State and explain the Kepler’s laws of planetary motion.

To explain the motion of planets, Kepler formulated three fundamental laws:

1. Law of Orbits (First Law):
Each planet revolves around the Sun in an elliptical orbit, with the Sun located at one of the two foci.
– Planets follow an elliptical path around the Sun. An ellipse has two foci, with the Sun situated at one focus.
– The points called perihelion (closest to the Sun) and aphelion (farthest from the Sun) mark the shortest and longest distances from the Sun, respectively.
– While the orbits of Neptune and Venus are nearly circular, other planets have slightly elliptical orbits, which can be approximated as circular.

2. Law of Areas (Second Law):
The radius vector drawn from the Sun to a planet sweeps out equal areas in equal intervals of time.
– This indicates that the areal velocity (area covered per unit time) of a planet around the Sun remains constant.
– For example, if a planet takes the same amount of time to move between two points when near the Sun and two points farther away, the areas swept out during both intervals are equal.
– A planet moves faster when closer to the Sun and slower when farther away, covering unequal distances in the same time.

3. Law of Periods (Third Law):
The square of the time taken by a planet to complete one orbit around the Sun is proportional to the cube of the semi-major axis of its orbit.
– This means that planets farther from the Sun take significantly longer to complete their orbits than those closer to the Sun.