Date of Award:


Document Type:


Degree Name:

Master of Science (MS)


Mechanical and Aerospace Engineering


David Geller


Through Spherical Harmonics, one can describe complex gravitational fields. However as the order and degree of the spherical harmonics increases, the computation speed rises exponentially. In addition, for onboard applications of spherical harmonics, the processors are radiation hardened in order to mitigate negative effects of the space environment on electronics. But, those processors have outdated processing speeds, resulting in a slower onboard spherical harmonic program.

This thesis examines a partial solution to the slow computation speed of spherical harmonics programs. The partial solution was to supplant the gravity models in the flight software. The spherical harmonics gravity model can be replaced by a hybrid model, a mass concentrations model and a secondary (lesser degree or order) spherical harmonics model. That hybrid model can lead to greater processing speeds while maintaining the same level of accuracy.

To compute the mass values for the mass concentration model, a potential estimation scheme was selected. In that scheme, mass values were computed by minimizing the integral of the difference between the correct and the estimated potential.

The best hybrid model for the 8 degree and 8 order, 15 degree and 15 order, and 30 degree and 30 order lunar potential fields is developed following three different approaches: potential zeros method, gravitational anomalies method, and iterative method. Afterwards, the accuracy and computation time of the models are measured and compared to the primary spherical harmonic lunar model.

In the aftermath, while the best hybrid model for all three cases was able to run faster than the primary spherical harmonic model, it was unable to be sufficiently accurate to replace the primary spherical harmonic model. The mass estimation scheme is severely hindered by the condition number and convergence issues resulting in inaccurate estimates for the mass values for a given distribution.

It is recommended to alleviate the condition number error by eliminating the inverse in the mass estimation scheme. Other recommendations include fixing the convergence error, investing in software and hardware development, and focusing on other hybrid research objectives.


This work made publicly available electronically on April 11, 2011.