Institute of Geodesy Research Research Projects
Highly physical penumbra solar radiation pressure modeling with atmospheric effects

Highly physical penumbra solar radiation pressure modeling with atmospheric effects

Led by:  Prof. Jakob Flury, Tamara Bandikova
Team:  Robbie Robertson (Virginia Tech, Blacksburg, VA)
Year:  2010
Funding:  RISE/QUEST
Duration:  2010
Is Finished:  yes


The fundamental GRACE (Gravity Recovery and Climate Experiment) mission observations are the inter-satellite microwave ranging and precise accelerometry. The accelerometers located in the center of mass of each spacecraft provide high accurate measurement of the non-gravitational forces (solar radiation pressure and residual air drag) acting on the satellites. Transitions of the GRACE satellites through Earth penumbra offer a unique opportunity to study the changing accelerations due to solar radiation pressure. Besides, penumbra transitions also allow validating advanced solar radiation pressure modeling.

Research project

The implemented solar radiation pressure (SRP) model is based on the approach of Vokrouhlicky et al. (1993) where the refraction is modeled due to a polytropic atmosphere for single rays originating from surface elements of the solar disk. Numerical integration leads to the total solar radiation field acting on the satellite surfaces. For the GRACE spacecraft modeling, a 8 surface satellite model with known reflectivity coefficients is applied.

We compare the 10 Hz Level-1A accelerometer time series for typical transitions with this SRP model. The match of timing and shape of observed and modeled acceleration demonstrates a good quality of the SRP modeling. In the same time, it helps to validate the accelerometer data, e.g. it allows a rough validation of the instrument scale factors.


This research was carried out within the frame of the Research Internships in Science and Engineering (RISE) funded by the German Academic Exchange Service (DAAD) and the Center for Quantum Engineering and Space-Time Research (QUEST).

We kindly thank prof. David Vokrouhlicky from the Charles University in Prague for his guidance on implementing his SRP modeling method.


Vokrouhlicky D, Farinella P, Mignard F (1993) Solar radiation pressure perturbations for Earth satellites -- I. A complete theory including penumbra transitions. Astron Astrophys 280:295-312 

Robertson et al (2015) Highly physical penumbra solar radiation pressure modeling with atmospheric effects. Celest Mech Dyn Astr, doi:10.1007/s10569-015-9637-0