Plz explain in brief Kepler’s laws of planetary motion:

1.Law of Orbits: Each planet revolves around the Sun in an elliptical orbit with Sun as one of the foci.

2.Law of Areas: This law states that the radius vector from the Sun to the planet sweeps out equal areas in equal time intervals, i.e.,  the areal velocity of a satellite is constant.

3.Law of periods: Its states that the square of the time period of the planet about the Sun is directly proportional to the cube of the semi major axis of the planet’s trajectory or simply the mean distance from the planet to the Sun.

LAW OF ORBITS : ALL THE PLANETS REVOLVE AROUND THE SUN IN ELLIPTICAL ORBITS WITH SUN AT ONE  OF  THE  FOCII.

LAW OF AREAS : EACH PLANET SWEEPS EQUAL AREAS IN EQUAL INTERVALS OF TIME.THIS MEANS, FOR A PLANET 

                                                                  AREA COVERED  / TIME TAKEN (A / T) = K(CONSTANT) 

LAW OF PERIODS : FOR A PLANET SQUARE OF THE TIME PERIOD IS DIRECTLY PROPORTINAL TO CUBE OF THE SEMI MAJOR AXIS

                                                                            T²=KR³

PROOF: FOR CELESTIAL BODIES CENTRIPETAL FORCE IS EQUAL TO GRAVITATIONAL FORCE EXERTED BY THE SUN.

                                                                                         mW²R=GMm/R²      (W means omega)

                                                                                                   W=2¶ / T                

                                                                                                   4¶²Rm/T² =GMm/R²

                                                                                                         T² = 4¶² R³/GM

                                                                              4¶² /GM  IS CONSTANT . SO, T² IS DIRECTLY PROPORTINAL TO R³