Refining Space Object Radiation Pressure Modeling with Bidirectional Reflectance Distribution Functions
Abstract
High-fidelity orbit propagation requires detailed knowledge of the solar radiation pressure on a space object. The solar radiation pressure depends not only on the space object’s shape and attitude, but also on the absorption and reflectance properties of each surface on the object. These properties are typically modeled in a simplistic fashion, but are here described by a surface bidirectional reflectance distribution function. Several analytic bidirectional reflectance distribution function models exist, and are typically complicated functions of illumination angle and material properties represented by parameters within the model. In general, the resulting calculation of the solar radiation pressure would require a time-consuming numerical integration. This might be impractical if multiple solar radiation pressure calculations are required for a variety of material properties in real time; for example, in a filter where the particular surface parameters are being estimated. This paper develops a method to make accurate and precise solar radiation pressure calculations quickly for some commonly used analytic bidirectional reflectance distribution functions. In addition, other radiation pressures exist, including Earth albedo/Earth infrared radiation pressure, and thermal radiation pressure from the space object itself, and are influenced by the specific bidirectional reflectance distribution function. A description of these various radiation pressures and a comparison of the magnitude of the resulting accelerations at various orbital heights and the degree to which they affect the space object’s orbit are also presented. Significantly, this study suggests that, for space debris whose interactions with electro-magnetic radiation are described accurately with a bidirectional reflectance distribution function, then hitherto unmodeled torques would account for rotational characteristics affecting both tracking signatures and the ability to predict the orbital evolution of the objects.
References
[1] , “Properties of the High Area-to-Mass Ratio Space Debris Population in GEO,” The Advanced Maui Optical and Space Surveillance Technologies Conference,
Wailea, Maui, HI , Sept. 2005, pp. 216–223.[2] , “Solar Radiation Pressure Estimation and Analysis of a GEO Class of High Area-to-Mass Ratio Debris Objects,” AAS Astrodynamics Specialist Conference, Vol. 129, Mackinac Island, MI, Paper 07-391, Aug. 2007, pp. 2205–2221;
[3] , “Prediction and Tracking Analysis of a Class of High Area-to-Mass Ratio Debris Objects in Geosynchronous Orbit,” The Advanced Maui Optical and Space Surveillance Technologies Conference,
Wailea, Maui, HI , Sept. 2008, p. 33.[4] , “Analysis of Orbit Prediction Sensitivity to Thermal Emissions Acceleration Modeling for High Area-to-Mass Ratio (HAMR) Objects,” The Advanced Maui Optical and Space Surveillance Technologies Conference,
Wailea, Maui, HI , Sept. 2009, p. 17.[5] , “Analysis of High Area-to-Mass Ratio (HAMR) GEO Space Object Orbit Determination and Prediction Performance: Initial Strategies to Recover and Predict HAMR GEO Trajectories with No A Priori Information,” Acta Astronautica, Vol. 69, Nos. 7–8, 2011, pp. 551–558. doi:https://doi.org/10.1016/j.actaastro.2011.04.019 AASTCF 0094-5765
[6] , “Application of a Multiple Hypothesis Filter to Near GEO High Area-to-Mass Ratio Space Objects State Estimation,” Acta Astronautica, Vol. 81, No. 2, 2012, pp. 435–444. doi:https://doi.org/10.1016/j.actaastro.2012.08.006 AASTCF 0094-5765
[7] , “Astrometric and Photometric Data Fusion for Resident Space Object Orbit, Attitude, and Shape Determination Via Multiple-Model Adaptive Estimation,” AIAA Guidance, Navigation, and Control Conference, Curran Associates Incorporated, Toronto, Ontario, Canada, Paper 2010-8341, Aug. 2010.
[8] , “Generalized Analytical Solar Radiation Pressure Modeling Algorithm for Spacecraft of Complex Shape,” Journal of Spacecraft and Rockets, Vol. 41, No. 5, 2004, pp. 840–848. doi:https://doi.org/10.2514/1.13097 JSCRAG 0022-4650
[9] , “An Anisotropic Phong BRDF Model,” Journal of Graphics Tools, Vol. 5, No. 2, 2000, pp. 25–32. doi:https://doi.org/10.1080/10867651.2000.10487522
[10] , “A Reflectance Model for Computer Graphics,” ACM Transactions on Graphics, Vol. 1, No. 1, Jan. 1982, pp. 7–24. doi:https://doi.org/10.1145/357290.357293 ATGRDF 0730-0301
[11] , “An Inexpensive BRDF Model for Physically-Based Rendering,” Computer Graphics Forum, Vol. 13, No. 3, 1994, pp. 233–246. doi:https://doi.org/10.1111/cgf.1994.13.issue-3 CGFODY 0167-7055
[12] , “Exponential Integral and Related Functions,” Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, edited by Abramowitz M. and Stegun I. A.,
National Bureau of Standards Applied Mathematics Series , Washington, DC, 1964, p. 272.[13] , “Earth Radiation Pressure Effects on Satellites,” Proceedings of the AIAA/AAS Astrodynamics Conference,
Minneapolis, MN , Paper 88-4292-CP, Aug. 1988, pp. 577–587.[14] , “A Computer Efficient Model of Earth Albedo Satellite Effects,” NASA Goddard Space Flight Center, Planetary Sciences Dept., Rept. 012-77, 1977.
[15] , “Minimal Discrete Energy on the Sphere,” Mathematical Research Letters, Vol. 1, No. 6, 1994, pp. 647–662.
[16] , “Distributing Many Points on a Sphere,” The Mathematical Intelligencer, Vol. 19, No. 1, 1997, pp. 5–11. doi:https://doi.org/10.1007/BF03024331 MAINDC 0343-6993
[17] , “Modeling Radiation Forces Acting on Topex/Poseidon for Precision Orbit Determination,” Journal of Spacecraft and Rockets, Vol. 31, No. 1, 1994, pp. 99–105. doi:https://doi.org/10.2514/3.26408 JSCRAG 0022-4650
[18] , Fundamentals of Astrodynamics and Applications, 3rd ed., McGraw–Hill, New York, 2007, pp. 574–578.
[19] , “A Survey of Attitude Representations,” Journal of the Astronautical Sciences, Vol. 41, No. 4, Oct.–Dec. 1993, pp. 439–517. JALSA6 0021-9142