Until the middle of the 20th century, orbit determination of celestial bodies could only be performed by making angular observations of those objects in the sky (e.g. elevation above the horizon and azimuth). One classical technique was developed by Laplace, and another was developed by Gauss. They both rely on different assumptions (namely how far apart in time the observations are made) and thus yield slightly different results.

Both techniques, however, assumed that the length unit and time unit (and therefore speed and acceleration) were non-dimensionalized. Having seen how this was not always desirable, and having encountered problems arising when the non-dimensionalization was incorrectly implemented, I re-derived both techniques such that non-dimensionalization would not be necessary.

1. Dimensionally-Aware Derivation of the Gauss and Laplace Angles-Only Orbit Determination Method
2. Example of Dimensionally-Aware Laplace Angles-Only Technique applied to a Low-Earth Orbit
3. Example of Dimensionally-Aware Gauss Angles-Only Technique applied to a Low-Earth Orbit
4. Example of Dimensionally-Aware Laplace Angles-Only Technique applied to an Interplanetary Orbit
5. Example of Dimensionally-Aware Gauss Angles-Only Technique applied to an Interplanetary Orbit

In it, I make use of notes from two classes taken at the University of Maryland

• Space Navigation and Guidance taught by Dr. Liam Healy
• Interplanetary Navigation and Guidance taught by Dr. Darryll Pines