data that he compiled were analyzed later by his assistant Johannes Kepler ( – ) and eventually the analysis led to the deduction of the laws of the planetary motion. These laws are termed as ‘Kepler’s laws of planetary motion’. - - - - Unit Gravitation where, T is the time period of revolution for a planet and a is the semi-major axis. Physically this law implies that as the distance of the planet from the Sun increases, the time period also increases but not at the same rate.
In Table . , the time period of revolution of planets around the Sun along with their semi-major axes are given. From column four, we can realize that T a is nearly a constant endorsing Kepler’s third law. .
Law of area: The radial vector (line joining the Sun to a planet) sweeps equal areas in equal intervals of time. In Figure . , the white shaded portion is the area D A swept in a small interval of time D t, by a planet around the Sun. Since the Sun is not at the center of the ellipse , the planets travel faster when they are nearer to the Sun and slower when they are farther from it, to cover equal area in equal intervals of time.
Kepler discovered the law of area by carefully noting the variation in the speed of planets. . Law of period: The square of the time period of revolution of a planet around the Sun in its elliptical orbit is directly proportional to the cube of the semi-major axis of the ellipse. It can be written as: a ∝ ( .
) a constant = ( . ) Radial vector One Month One Month ( t) Planet Sun Planet’s Orbit All white shaded area are equal Both areas ( A) are equal Sun January February March April May June July August October November December Radial vector Su n y Rad Figure . Motion of a planet around the Sun depicting ‘law of area’. Table .
The time period of revolution of the planets revolving around