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Orbit Lifetime Prediction

Orbit Lifetime Prediction. Jim Woodburn. Orbit Lifetime Prediction Methods. Interactively determine the “right answer” Employ the services of a mystic Astrology Try to compute it…. History. Research motivated by questions from STK users

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Orbit Lifetime Prediction

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  1. Orbit Lifetime Prediction Jim Woodburn

  2. Orbit Lifetime Prediction Methods • Interactively determine the “right answer” • Employ the services of a mystic • Astrology • Try to compute it…

  3. History • Research motivated by questions from STK users • Extension of work presented at the AAS/AIAA Astrodynamics Specialists Conference in Lake Tahoe, August 2005 • Coauthor, AGI Application Support Engineer, Shannon Lynch • Community benefit • Extensions to STK/Lifetime capabilities • Public presentation of results

  4. Agenda • Orbit lifetime drivers • Sources of uncertainty • Solar weather characterization • Atmospheric density model selection • Numerical methods • Wrap up • What’s next

  5. What affects orbit lifetime? • Orbit lifetime mainly driven by atmospheric drag • Removes energy from the orbit • Lowers the altitude of the orbit more drag • Atmospheric drag depends on • Satellite area to mass ratio • Satellite velocity relative to the atmosphere • Atmospheric density Atmospheric Density

  6. What affects atmospheric density? • Solar weather • Geomagnetic activity • Selection of density model • Satellite altitude • Relative position of the Sun • Time of the year

  7. Solar weather Cycle amplitude Daily variability Cycle timing Storms Geomagnetic activity A priori density models Initial conditions Projected area Numerical Methods Uncertainty UncertaintyUncertainty… We need to predict the future, but… BLUE = Addressed in this study

  8. Solar Weather Characterization

  9. How well can we predict F10.7? from Schatten K.H., Solar Activity and the Solar Cycle

  10. Prediction appears difficult • Uncertainty in the mean behavior • Random looking variations on a daily basis • Can we simulate it?

  11. Desire statistical similarity to historical data • Separate into a mean behavior and variation about the mean • Random deviations on amplitude of mean trajectory, assume no timing error • Superimpose daily variations • Amplitude varies through solar cycle • Time correlation varies through solar cycle • Simulate with a stochastic sequence

  12. Another look at F10.7 from Schatten K.H., Solar Activity and the Solar Cycle

  13. 2 Problems in 2 Parts • Looking deep into the future • Unknown solar cycle behavior • Unknown daily variations • Analysis for existing satellites • Average characteristics of cycle may be known • Daily variations still unknown • Look at effects separately and combined

  14. Random deviation of mean • Schatten predicts • Nominal • Plus/minus 2 sigma • Early/nominal/late timing • Perform Monte-Carlo analyses • Draw a random sigma level • Generate associated solar flux trajectory • Compute an orbit lifetime prediction

  15. Lifetime distribution – Variations of Mean F10.7 Solar Min Solar Max Jacchia 1970 Density Model Alt0 = 375 Km, A/M = 0.02, Cd = 2.0

  16. Lifetime distribution – Variations of Mean F10.7 Solar Min Solar Max Mean Mean -2 Sigma +2 Sigma +2 Sigma -2 Sigma Jacchia 1970 Density Model Alt0 = 450 Km, A/M = 0.02, Cd = 2.0

  17. Characterizing daily variations • Generated functional fits to last 3 solar cycles • Emulate an accurate mean prediction • Schatten predictions had significant timing errors • Divided each solar cycle into 8 segments • Constructed sample variances and time correlations • Fit data using simple functional forms • Goal: Produce simple functions to drive our stochastic sequence

  18. Solar Cycle 21

  19. Flux history revisited

  20. Sample Data & Functional Forms Time Correlation Standard Deviation

  21. Simulated solar flux

  22. Daily variation simulations • Daily variations only • Select a single mean solar flux trajectory • Monte-Carlo analyses of daily variations • Appropriate for near term studies • Daily and mean variations • Monte-Carlo analyses vary both the mean trajectory and daily variations about the mean • Appropriate for studies in future solar cycles

  23. Effects of Daily Variations on Orbit Lifetime – 375 Km Alt Solar Max Solar Min Daily Variation Only Daily Variation Only Mean Variation Only Mean Variation Only

  24. Mean and daily variations – 375 Km Vary Only Mean Flux Mean = 181.798 StDev = 22.11 Solar Min Solar Max Vary Only Mean Flux Mean = 34.476 StDev = 3.115

  25. Effects of Daily Variations on Orbit Lifetime – 450 Km Alt Solar Max Solar Min Daily Variation Only Daily Variation Only Mean Variation Only Mean Variation Only

  26. Mean and daily variations – 450 Km Vary Only Mean Flux Mean = 1752.6 StDev = 626.8 Solar Min Solar Max Vary Only Mean Flux Mean = 263.8 StDev = 43.5

  27. How do I do that in STK? • New scenario level connect command to generate randomly deviated solar flux histories from Schatten predict files. Written out as .fxm files. • STK/Lifetime has been enhanced to accept solar flux input from .fxm files • Supported through STK/Connect interface • STK/Connect based scripts used to perform Monte-Carlo analyses

  28. Atmospheric Density Model Selection

  29. Models Considered Jacchia 1970 Jacchia 1971 MSIS 1986 MSISE 1990 NRL MSISE 2000 Harris Priester F10.7 uncertainty is larger effect mean < 0.5  at solar max mean < 1.0  at solar min MSIS models consistent Lower density predictions at solar min than Jacchia models Longer solar min lifetimes with larger standard deviations Harris Priester did not perform well Which density model should I use??? Survey says…

  30. Different density models – same results – 375 Km MSIS 86 Jacchia 70 Solar max Jacchia 71 MSISE 90

  31. Different density models – same results – 450 km MSIS 86 Jacchia 70 Solar max Solar max Jacchia 71 MSISE 90 Solar max Solar max

  32. How do I do that in STK? • STK/Lifetime has been enhanced to allow for selection of various atmospheric density models • Supported through STK/Connect interface • STK/Connect based scripts used to perform Monte-Carlo analyses

  33. Selection of a Numerical Method

  34. Numerical method selection • How much time do you have? • How long do you expect your orbit to last? • What method do you trust?

  35. Numerical methods • Simplified model (Lifetime) • Semi-analytic model • Earth gravity through J5 • Solar and lunar 3rd body • Solar radiation pressure • Atmospheric drag via Gaussian quadrature • Numerical integration • Complete force model • Gauss Jackson 12th order integrator

  36. Design of comparison experiment • Generate a “Truth” solar flux trajectory • Generate “Truth” ephemeris using “Truth” solar flux • Perform Monte-Carlo analyses at several times between original initial conditions and predicted end of life • Each run is seeded from “Truth” solar and orbit trajectories • Compare results

  37. Comparison methodology Truth Ephemeris Solar Flux With Daily Random Variations Orbit Lifetime Estimate Initialization from truth Truth Solar Flux Trajectory Time

  38. Comparison of approaches Num Integ - Solar Max Lifetime - Solar Max 4 weeks out Lifetime - Solar Max 3 weeks out Lifetime - Solar Max

  39. Comparison of approaches Num Integ - Solar Min Lifetime - Solar Min 6 months out Lifetime – Solar Min 4 months out Lifetime – Solar Min

  40. Method comparison findings • Additional study required for useful conclusions • Results of numerical integration seem to follow expected behavior • Mean errors lie well with 1 sigma • Standard deviation decreases as end of life approaches • Lifetime algorithm results varied • Look good for solar max test case • Errors are larger for solar min (consistently low)

  41. How do I do that in STK? • STK/Connect based scripts used to perform Monte-Carlo analyses • Existing HPOP and Lifetime commands • New Lifetime commands

  42. STK/Lifetime enhancements • Random solar flux history generation (Scenario) • Atmospheric density model selection • Duration stopping condition • Reportable data after error conditions • Enhanced documentation

  43. Conclusions… • Monte-Carlo analyses are an effective tool in the prediction of orbit lifetime • There is a lot of uncertainty • Solar flux daily variations important contributor in spread of orbit lifetime distributions • Who knows what’s going to happen tomorrow • Atmospheric density model selection not primary importance • Statistically similar answers, all fairly uncertain

  44. Disclaimer All analyses in this study were performed on orbits with short lifetime Actual results may vary Conclusions • Similar accuracy was achieved using simplified lifetime prediction algorithms and numerical integration during solar max test case • Additional investigation is required for solar min test case, uncertainty still exists This much is certain

  45. Solar weather Cycle amplitude Daily variability Cycle timing Storms Geomagnetic activity A priori density models Initial conditions Projected area Numerical methods Real data comparisons What’s Next BLUE = Addressed in this study RED = To be addressed in next study

  46. Ultimate Recommendation Compare results from 2 independent approaches • Monte-Carlo • Madame Zora

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