The history of orbital element methods

[solarblast]

There seem to be several methods for calculating the orbital element. Newcomb, Laplace, Lagrange, Gauss, Olbers, ... I'm sure over time a new method came to light. However, what basically was the difference between a new method and the one it replaced? Improvements in calculations (computer), correct problems in a predecessor, simplifications, ...?

[solarblast]

See chapter 7 in?
<http://200.105.152.242/olimpiada/file.php/1/LIBROS_OLIMPIADAS/Textos%20de%20Astronomia%20y%20Astrofisica/The%20Foundations%20of%20Celestial%20Mechanics%20-%20G.%20W.%20Collins.pdf>

You might want to download the pdf book too.