Today’s Eponymy in August is Kepler’s Second Law of Planetary Motion.
Johannes Kepler was an early 17th century astronomer, and the protege of Tycho Brahe. Kepler had published a defense of the Copernican (heliocentric) system of planets and stars in the late 16th century, and attempted to tie the Platonic solids to the orbits of the known planets. When Brahe and Kepler started corresponding, much of the content centered on the inaccuracy of Copernicus’s data. Kepler later worked with Brahe at his observatories and was promoted to Brahe’s position of imperial astronomer in 1601 on the latter’s death. After four more years of research and calculation, Kepler abandoned the idea that the oddities in the orbits of planets followed an ovoid shape, and settled on the ellipse instead. The resulting work, Astronomia nova, marked a major turning point in astronomy.
Today we focus on Kepler’s Second Law since the first one (planetary orbits are ellipses) is now widely known and taught in elementary school astronomy. The second one happens to be a neat thing that is not intuitive about how planets orbit the Sun, but makes sense if you think about it:
“A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time”
It’s worth noting that the motion of planets around the Sun does not happen at a fixed speed. Gravity increases the speed of orbit as a planet gets closer to the Sun, and this happens inversely proportionally to the distance from the Sun (i.e. the closer you get, the faster you go). The math works out such that as the conical section of a planet’s orbit for a unit of time gets squatter, the speed of the orbit increases to make the slice wider and keep the area the same. When considering how little eccentricity the planets have (the Earth varies by about +/-1million miles in its average-93-million-mile radius), it’s no surprise that observations would have to have a certain degree of mechanical accuracy before this could be noted.