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.