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## Satellite Drag Modeling using Direct Simulation Monte Carlo (DSMC)

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**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**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**Density**Mehta et al., 2011**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**Analytical Solution**Sentman, 1961, Bird, 1994, Pilinski et al., 2011**Energy Accommodation**Defined as the fraction of the energy lost by free stream molecules on spacecraft surface impact Pilinski et al., 2010**Gas Surface Interaction (GSI)**Sentman, 1961, Schamberg, 1959, Pilinski et al., 2011**Results**Each data point is a DSMC simulation Each simulation take between 3-5 hrs depending on the machine Reference Simulation Conditions Tatm = 1157 K Tsc = 300 K Vr = 7590 m/s Molecular mass (m) = 11.35 amu**GRACE**Altitude: 485 km at launch Eccentricity: <0.005 Inclination: 89 deg Mass: 432 kg**GRACE DSMC Results**July 19, 2005**GRACE DSMC Results compared with Sutton**July 19, 2005**Drag Coefficient Modeling for GRACE**Correlation Coefficients Data from July 19, 2005**Drag Coefficient Modeling for GRACE**• 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.**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.**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