Kepler’s Planetary Motion
Kepler’s laws of planetary motion, in astronomy and
classical physics, laws describing the motions of the planets in
the solar system. They were derived by the German
astronomer Johannes Kepler, whose analysis of the observations of
the 16th-century Danish astronomer Tycho Brahe enabled him to
announce his first two laws in the year 1609 and a third law
nearly a decade later, in 1618. Kepler himself never numbered
these laws or specially distinguished them from his other
discoveries
Kepler’s three laws of planetary motion can be stated as follows:
1) All planets move about the Sun in elliptical orbits, having
the Sun as one of the foci.
2) A radius vector joining any planet to the Sun sweeps out equal
areas in equal lengths of time.
3) The squares of the sidereal periods (of revolution) of the
planets are directly proportional to the cubes of their mean
distances from the Sun.
Knowledge of these laws, especially the second (the law of
areas), proved crucial to Sir Isaac Newton in 1684–85, when he
formulated his famous law of gravitation between Earth and the
Moon and between the Sun and the planets, postulated by him to
have validity for all objects anywhere in the universe. Newton
showed that the motion of bodies subject to central
gravitational force need not always follow the elliptical orbits
specified by the first law of Kepler but can take paths defined
by other, open conic curves; the motion can be in parabolic or
hyperbolic orbits, depending on the total energy of the body.
Thus, an object of sufficient energy—e.g., a comet—can enter the
solar system and leave again without returning. From Kepler’s
second law, it may be observed further that the angular
momentum of any planet about an axis through the Sun and
perpendicular to the orbital plane is also unchanging
Most planetary orbits are nearly circular, and careful
observation and calculation are required in order to establish
that they are not perfectly circular. Calculations of the orbit
of Mars, whose published values are somewhat suspect, indicated
