Kepler's law of planetary motion.Expressing governing them.

Kepler's laws of planetary motion describe the orbits of planets around the Sun. There are three laws:

1. First Law (Law of Ellipses): The orbit of every planet is an ellipse with the Sun at one of the two foci.

2. Second Law (Law of Equal Areas): A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. This implies that a planet moves faster when it is closer to the Sun and slower when it is farther away.

3. Third Law (Law of Harmonies): The square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit. Mathematically, this is expressed as:

   T² ∝ a³

   Or, more precisely, for orbits around the Sun:

   T² = (4π²)/(GM) × a³

   Where:

   • T is the orbital period.
   • a is the semi-major axis of the elliptical orbit.
   • π is the mathematical constant pi.
   • G is the universal gravitational constant.
   • M is the mass of the Sun.

These laws were derived empirically by Johannes Kepler from Tycho Brahe's meticulous astronomical observations and were later explained by Isaac Newton's law of universal gravitation.