Celestial Mechanics and Dynamical Astronomy

, Volume 123, Issue 2, pp 169–202 | Cite as

Highly physical penumbra solar radiation pressure modeling with atmospheric effects

  • Robert Robertson
  • Jakob Flury
  • Tamara Bandikova
  • Manuel Schilling
Original Article


We present a new method for highly physical solar radiation pressure (SRP) modeling in Earth’s penumbra. The fundamental geometry and approach mirrors past work, where the solar radiation field is modeled using a number of light rays, rather than treating the Sun as a single point source. However, we aim to clarify this approach, simplify its implementation, and model previously overlooked factors. The complex geometries involved in modeling penumbra solar radiation fields are described in a more intuitive and complete way to simplify implementation. Atmospheric effects are tabulated to significantly reduce computational cost. We present new, more efficient and accurate approaches to modeling atmospheric effects which allow us to consider the high spatial and temporal variability in lower atmospheric conditions. Modeled penumbra SRP accelerations for the Gravity Recovery and Climate Experiment (GRACE) satellites are compared to the \(\hbox {sub-nm}/\hbox {s}^{2}\) precision GRACE accelerometer data. Comparisons to accelerometer data and a traditional penumbra SRP model illustrate the improved accuracy which our methods provide. Sensitivity analyses illustrate the significance of various atmospheric parameters and modeled effects on penumbra SRP. While this model is more complex than a traditional penumbra SRP model, we demonstrate its utility and propose that a highly physical model which considers atmospheric effects should be the basis for any simplified approach to penumbra SRP modeling.


Penumbra Solar radiation pressure Spacecraft navigation Orbit determination Atmospheric optics Refraction Satellite accelerometry GRACE 



This research began in 2010 during a Research Internships in Science and Engineering (RISE) internship funded by the German Academic Exchange Service (DAAD) and carried out at the Institute for Geodesy (IFE) at Leibniz Universität in Hannover, Germany. Robert Robertson was supported by a Virginia Space Grant Consortium (VSGC) Graduate Research Fellowship. The authors would like to thank Professor David Vokrouhlický from Charles University in Prague for providing invaluable guidance on understanding and implementing his SRP modeling methods which our work builds upon. Jakob Flury was supported by the Center of Excellence QUEST and by the DFG Sonderforschungsbereich SFB1128 “Relativistic Geodesy and Gravimetry with Quantum Sensors”.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Robert Robertson
    • 1
  • Jakob Flury
    • 2
  • Tamara Bandikova
    • 2
  • Manuel Schilling
    • 2
  1. 1.Center for Space Science and Engineering ResearchVirginia TechBlacksburgUSA
  2. 2.Institute of GeodesyLeibniz Universität HannoverHannoverGermany

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