Kepler's laws of planetary motion of solar system body number "i" is, according to Newton's laws: where formula_72 is the mass of body "j", formula_73 is the distance between body "i" and body "j", formula_74 is the unit vector from body "i" towards body "j", and the vector summation is over all bodies in the world, besides "i" itself. In the special case where there are only two bodies in the world, Earth and Sun, the acceleration becomes which is the acceleration of the Kepler motion. So this Earth moves around the Sun according to Kepler's laws. If the two bodies in the world are
Kepler's laws of planetary motion Moon and Earth the acceleration of the Moon becomes So in this approximation the Moon moves around the Earth according to Kepler's laws. In the three-body case the accelerations are These accelerations are not those of Kepler orbits, and the three-body problem is complicated. But Keplerian approximation is the basis for perturbation calculations. See Lunar theory. Kepler used his two first laws to compute the position of a planet as a function of time. His method involves the solution of a transcendental equation called Kepler's equation. The procedure for calculating the heliocentric polar coordinates ("r","θ") of a planet as a