Kepler's First Law

Significance

Planets travel ellipses with the Sun at one focus — not the perfect circles two millennia of astronomy had insisted on. Kepler got there through Tycho's data and eight arcminutes of Martian residual he refused to round away. The ellipse is not a fact about the solar system: an inverse-square attraction is one of only two force laws whose bound orbits close on themselves at all, so the shape falls out of Newton's law rather than having to be assumed. Written here as the polar equation of the orbit.