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
Elements of the Philosophy of Newton mutual Action of Bodies upon Light. Of the Resemblance between the seven Primitive Colours and the seven Notes in Musick. Introductory Ideas concerning Gravity and the Laws of Attraction: That the Opinion of a subtil Matter, Vortices, and a Plenitude, ought to be rejected (But not that subtile Aether which Sir Isaac makes the Cause of Attraction, Refraction, Animal Motion, &c. which pervades the Universe). That the Vortices and Plenitude of Descartes are impossible, and consequently that there is some other Cause of Gravity. What is meant by Vacuity and Space, without which there could be neither Gravity nor Motion.