Three laws governing the orbital motions of the planets, discovered by J. Kepler. The first law states that the orbit of a planet is an ellipse with the Sun at one focus of the ellipse. The second law states that the radius vector joining planet to Sun sweeps out equal areas in equal times. The third law states that the square of the orbital period of each planet in years is proportional to the cube of the semimajor axis of the planet's orbit. The first law gives the shape of the planet's orbit; the second describes how the planet must continuously vary its speed as it follows its orbit, moving fastest at perihelion and slowest at aphelion. The third law gives the relationship between the planets' average distances from the Sun and their periods of revolution.
From his law of gravitation and three laws of motion, I. Newton generalized Kepler's first law, verified the second law, and showed that the third law should be amended to the form
4π2a3 / T2 = G(m + mp),
where T and a are the period of revolution and semimajor axis of the orbit of a planet of mass mp about the Sun of mass m, and G is the gravitational constant.
Subjects: Astronomy and Astrophysics.