Abstract
The first absolute measurement of thermospheric density was made by combining simultaneous observations of spin and semimajor axis decay of Explorer VI. Providing two independent measures of the interaction with the airstream enabled the determination of both air density and drag coefficient. Then by using a realistic model of the gas-surface interaction, the energy accommodation coefficient was determined. Only four such measurements were made prior to the time of writing. In this paper, we review the history of paddlewheel measurements and explain their importance to ongoing work in satellite drag. Next, a novel concept for paddlewheel satellites based on the CubeSat platform is discussed along with the relevant design parameters. A rudimentary error analysis for paddlewheel measurements evaluated the feasibility of these designs and it was found that the drag torques generated on a three-kilogram paddlewheel are within the measurement capabilities of today’s technologies. For certain types of paddlewheel configurations, the use of direct simulation methods is important for accurately analyzing the data. This is because a paddlewheel with the spin axis oriented in the orbit normal direction undergoes significant flow-shadowing and this is not easily represented by analytical methods. Increasing the availability of accommodation measurements via the paddlewheel method represents an improvement in the accuracy of Earth’s total density models as well as the understanding of gas-surface interactions in low Earth orbit. This is of profound importance in the prediction of satellite orbits as well as the understanding of atmospheric phenomena.
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References
PARDINI, C., ANSELMO, L., MOE, K., and MOE, M. “Drag and Energy Accommodation Coefficients During Sunspot Maximum,” Advances in Space Research, Vol. 45, No. 5, 2010, pp. 638–650.
REITER, G.S. and MOE, K. “Surface-Particle-Interaction Measurements Using Paddlewheel Satellites,” Proceedings of the International Symposium on Rarefied Gas Dynamics (H. Y. Wachman, ed.), Vol. 6, Boston, MA, 1968, pp. 6–20.
MOE, K. and MOE, M. “Gas-Surface Interactions and the Satellite Drag Coefficients,” Planetary and Space Science, Vol. 53, 2005, pp. 793–801.
THOMAS, L. “Thermal Accommodation of Gases on Solids,” Fundamentals of Gas Surface Interactions (H. Saltsburg, J. Smith, and M. Rogers, eds.), NY and London, Academic Press, 1967, pp. 346–369.
FEIBELMAN, P.J. “The First Wetting Layer on a Solid,” Physics Today, Vol. 63, No. 2, 2010, pp. 34–39.
MOE, K. and MOE, M. “The Effect of Adsorption on Densities Measured by Orbiting Pressure Gauges,” Planetary and Space Science, Vol. 15, 1967, pp. 1329–1332.
PILINSKI, M.D., ARGROW, B.M., and PALO, S. E. “Semi-Empirical Model for Satellite Energy-Accommodation Coefficients,” Journal of Spacecraft and Rockets, Vol. 47, No. 6, 2010, pp. 951–956.
GREGORY, J.C. and PETERS, P.N. “A Measurement of the Angular Distribution of 5 eV Atomic Oxygen Scattered off a Solid Surface in Earth Orbit,” Proceedings of the International Symposium on Rarefied Gas Dynamics (B. G. Teubner, ed.), Vol. 15, Stuttgart, Germany, 1987, pp. 644–656.
SCHAAF, S.A. and CHAMBRE, P.L. Flow of Rarefied Gases. New Jersey: Princeton University Press, 1961.
Bird, G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows, New York, Oxford Science Publications, 1994.
SENTMAN, L.H. “Free Molecule Flow Theory and its Application to the Determination of Aerodynamic Forces,” Technical Report LMSC-448514, Lockheed Missiles and Space Co., 1961.
SUTTON, E. “Normalized Force Coefficients for Satellites with Elongated Shapes,” Journal of Spacecraft and Rockets, Vol. 46, No. 1, 2009, pp. 112–116.
DOORNBOS, E., FORSTER, M., V. HELLEPUTTE, T., V. D. IJSSEL, J., KOPPEN-WALLNER, G., et al. “Air Density Models Derived from Multi-Satellite Drag Observations,” Technical Report 21022/07/NL/HE, European Space Agency Study Contract Report, 2009.
MOE, K. “Absolute Atmospheric Densities Determined from the Spin and Orbit Decays of Explorer VI,” Planetary and Space Science, Vol. 14, 1966, pp. 1065–1075.
BELETSKY, V.V. “An Estimate of the Character of the Interaction Between the Airstream and a Satellite,” Kosmicheskie Issledovaniya, Vol. 8, No. 10, 1970, pp. 206–217. (in Russian).
IMBRO, D.R., MOE, M.M., and MOE, K. “On Fundamental Problems in the Deduction of Atmospheric Densities from Satellite Drag,” Journal of Geophysical Research, Vol. 80, 1975, pp. 3077–3086.
MOE, K., MOE, M.M., and WALLACE, S.D. “Improved Satellite Drag Coefficient Calculations from Orbital Measurements of Energy Accomodation,” Journal of Spacecraft and Rockets, Vol. 35, 1998, pp. 266–272.
KING-HELE, D. G. “Improved Formulae for Determining Upper Atmosphere Density from the Change in a Satellites Orbital Period,” Planetary Space Science, Vol. 11, 1963, pp. 261–268.
PILINSKI, M.D. “An Innovative Method for Measuring Drag on Small Satellites,” Proceedings of the 23rd Annual AIAA/USU Conference on Small Satellites, Logan, UT, August 2009.
SUTTON, E. Effects of Solar Disturbances on the Thermosphere Densities and Winds from CHAMP and GRACE Accelerometer Data, Ph.D. Dissertation, University of Colorado at Boulder, 2008.
STORZ, M.F. “Satellite Drag Accuracy Improvements Estimated from Orbital Energy Dissipation Rates,” presented as paper AAS 99-385 at the AAS/Aiaa Astrodynamics Specialists Conference, Girdwood, AK, 1999.
BOWMAN, B.R. and STORZ, M.F. “High Accuracy Satellite Drag Model (HASDM) Review,” presented as paper AAS 03-625 at the AAS/Aiaa Astrodynamics Specialists Conference, Big Sky, MT, 2003.
EMMERT, J.T., PICONE, J.M., and LEAN, J.L. “Global Change in the Thermosphere: Compelling Evidence of a Secular Decrease in Density,” Journal of Geophysical Research, Vol. 109, No. A02301, 2004.
PICONE, J.M., EMMERT, J.T., and LEAN, J.L. “Thermospheric Densities Derived from Spacecraft Orbits: Accurate Processing of Two-Line Element Sets,” Journal of Geophysical Research, Vol. 110, No. A03301, 2002.
EMMERT, J.T. “A Long-Term Data Set of Globally Averaged Thermospheric Total Mass Density,” Journal of Geophysical Research, Vol. 114, No. A06315, 2009.
MOE, K. “Recent Experimental Evidence Bearing on Satellite Drag Coefficients,” AIAA Journal, Vol. 6, No. 7, 1968, pp. 1375–1377.
CHING, B.K., HICKMAN, D.R., and STRAUS, J.M. “Effects of Atmospheric Winds and Aerodynamic Lift on the Inclination of the Orbit of the S3-1 Satellite,” Journal of Geophysical Research, Vol. 82, No. 10, 1977, pp. 1471–1480.
MARCOS, F.A. “Requirements for Improved Thermospheric Neutral Density Models,” Advances in the Astronautical Sciences, Vol. 58, No. 85–312, 1985, pp. 1–21.
MOE, K. “Density and Composition of the Lower Thermosphere,” Journal of Geophysical Research Vol. 78, No. 10, 1973, pp. 1633–1644.
MINZNER, R.A. “The 1976 Standard Atmosphere and Its Relationship to Earlier Standards,” Review of Geophysics and Space Physics, Vol. 15, No. 3, 1977, pp. 375–384.
MOE, K. and BOWMAN, B.R. “The Effects of Surface Composition and Treatment on Drag Coefficients of Spherical Satellites,” Advances in the Astronautical Sciences, Vol. 123, No. 05–258, 2005, pp. 137–152.
BOWMAN, B.R. and MOE, K. “Drag Coefficient Variability at 175–500 km from the Orbit Decay Analyses of Spheres,” Advances in the Astronautical Sciences, Vol. 123, No. 05–257, 2005, pp. 117–136.
DOUGHTY, R.O. and SCHAETZLE, W.J. “Experimental Determination of Momentum Accommodation Coefficients at Velocities up to and Exceeding Earth Escape Velocity,” Rarefied Gas Dynamics, Vol. 2, 1969, pp. 1035–1054.
BRUINSMA, S., FORBES, J.M., NEREM, S., and ZHANG, X. “Thermosphere Density Response to the 20–21 November 2003 Solar and Geomagnetic storm from CHAMP and GRACE Accelerometer Data,” Journal of Geophysical Research, Vol. 111, 2006.
PICONE, J.M., HEDIN, A.E., and DROB, D.P. “NRLMSISE-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues,” Journal of Geophysical Research, Vol. 110, 2002.
GOODING, R.H. “The Orbit of Ariel 2,” Planetary and Space Science, Vol. 14, 1966, pp. 1173–1192.
LI, J., BENCZE, W.J., DEBRA, D.B., HANUSCHAK, G., and HOLMES, T. ET AL. “On-Orbit Performance of Gravity Probe B Drag-Free Translation Control and Orbit Determination,” Advances in Space Research, Vol. 40, No. 1, 2007, pp. 1–10.
PEARLMAN, M.R., DEGNAN, J.J., and BOSWORTH, J.M. “The International Laser Ranging System,” Advances in Space Research, Vol. 30, No. 2, 2002, pp. 135–143.
MOE, K. Atmospheric Densities Determined from the Spin Decay of Explorer VI, Ph.D. Dissertation, University of California, Los Angeles, 1966.
BIRD, G.A. “Sophisticated DSMC,” Notes from DSMC07 meeting, Santa Fe, September 2007. Available from: http://www.gab.com.au/Resources/DSMC07notes.pdf.
DROB, D.P. “An Empirical Model of the Earth’s Horizontal Wind Fields: HWM07,” Journal of Geophysical Research, Vol. 113, 2008.
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Pilinski, M.D., Moe, K., Palo, S.E. et al. Measuring Absolute Thermospheric Densities And Accommodation Coefficients Using Paddlewheel Satellites: Past Findings, Present Uses, And Future Mission Concepts. J of Astronaut Sci 58, 531–549 (2011). https://doi.org/10.1007/BF03321184
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DOI: https://doi.org/10.1007/BF03321184