In 1678, Newton published in Principia a demonstration that the planets' orbits are ellipses (r₁+r₂=c) with the Sun at one of the foci. 7 years earlier, Cassini proposed that the orbits follow the curve with r₁r₂=c². pic.twitter.com/swl8fbdMbz
It's a very good question! What follows are many tweets attempting to answer in a possibly way-too-verbose manner. No pictures (sorry), but I'll trust in the readers' mind's eye. https://t.co/d9fbrWyenm