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Pg 1 of xx AGI www.agiuc.com Orbit Lifetime Prediction Jim Woodburn.

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Presentation on theme: "Pg 1 of xx AGI www.agiuc.com Orbit Lifetime Prediction Jim Woodburn."— Presentation transcript:

1 Pg 1 of xx AGI www.agiuc.com Orbit Lifetime Prediction Jim Woodburn

2 Pg 2 of 46 AGI www.agiuc.com Orbit Lifetime Prediction Methods Interactively determine the “right answer” Employ the services of a mystic Astrology Try to compute it…

3 Pg 3 of 46 AGI www.agiuc.com 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 Pg 4 of 46 AGI www.agiuc.com Agenda Orbit lifetime drivers Sources of uncertainty Solar weather characterization Atmospheric density model selection Numerical methods Wrap up What’s next

5 Pg 5 of 46 AGI www.agiuc.com 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 Pg 6 of 46 AGI www.agiuc.com What affects atmospheric density? Solar weather Geomagnetic activity Selection of density model Satellite altitude Relative position of the Sun Time of the year

7 Pg 7 of 46 AGI www.agiuc.com Uncertainty Uncertainty Uncertainty … Solar weather –Cycle amplitude –Daily variability –Cycle timing –Storms Geomagnetic activity A priori density models Initial conditions Projected area Numerical Methods BLUE = Addressed in this study We need to predict the future, but…

8 Pg 8 of 46 AGI www.agiuc.com Solar Weather Characterization

9 Pg 9 of 46 AGI www.agiuc.com How well can we predict F10.7? from Schatten K.H., Solar Activity and the Solar Cycle

10 Pg 10 of 46 AGI www.agiuc.com Prediction appears difficult Uncertainty in the mean behavior Random looking variations on a daily basis Can we simulate it?

11 Pg 11 of 46 AGI www.agiuc.com 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 Pg 12 of 46 AGI www.agiuc.com Another look at F10.7 from Schatten K.H., Solar Activity and the Solar Cycle

13 Pg 13 of 46 AGI www.agiuc.com 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 Pg 14 of 46 AGI www.agiuc.com 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 Pg 15 of 46 AGI www.agiuc.com Lifetime distribution – Variations of Mean F10.7 Solar Max Solar Min Jacchia 1970 Density Model Alt 0 = 375 Km, A/M = 0.02, C d = 2.0

16 Pg 16 of 46 AGI www.agiuc.com Lifetime distribution – Variations of Mean F10.7 Solar Max Solar Min Jacchia 1970 Density Model Alt 0 = 450 Km, A/M = 0.02, C d = 2.0 +2 Sigma-2 Sigma Mean +2 Sigma -2 Sigma Mean

17 Pg 17 of 46 AGI www.agiuc.com 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 Pg 18 of 46 AGI www.agiuc.com Solar Cycle 21

19 Pg 19 of 46 AGI www.agiuc.com Flux history revisited

20 Pg 20 of 46 AGI www.agiuc.com Sample Data & Functional Forms Standard Deviation Time Correlation

21 Pg 21 of 46 AGI www.agiuc.com Simulated solar flux

22 Pg 22 of 46 AGI www.agiuc.com 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 Pg 23 of 46 AGI www.agiuc.com Effects of Daily Variations on Orbit Lifetime – 375 Km Alt Daily Variation Only Mean Variation Only Solar MaxSolar Min

24 Pg 24 of 46 AGI www.agiuc.com Mean and daily variations – 375 Km Solar Max Solar Min Vary Only Mean Flux Mean = 34.476 StDev = 3.115 Vary Only Mean Flux Mean = 181.798 StDev = 22.11

25 Pg 25 of 46 AGI www.agiuc.com Effects of Daily Variations on Orbit Lifetime – 450 Km Alt Daily Variation Only Mean Variation Only Solar MaxSolar Min Mean Variation Only

26 Pg 26 of 46 AGI www.agiuc.com Mean and daily variations – 450 Km Solar Max Solar Min Vary Only Mean Flux Mean = 263.8 StDev = 43.5 Vary Only Mean Flux Mean = 1752.6 StDev = 626.8

27 Pg 27 of 46 AGI www.agiuc.com 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 Pg 28 of 46 AGI www.agiuc.com Atmospheric Density Model Selection

29 Pg 29 of 46 AGI www.agiuc.com Which density model should I use??? 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 Survey says…

30 Pg 30 of 46 AGI www.agiuc.com Different density models – same results – 375 Km Jacchia 70 Jacchia 71 MSIS 86 MSISE 90 Solar max

31 Pg 31 of 46 AGI www.agiuc.com Different density models – same results – 450 km Jacchia 70 Jacchia 71 MSIS 86 MSISE 90 Solar max

32 Pg 32 of 46 AGI www.agiuc.com 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 Pg 33 of 46 AGI www.agiuc.com Selection of a Numerical Method

34 Pg 34 of 46 AGI www.agiuc.com Numerical method selection How much time do you have? How long do you expect your orbit to last? What method do you trust?

35 Pg 35 of 46 AGI www.agiuc.com Numerical methods Simplified model (Lifetime) –Semi-analytic model –Earth gravity through J5 –Solar and lunar 3 rd body –Solar radiation pressure –Atmospheric drag via Gaussian quadrature Numerical integration –Complete force model –Gauss Jackson 12 th order integrator

36 Pg 36 of 46 AGI www.agiuc.com 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 Pg 37 of 46 AGI www.agiuc.com Comparison methodology Time Truth Solar Flux Trajectory Truth Ephemeris Initialization from truth Solar Flux With Daily Random VariationsOrbit Lifetime Estimate

38 Pg 38 of 46 AGI www.agiuc.com Comparison of approaches 4 weeks out 3 weeks out Num Integ - Solar Max Lifetime - Solar Max

39 Pg 39 of 46 AGI www.agiuc.com Comparison of approaches Num Integ - Solar Min Lifetime - Solar Min 6 months out 4 months out Lifetime – Solar Min

40 Pg 40 of 46 AGI www.agiuc.com 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 Pg 41 of 46 AGI www.agiuc.com 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 Pg 42 of 46 AGI www.agiuc.com STK/Lifetime enhancements Random solar flux history generation (Scenario) Atmospheric density model selection Duration stopping condition Reportable data after error conditions Enhanced documentation

43 Pg 43 of 46 AGI www.agiuc.com 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 Pg 44 of 46 AGI www.agiuc.com 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 All analyses in this study were performed on orbits with short lifetime Actual results may vary Disclaimer

45 Pg 45 of 46 AGI www.agiuc.com What’s Next Solar weather –Cycle amplitude –Daily variability –Cycle timing –Storms Geomagnetic activity A priori density models Initial conditions Projected area Numerical methods Real data comparisons BLUE = Addressed in this study RED = To be addressed in next study

46 Pg 46 of 46 AGI www.agiuc.com Ultimate Recommendation Compare results from 2 independent approaches Monte-Carlo Madame Zora

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