Kepler's three planetary laws are nowadays expressed as follows:
- The path of a planet is an ellipse, with the Sun at one focus (the Ellipse Law).
- The radius vector (the line joining the planet to the Sun) sweeps out equal areas in equal times (the Area Law).
- The squares of the periodic (orbital) times of the planets are proportional to the cubes of their mean distances from the Sun (major semi-axis of the ellipse).
The planetary laws were not designated as such by Kepler himself, though the first two laws, discovered in Astronomia Nova (1609), completely determined the motion of a particular planet (Mars). The third law was published in Harmonice Mundi (1619) and provided a relationship to synthesize the planetary system.
The formulations of the laws are set out here in Kepler's own words:
- „... sequenti capite, ubi simul etiam demonstrabitur, nullam Planetae relinqui figuram Orbitae, praeterquam perfecte ellipticam; conspirantibus rationibus, a principiis Physicis, derivatis, cum experientia observationum et hypotheseos vicariae hoc capite allegata” (Astronomia Nova, 1609, caput 58; KGW III, 366)
Translation: „It will be demonstrated through the agreement of arguments from physical principles with the body of experience, mentioned in this chapter, that is contained in the observations, ... that no figure is left for the planet to follow other than a perfectly elliptical one.” [Donahue, p. 576]
- „Invenitur et area [AKN], mensura temporis” (Astronomia Nova, 1609, caput 60; KGW III, 380.).
Translation: „the area [AKN], the measure of the time, ... is found.” [Donahue, p. 599]
- „... res est certissima exactissimaque, quod proportio quae est inter binorum quorumcunque Planetarum tempora periodica, sit praecise sesquialtera proportionis mediarum distantiarum, id est Orbium ipsorum” (Harmonice Mundi, 1619, liber V, caput 3, 8; KGW VI, 302).
Translation: „It is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances” [Aiton et al., p. 411]