AGI An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs David A Vallado Analytical Graphics Inc. Center for Space Standards and Innovation Paper AAS , Presented at the AAS/AIAA Space Flight Mechanics Conference, Copper Mountain Colorado, January 23-27, 2005

Pg 2 of 30 AGI Overview Introduction Standards Objective Potential Error Sources Initial State Vectors Programs –Input Data Sources –Using the Input Data Interpolation, timing, etc State vector format –Study Process Build up the force models

Pg 3 of 30 AGI Overview (continued) Results –Force Model Sensitivity Analysis Individual Force Model Contributions Gravity Atmospheric Drag Solar Radiation Pressure –Ephemeris Comparison Results Gravity Third Body Solar Radiation Pressure Atmospheric Drag Combined Forces –POE Comparison Results Community Standard Ephemeris Baseline Conclusions

Pg 4 of 30 AGI Introduction Numerically derived state vectors –Not new to astrodynamics –Navy 1 st full numerical catalog in 1997 Answer fundamental question –What observations and processing are needed to achieve a certain level of accuracy on a particular satellite, now, and at a future time? –Requires Orbit Determination Propagation* Standards Other

Pg 5 of 30 AGI Objectives Demonstrate the inconsistencies of AFSPC Instructions – and Standards are useful when properly applied –Computer code is not a standard –Mathematical theory is a standard Historically –SGP4 vs. PPT –Mathematical theory differences Bad example of a need for standards  –WGS-72 vs WGS-84 Good examples of a need for standards –1950 Nutation theory and 1980 IAU nutation theory Example of need for a recommended practice –1980 IAU Nutation sum terms from vs. 106 to 1

Pg 6 of 30 AGI Potential Error Sources Inaccurate models Measurement errors Truncation error Round-off Mathematical simplifications Human error Tracking all input parameters* Treatment of input data* * indicates important outcome from the paper

Pg 7 of 30 AGI Tracking All Input Data Critical to provide adequate information –Proposed format at end of paper and on web –Detail treatment of Satellite positional information Forces included –Sizes, coefficients, etc. Satellite characteristics –BC, mass, area, attitude, etc. Source and use of data –Solar weather data, EOP, other Integrator information Covariance information Current formats simply not adequate

Pg 8 of 30 AGI Programs Legacy Programs –GEODYN –GTDS –Raytheon TRACE –Special-K –STK/HPOP

Pg 9 of 30 AGI Input Data Need correct constants and data Coordinate system –Mean equator Mean equinox of J2000 Integrator Gravitational Model / Constants –EGM-96 Rotational vel rad/min –EGM-96 Radius earth km –EGM-96 Gravitational param km3/s2 EOP Timing coefficients from actual (EOPC04 or USNO) Solar flux from actual (NGDC) measurements

Pg 10 of 30 AGI Test Conditions Best approach built up force models incrementally –Two-body Numerical integrators, Coordinate and Time Systems –Gravity Field Checks mu, re, gravitational coefficients –Two-body plus Atmospheric Drag Atmospheric density model, solar weather data handling –Two-Body plus Third-body JPL DE/LE file incorporation, constants –Two-body plus Solar Radiation Pressure Earth shadow model, solar constants

Pg 11 of 30 AGI Sensitivity Results Force model contributions –Determine which forces contribute the largest effects 12x12 gravity field is the baseline –Note Gravity and Drag are largest contributors 3 rd body ~km effect for higher altitudes –Point to take away: Trying to get the last cm from solid earth tides no good unless all other forces are at least that precise

Pg 12 of 30 AGI Force Model Contributions

Pg 13 of 30 AGI Sensitivity Results Gravitational modeling –Typically square gravity field truncations Appears the zonals contribute more –Point to take away: Use “complete” field Any truncations should include additional, if not all, zonals

Pg 14 of 30 AGI Gravitational Modeling Satellite JERS (21867) –Note the dynamic variability over time

Pg 15 of 30 AGI Sensitivity Results Atmospheric Drag –Large variations –Several sources Using predicted values of F 10.7, k p, a p for real-time operations Not using the actual measurement time for the values (particularly F 10.7 at 2000 UTC) Using step functions for the atmospheric parameters vs interpolation Using the last 81-day average F 10.7 vs. the central 81-day average Using undocumented differences from the original atmospheric model definition Not accounting for [possibly] known dynamic effects – changing attitude, molecular interaction with the satellite materials, etc. Inherent limitations of the atmospheric models Use of differing interpolation techniques for the atmospheric parameters Using approximations for the satellite altitude, solar position, etc. Using a p or k p and converting between these values Use of F 10.7 vs E 10.7 in the atmospheric models (not well characterized yet)

Pg 16 of 30 AGI Sensitivity Results Plot –Note Dap almost as large as a p values –Note Last - Ctrd 81 day, SFU Factors examined –Daily –3-Hourly –3-Hourly interp –Last 81 day –Last 81 day, 2000 –F 10.7 Day Con –F 10.7 Avg Con –F 10.7 All Con –All Con

Pg 17 of 30 AGI Atmospheric Drag Differing models (left) –Note grouping of similar models –“transient” effects only for first day or so Options for processing data (right) –Note km effect

Pg 18 of 30 AGI Sensitivity Results Solar Radiation Pressure –Several variations shown –Notice maximum is only about 100m –Point to take away Relatively small effect Some variations

Pg 19 of 30 AGI Ephemeris Comparisons Gravitational –GTDS (left) and Ray TRACE (right) examples –Generally cm and mm-level comparisons –Regularized time not explored

Pg 20 of 30 AGI Ephemeris Comparisons Third-Body –GTDS (left) and Ray TRACE (right) examples –Generally a few cm

Pg 21 of 30 AGI Ephemeris Comparisons Solar Radiation Pressure –GTDS (left) and Ray TRACE (right) examples –Generally a few m

Pg 22 of 30 AGI Ephemeris Comparisons Atmospheric Drag –GTDS (left) and Ray TRACE (right) examples –A few km to many km Recall sensitivity results which were even higher

Pg 23 of 30 AGI Ephemeris Comparisons Combined forces –Several runs made without detailed build-up of forces –Included drag

Pg 24 of 30 AGI Ephemeris Comparisons GEODYN tests –Starlette (7646) –Note plot on right Difference of 2 GEODYN runs with different models Nearly identical to sensitivity tests run for 7646

Pg 25 of 30 AGI Ephemeris Comparisons GEODYN (cont) –TDRS comparison (4 days and 1 month)

Pg 26 of 30 AGI Ephemeris Comparisons Special-K Comparisons

Pg 27 of 30 AGI POE Ephemeris Comparisons POE Comparisons –Initial state taken and propagated –No coordination, estimate of drag and solar radiation pressure –Perturbed initial state results

Pg 28 of 30 AGI Community Ephemeris Baseline Need to provide standard ephemeris comparison data –Provide community baseline on the web –Interactive forum for cooperative comparisons Initial release designed to stimulate community involvement –NOT intended to force compliance –CSSI clearinghouse for this innovation Data hosted under CenterForSpace website – Scenarios available for use in STK –CSSI available for consultation, analysis, inputs, questions

Pg 29 of 30 AGI Conclusions Numerous conclusions in topical areas –Standards, Code, Instructions Recommended Practice needed –Data Formats Proposed format of additional information –Force model contributions Summary for a particular satellite –Identify which are important Results for comparisons –Conservative, cm-level –Non Conservative, km-level »Tremendous variability just with input data –Sensitivity studies Tremendous variation –POE “analyses” No propagation perfectly matches “truth”

Pg 30 of 30 AGI Conclusions Bottom line –With variability on treatment of input data, What does exact agreement mean? –Nothing –Right and wrong are indistinguishable! –Identical code is not needed to align programs Attention to detail is Adequate data formats is Standardized approach for treating input data is Cooperation is –Organizations involved in this study were tremendously helpful and cordial