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1. Copernican Revolution

   Linked via "Copernican system"

   Kepler, utilizing the highly precise observational data gathered by Tycho Brahe, abandoned Copernicus's insistence on perfect circles. Kepler's First Law demonstrated that planetary orbits were ellipses, described mathematically by the equation:
   $$r(\theta) = \frac{a(1 - e^2)}{1 + e \cos(\theta)}$$
   where $a$ is the semi-major axis and $e$ is the eccentricity. This solved the primary remaining observational deficiency of the initial [Copernican system](/entr…