ACDCA
Austrian Center for Didactics of Computer Algebra

Kepler's Ellipses: Challenges From Compasses to Computer Algebra

Tomass Romanovskis
(Riga, Latvia University)
 
Download PDF-File: g_romano.pdf (50 KB)

Abstract:

In 300 years the special case of planetary motion in a circular orbit is the only exact solution of planetary motion to have been found. To find x(t), y(t) for the more general case of an elliptic orbit, it is necessary to use approximate numerical methods, employing the transcendent equation t=t(E) named after Kepler. Another method which can be employed in looking for the exact solution of the equation of motion in inverse square force field is parametric set of expressions: t=(E), x(E), y(E). The solution is time cycloid, proposed by Newton in famous PRINCIPIA, but never used.

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