Utilizing NASA HORIZONS Web-Interface we obtain the position vectors for some of the planets in our solar system and compute the parametrizations of their orbits around the sun. For sake of completeness, leading up to the results we discuss ways of finding best fitting lines, hyperplanes, and then the ellipse. For each we consider ways of measuring the error of the best-fit solution. There are many examples done in Mathematica illustrating the procedures and techniques discussed.
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