Modeling and Analysis of a Thermospheric Density Measurement System Based on Torque Estimation

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Tech


This thesis models and analyzes an in-situ method for measuring the density of the thermosphere at low Earth orbit (LEO) altitudes in real time. As satellites orbit in the thermosphere, the sparse yet present air perturbs their orbits via the drag force. The drag force is poorly characterized and has a significant effect at LEO altitudes relative to other forces, making this perturbation force one of the greatest uncertainties in LEO orbit propagation. A steadily increasing number of satellites orbit at LEO altitudes, so for safety, it is critical to accurately track these satellites to avoid collisions. Therefore, better knowledge of the drag force is required. The drag force depends directly on the air mass density in the thermosphere, and current knowledge of the thermospheric density is limited. Models exist to describe the variations in density over time, but due to the many unpredictable factors which affect the thermosphere, the best of these models are only accurate to within 10%. Also, currently available techniques to measure the thermospheric density can only return time-averaged measurements, which causes inaccuracies in orbit propagation due to local density variations. Some planned in-situ density measurement missions rely on measuring acceleration caused by the drag force, but this requires a highly accurate accelerometer to be able to separate the drag force from other stronger forces acting on a satellite. The Satellite Producing Aerodynamic Torque to Understand LEO Atmosphere (SPATULA) concept was introduced as an alternative method, which infers density based on measurements of the drag torque. In the rotational regime, drag produces the strongest torque at LEO altitudes by far, making it possible to acquire accurate density measurements with inexpensive, commercially available sensors and actuators on a SPATULA spacecraft. This thesis expands upon a preliminary study of the SPATULA concept. A SPATULA spacecraft's dynamics are modeled in three dimensions, and a novel method is introduced for modeling the dependence of external torques on the geometry and attitude of the spacecraft. In addition to the dynamics model, discrete-time algorithms for guidance, system state filtering, attitude control, and density estimation are developed for the six degrees of freedom case. The MathWorks tools MATLAB and Simulink are used to simulate the physics and system models. The simulations are used to evaluate the performance of the SPATULA system's density measurements and compare them to conventional methods. It is found that the accuracy and bandwidth of the SPATULA system have a significant dependence on the assumed accuracy of the torque models in the system's filter. When the bandwidth is set to avoid significant phase shift errors, the SPATULA system can produce real-time measurements of density accurate over a minimum time scale of about 60 seconds, and the density error has a standard deviation of about 2 x 10^-14 kg/m^3. This accuracy is about 6 times better than the best thermospheric models, and it is also better than reported accuracies of most other density measurement methods. If bandwidth is sacrificed, the density error standard deviation can be decreased by a factor of 4. This introduces additional error due to phase shift delays, but these can be corrected with signal processing techniques. With the higher accuracy, the SPATULA system loses its real-time ability, but the data it produces would still provide excellent insight for improving thermospheric models. With high accuracy and low cost, the SPATULA concept is a promising path to pursue toward improving thermospheric density knowledge.



Thermospheric density, Density measurement, Drag perturbation, Torque estimation, Attitude control