Kepler's laws of planetary motion formula_16 The area enclosed by the elliptical orbit is formula_17 So the period formula_18 satisfies and the mean motion of the planet around the Sun satisfies This captures the relationship between the distance of planets from the Sun, and their orbital periods. Kepler enunciated in 1619 this third law in a laborious attempt to determine what he viewed as the "music of the spheres" according to precise laws, and express it in terms of musical notation. So it was known as the "harmonic law". Using Newton's Law of gravitation (published 1687), this relation can be found in the case of
Kepler's laws of planetary motion Kepler (p. 620) states that the terminology of scientific laws for these discoveries was current at least from the time of Joseph de Lalande. It was the exposition of Robert Small, in "An account of the astronomical discoveries of Kepler" (1814) that made up the set of three laws, by adding in the third. Small also claimed, against the history, that these were empirical laws, based on inductive reasoning. Further, the current usage of "Kepler's Second Law" is something of a misnomer. Kepler had two versions, related in a qualitative sense: the "distance law" and the "area law". The "area