for ORDEM2008

The new version of the NASA Orbital Debris Engineering Model (ORDEM2008) requires accurate populations as input template files to be used in the calculation of orbital debris fluxes on chosen spacecraft or within telescope/radar fields-of-view. Populations in ORDEM2008 are derived from a consortium of data and modeling. Geosynchronous (GEO) satellites and debris form a distinct ORDEM2008 population that is applied to the distinct analysis of GEO fluxes. Low Earth orbit (LEO) populations are derived by combining modeling results with ground-based data, primarily from radar systems and in-situ data. In contrast, the GEO region has not been as well observed. The distance between orbiting objects and ground-based instruments precludes the wide usage of radar as a means of observation. Instead, optical instruments dominate in the study of GEO. Of these, the NASA sponsored Michigan Orbital Debris Survey Telescope (MODEST) has provided 4 years of surveys of the region detecting cataloged objects (correlated targets) and non-cataloged objects (uncorrelated targets) to an estimated minimum size of 30 cm. This paper describes the methods of combining NASA launch database and satellite breakup and orbital propagation modeling with MODEST 2004-to-2006 uncorrelated target data to attain a GEO environment to 10 cm. Assuming that MODEST uncorrelated targets are breakup debris allows for the extension of the debris survey data to smaller sizes with the NASA Standard Breakup model. Each orbit within the total resulting GEO population is marked by a random argument of perigee and nearly constant mean motion, eccentricity, inclination, and node over the nearly 3 years of observation. Lack of published references of past breakups in GEO is mitigated by the orbital propagation of MODEST extended data to 1995 (the beginning epoch of ORDEM2008).

Krisko, Paula H.

The Geosynchrous Environment for ORDEM2010

The new version of the NASA Orbital Debris Engineering Model (ORDEM2010) requires accurate populations as input files to be used in the calculation of orbital debris fluxes on chosen spacecraft or within telescope/radar fields-of-view. Populations in ORDEM2010 are derived from an amalgam of data and modeling. Geosynchronous orbit (GEO) satellites and debris form a distinct ORDEM2010 population that is applied to the distinct analysis of GEO fluxes. Low Earth orbit (LEO) populations are derived by combining modeling results with ground-based data, primarily from radar systems, and in-situ data. In contrast, the GEO region has not been as well observed. The distance between orbiting objects and ground-based instruments precludes the wide usage of radar as a means of observation. Instead, optical instruments dominate in the study of GEO. Of these, the NASA sponsored Michigan Orbital Debris Survey Telescope (MODEST) has provided 3 years of surveys of the region detecting cataloged objects (correlated targets) and non-cataloged objects (uncorrelated targets) to an estimated minimum size of 30 cm. This paper describes the methods of combining NASA launch database and satellite breakup and orbital propagation modeling with MODEST 2004-to-2006 uncorrelated target data to attain a GEO environment to 10 cm. Assuming that MODEST uncorrelated targets are breakup debris allows for the extension of the debris survey data to smaller sizes using the NASA Standard Breakup Model. Each orbit within the total resulting GEO population is marked by a random argument of perigee and nearly constant mean motion, eccentricity, inclination, and right ascension of ascending node (RAAN) over the nearly 3 years of observation. Lack of published references of past breakups in GEO is mitigated by the orbital propagation of MODEST extended data to 1995 (the beginning epoch of ORDEM2010).

Krisko, Paula H.

Investigation into Scalable and Detection-Enhanced Satellite Conjunction Assessment

Imaging opportunities (viewable conjunctions) of Resident Space Objects (RSOs) by satellites are not continuously discovered. We propose to continuously produce and report viewable conjunctions among objects in orbit. Viewable conjunctions are events in space and time when a satellite may favorably view a Resident Space Object (RSO). Favorability is defined by a set of constraints, e.g., solar illumination, distance between observer and target, orbital location for viewable event. Computing viewable conjunctions requires calculation of orbital propagation while considering constraints based on the state vectors of position, velocity, with covariance for both satellite and RSO. We propose two parallel lanes of effort: acceleration and research. The objective of acceleration is to avoid missed opportunities and reduce latency for satellite maneuver requests through continuous prediction and reporting of viewable conjunctions. The effort will begin by deploying currently available software on dedicated systems and continue with optimizing the code for high performance computing hardware. The research lane aims to expand RSO inspection and modeling capabilities. Among our current research ideas are spectral characterization of RSO materials and planning multiple observations to recover RSO 3D form. Computing resources at Oak Ridge National Laboratory (ORNL) are available for the acceleration work. Laika, Maxar conjunction prediction dashboard software, and Bluesim, Maxar orbital propagation software, are expected to be the first software in the acceleration lane. Laike and Bluesim are to be provided by the sponsor, and output will be made accessible through its dashboard. Deliverables will follow a gated schedule to the sponsor. ORNL will provide progressively more robust viewable conjunction assessments from both modelled and actual ephemerides.

97 MATHEMATICS AND COMPUTING

Algorithms for Autonomous GPS Orbit Determination and Formation Flying: Investigation of Initialization Approaches and Orbit Determination for HEO

This report summarizes the efforts to date in processing GPS measurements in High Earth Orbit (HEO) applications by the Colorado Center for Astrodynamics Research (CCAR). Two specific projects were conducted; initialization of the orbit propagation software, GEODE, using nominal orbital elements for the IMEX orbit, and processing of actual and simulated GPS data from the AMSAT satellite using a Doppler-only batch filter. CCAR has investigated a number of approaches for initialization of the GEODE orbit estimator with little a priori information. This document describes a batch solution approach that uses pseudorange or Doppler measurements collected over an orbital arc to compute an epoch state estimate. The algorithm is based on limited orbital element knowledge from which a coarse estimate of satellite position and velocity can be determined and used to initialize GEODE. This algorithm assumes knowledge of nominal orbital elements, (a, e, i, omega, omega) and uses a search on time of perigee passage (tau(sub p)) to estimate the host satellite position within the orbit and the approximate receiver clock bias. Results of the method are shown for a simulation including large orbital uncertainties and measurement errors. In addition, CCAR has attempted to process GPS data from the AMSAT satellite to obtain an initial estimation of the orbit. Limited GPS data have been received to date, with few satellites tracked and no computed point solutions. Unknown variables in the received data have made computations of a precise orbit using the recovered pseudorange difficult. This document describes the Doppler-only batch approach used to compute the AMSAT orbit. Both actual flight data from AMSAT, and simulated data generated using the Satellite Tool Kit and Goddard Space Flight Center's Flight Simulator, were processed. Results for each case and conclusion are presented.

Axelrad, Penina

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

Improved Chebyshev series ephemeris generation capability of GTDS

An improved implementation of the Chebyshev ephemeris generation capability in the operational version of the Goddard Trajectory Determination System (GTDS) is described. Preliminary results of an evaluation of this orbit propagation method for three satellites of widely different orbit eccentricities are also discussed in terms of accuracy and computing efficiency with respect to the Cowell integration method. An empirical formula is deduced for determining an optimal fitting span which would give reasonable accuracy in the ephemeris with a reasonable consumption of computing resources.

Liu, S. Y.

Lunar Orbit Stability for Small Satellite Mission Design

The irregular nature of the lunar gravity field will severely affect the orbit lifetime and behavior of future lunar small satellite missions. These spacecraft need stable orbits that do not require large deltaV budgets for station-keeping maneuvers. The initial classical elements of any lunar orbit are critical to address its stability and to comply with mission requirements. This publication identifies stable regions according to different initial conditions at the time of lunar orbit insertion (LOI). High fidelity numerical simulations with two different gravity models were performed. We focus in low altitude orbits where the dominant force in orbit propagation is the existence of unevenly distributed lunar mass concentrations. These orbits follow a periodic oscillation in some of the classical elements that is particularly useful for mission design. A set of orbital maintenance strategies for various mission concepts is presented.

Lunar Science

Effect of ephemeris errors on the accuracy of the computation of the tangent point altitude of a solar scanning ray as measured by the SAGE 1 and 2 instruments

An analysis was made of the error in the minimum altitude of a geometric ray from an orbiting spacecraft to the Sun. The sunrise and sunset errors are highly correlated and are opposite in sign. With the ephemeris generated for the SAGE 1 instrument data reduction, these errors can be as large as 200 to 350 meters (1 sigma) after 7 days of orbit propagation. The bulk of this error results from errors in the position of the orbiting spacecraft rather than errors in computing the position of the Sun. These errors, in turn, result from the discontinuities in the ephemeris tapes resulting from the orbital determination process. Data taken from the end of the definitive ephemeris tape are used to generate the predict data for the time interval covered by the next arc of the orbit determination process. The predicted data are then updated by using the tracking data. The growth of these errors is very nearly linear, with a slight nonlinearity caused by the beta angle. An approximate analytic method is given, which predicts the magnitude of the errors and their growth in time with reasonable fidelity.

Buglia, James J.

Stochastic Analysis of Orbital Lifetimes of Spacecraft

A document discusses (1) a Monte-Carlo-based methodology for probabilistic prediction and analysis of orbital lifetimes of spacecraft and (2) Orbital Lifetime Monte Carlo (OLMC)--a Fortran computer program, consisting of a previously developed long-term orbit-propagator integrated with a Monte Carlo engine. OLMC enables modeling of variances of key physical parameters that affect orbital lifetimes through the use of probability distributions. These parameters include altitude, speed, and flight-path angle at insertion into orbit; solar flux; and launch delays. The products of OLMC are predicted lifetimes (durations above specified minimum altitudes) for the number of user-specified cases. Histograms generated from such predictions can be used to determine the probabilities that spacecraft will satisfy lifetime requirements. The document discusses uncertainties that affect modeling of orbital lifetimes. Issues of repeatability, smoothness of distributions, and code run time are considered for the purpose of establishing values of code-specific parameters and number of Monte Carlo runs. Results from test cases are interpreted as demonstrating that solar-flux predictions are primary sources of variations in predicted lifetimes. Therefore, it is concluded, multiple sets of predictions should be utilized to fully characterize the lifetime range of a spacecraft.

Sasamoto, Washito

Constellation Coverage Analysis

The design of satellite constellations requires an understanding of the dynamic global coverage provided by the constellations. Even for a small constellation with a simple circular orbit propagator, the combinatorial nature of the analysis frequently renders the problem intractable. Particularly for the initial design phase where the orbital parameters are still fluid and undetermined, the coverage information is crucial to evaluate the performance of the constellation design. We have developed a fast and simple algorithm for determining the global constellation coverage dynamically using image processing techniques. This approach provides a fast, powerful and simple method for the analysis of global constellation coverage.

Martin W. Lo

GLAS Spacecraft Pointing Study

Science requirements for the GLAS mission demand that the laser altimeter be pointed to within 50 m of the location of the previous repeat ground track. The satellite will be flown in a repeat orbit of 182 days. Operationally, the required pointing information will be determined on the ground using the nominal ground track, to which pointing is desired, and the current propagated orbit of the satellite as inputs to the roll computation algorithm developed by CCAR. The roll profile will be used to generate a set of fit coefficients which can be uploaded on a daily basis and used by the on-board attitude control system. In addition, an algorithm has been developed for computation of the associated command quaternions which will be necessary when pointing at targets of opportunity. It may be desirable in the future to perform the roll calculation in an autonomous real-time mode on-board the spacecraft. GPS can provide near real-time tracking of the satellite, and the nominal ground track can be stored in the on-board computer. It will be necessary to choose the spacing of this nominal ground track to meet storage requirements in the on-board environment. Several methods for generating the roll profile from a sparse reference ground track are presented.

Born, George H.

Effects of Orbital Lifetime Reduction on the Long-Term Earth Satellite Population as Modeled by EVOLVE 4.0

The latest update of the NASA orbital debris environment model, EVOLVE 4.0, has been used to study the effect of various proposed debris mitigation measures, including the NASA 25-year guideline. EVOLVE 4.0, which includes updates of the NASA breakup, solar activity, and the orbit propagator models, a GEO analysis option, and non-fragmentation debris source models, allows for the statistical modeling and predicted growth of the particle population >1 mm in characteristic length in LEO and GEO orbits. The initial implementation of this &odel has been to study the sensitivity of the overall LEO debris environment to mitigation measures designed to limit the lifetime of intact objects in LEO orbits. The mitigation measures test matrix for this study included several commonly accepted testing schemes, i.e., the variance of the maximum LEO lifetime from 10 to 50 years, the date of the initial implementation of this policy, the shut off of all explosions at some specified date, and the inclusion of disposal orbits. All are timely studies in that all scenarios have been suggested by researchers and satellite operators as options for the removal of debris from LEO orbits.

Krisko, Paula H.

Jupiter orbiter lifetime - The hazard of Galilean satellite collision

An assessment of the long-term collision risk is made for an uncontrolled orbiting spacecraft that repeatedly enters the spatial region occupied by the satellites. Numerical data are obtained for 50-year orbit propagations which account approximately for the major perturbative effects of Jupiter oblateness, solar gravity and satellite gravity. A broad statistical viewpoint regarding the question of collision likelihood is adopted and is based on a total sample size of 480 initial orbits distributed among 4 orbit classes, 8 inclinations and 15 initial epochs. Numerical results compare favorably with an analytical prediction formula which shows that eccentric, low-inclination orbits have high collision probability.

Friedlander, A. L.

Jupiter orbiter lifetime - The hazard of Galilean satellite collision

An assessment of the long-term collision risk is made for an uncontrolled orbiting spacecraft that repeatedly enters the spatial region occupied by the satellites. Numerical data are obtained for 50-year orbit propagations which account approximately for the major perturbative effects of Jupiter oblateness, solar gravity and satellite gravity. A broad statistical viewpoint regarding the question of collision likelihood is adopted and is based on a total sample size of 480 initial orbits distributed among 4 orbit classes, 8 inclinations and 15 initial epochs. Numerical results compare favorably with an analytical prediction formula which shows that eccentric low-inclination orbits have high collision probability.

Friedlander, A. L.

Evaluation of spacecraft navigation using the Tracking and Data Relay Satellite System (TDRSS)

The navigational capabilities of the TDRSS for the operational support of user spacecraft is evaluated. A batch-weighted least-squares algorithm is used to fit tracking measurements and to generate orbit solutions for the TDRS-E spacecraft and the following user spacecraft: (1) the SMM, (2) the Landsat-5, (3) the Earth Radiation Budget Satellite (ERBS), and (4) the Solar Mesosphere Explorer (SME). TDRS-E orbit accuracy was evaluated by using the consistency of consecutive orbit solutions as a measure; user orbit accuracy was estimated by comparing orbits determined from TDRSS tracking with orbits obtained from ground tracking for the same time periods. It was found that the predicted accuracy of the TDRS-E orbit propagation was improved by as much as seven times by refining the spherical harmonic expansion model of the earth's potential field. The results obtained for SMM were fairly consistent, while those obtained for Landsat-5 were consistent to better than 80 meters. The orbits obtained using ERBS tracking were consistent to better than 60 meters and the SME orbits for two arcs with 14 and 20 passes of TDRSS tracking had a maximum position difference of 140 meters.

Samii, M. V.

Validation of A Simulation Environment for Future Space Traffic Management

This study presents initial results of a newly developed simulation environment intendedto explore and assess future Space Traffic Management (STM) scenarios. The number ofnew Resident Space Objects (RSOs) in near-Earth orbit is expected to increase significantlywith the expected future deployment of a number of large constellations. These futurescenarios involve the addition of many tens of thousands of new RSOs, making the analysisinto their impact on collision risk extend beyond what traditional data-mining of present-dayconjunction data can reliably predict. To address this, a robust simulation environment wasdeveloped that implements a full force-model for orbit propagation, and computes continuousall-on-all conjunction statistics for arbitrarily large catalog sizes and simulation timeframes.Collision avoidance and station-keeping maneuvers can be optionally implemented based onconfigurable user inputs including physical characteristics and spacecraft meta-data (e.g.,commercial/government, owner country, etc.). Constellation build-out and de-orbit scenarioswere also implemented and modeled based on real-data analysis. Validation of the simulationresults was a critical component of the simulation development, and was done using the currentcatalog with comparisons against both public and internal NASA data-sets. The comparisonsdemonstrate that, with the appropriate settings, representative levels of conjunction ratesand probabilities can be obtained, providing confidence that the simulation tool can generatemeaningful outcomes for test scenarios. As an initial demonstration of the tool’s capabilities,year-long simulations with station-keeping were conducted to examine conjunction historiesusing both the current object catalog (5800 active satellites) and a hypothetical 60,000 objectscenario involving five potential large constellations. Output metrics include the number ofconjunction events, estimates of collision consequence (fragmentation), delta-V maneuver costs,and the probability of at least one collision occurring. The results highlight the potential thatthe simulation tool has for incorporating and running performance comparisons between, e.g.,various sets of maneuver guidelines, industry norms, and definitions of risk, with the overallobjective of providing actionable data to STM policy makers. The presentation will providean overview of the simulation development and validation efforts, as well as a discussion ofobservations gathered from the initial simulations performed.

conjunction assessment

Improvements to NASA's Debris Assessment Software

NASA's Debris Assessment Software (DAS) has been substantially revised and expanded. DAS is designed to assist NASA programs in performing orbital debris assessments, as described in NASA s Guidelines and Assessment Procedures for Limiting Orbital Debris. The extensive upgrade of DAS was undertaken to reflect changes in the debris mitigation guidelines, to incorporate recommendations from DAS users, and to take advantage of recent software capabilities for greater user utility. DAS 2.0 includes an updated environment model and enhanced orbital propagators and reentry-survivability models. The ORDEM96 debris environment model has been replaced by ORDEM2000 in DAS 2.0, which is also designed to accept anticipated revisions to the environment definition. Numerous upgrades have also been applied to the assessment of human casualty potential due to reentering debris. Routines derived from the Object Reentry Survival Analysis Tool, Version 6 (ORSAT 6), determine which objects are assessed to survive reentry, and the resulting risk of human casualty is calculated directly based upon the orbital inclination and a future world population database. When evaluating reentry risks, the user may enter up to 200 unique hardware components for each launched object, in up to four nested levels. This last feature allows the software to more accurately model components that are exposed below the initial breakup altitude. The new DAS 2.0 provides an updated set of tools for users to assess their mission s compliance with the NASA Safety Standard and does so with a clear and easy-to-understand interface. The new native Microsoft Windows graphical user interface (GUI) is a vast improvement over the previous DOS-based interface. In the new version, functions are more-clearly laid out, and the GUI includes the standard Windows-style Help functions. The underlying routines within the DAS code are also improved.

Opiela, J.