1. Slide 1 Satellite Drag Modeling using Direct Simulation Monte Carlo (DSMC) Piyush M. Mehta and Craig A. McLaughlin The University of Kansas Acknowledgement: Part of the work was done at the Los Alamos National Laboratory as part of the Space Weather Summer School

2. Introduction Satellite Drag Model Sources of error: Density, Drag Coefficient and Area Density Modeling:  Typically uses constant drag coefficient to derive densities from satellite data  High Accuracy Satellite Drag Model (HASDM) uses drag coefficients varying with altitude Drag Coefficient Modeling:  Orbit Prediction and Conjunction Analysis typically uses a constant drag coefficient Slide 2

3. Density Slide 3 Mehta et al., 2011

4. Drag Coefficient Drag Coefficient is a strong function of:  Energy Accommodation (model)  Gas Surface Interactions (GSI) (model)  Attitude  Surface Geometry  Atmospheric Composition and Temperature (NRLMSISE-00)  Surface Temperatures (Equations in Brown, AIAA Education Series, 2002)  Spacecraft Relative Velocity Slide 4

5. Analytical Solution Slide 5 Sentman, 1961, Bird, 1994, Pilinski et al., 2011

6. DSMC DS3V Slide 6

7. Energy Accommodation Slide 7 Pilinski et al., 2010 Defined as the fraction of the energy lost by free stream molecules on spacecraft surface impact

8. Gas Surface Interaction (GSI) Sentman, 1961, Schamberg, 1959, Pilinski et al., 2011 Slide 8

9. Results Slide 9  Each data point is a DSMC simulation  Each simulation take between 3-5 hrs depending on the machine Reference Simulation Conditions T atm = 1157 K T sc = 300 K V r = 7590 m/s Molecular mass (m) = 11.35 amu

10. Results Slide 10

11. Results Slide 11

12. GRACE Slide 12  Altitude: 485 km at launch  Eccentricity: <0.005  Inclination: 89 deg  Mass: 432 kg

13. GRACE model for DSMC Slide 13 Φ 3 deg0 deg-3 deg β 0 deg1.311 m 2 1.004 m 2 1.299 m 2 -3 deg1.335 m 2 1.139 m 2 1.323 m 2

14. Grace: All Models Slide 14

15. Slide 15 Grace: Mesh for DS3V

16. GRACE DSMC Results Slide 16 July 19, 2005

17. GRACE DSMC Results compared with Sutton Slide 17 July 19, 2005

18. Atmospheric Properties Accommodation Coefficient Helium Number Density Free-Stream Temperature Drag Components Pressure-0.9960.894-0.848 Shear0.900-0.8660.967 Drag Coefficient Modeling for GRACE Slide 18 Correlation Coefficients Data from July 19, 2005

19. Various curve fits were use for both Pressure and Shear drag contributions Additional simulations performed at random times to validate models. Error in using all the the models <1% More simulations need to be performed at different space weather conditions for a complete model. Slide 19 Drag Coefficient Modeling for GRACE

20. Conclusion: Drag Coefficient Modeling The Direct Simulation Monte Carlo (DSMC) technique performed well in explicitly calculating drag coefficients for satellites with simple (sphere and cylinder) and complex geometries with complete and partial accommodation. Results show strong correlation of the total drag coefficient for a sphere with energy-accommodation, spacecraft relative velocity, and free-stream atmospheric temperature. Drag coefficients can vary by more than 20% for complex geometries and by as much as 10% for a sphere along the satellite orbit. Therefore, use of a constant drag coefficient should be avoided in deriving densities from orbit data or for satellite conjunction. Drag coefficients calculated by Sutton lie within the extreme cases of attitude simulated for GRACE. A high fidelity drag coefficient model for GRACE is highly feasible. Slide 20

21. Future Work Create and validate GRACE Drag Coefficient model Create Drag Coefficient Models for other satellites Use the drag coefficient model to update density models Work on ways to improve model fidelity Slide 21

22. Questions? Slide 22