Kepler (1571-1630) studied the researches of Tycho Brahe for many years and gave the following three laws :
First Law or Law of Orbit : Every planet revolves around the Sun in elliptical orbit and with the Sun at one of the focus.
Fig: Elliptical path around the sun
Second Law or Law of Area’s: An imaginary line drawn from the centre of the Sun to the centre of the planet will sweep out equal areas in equal intervals of time.
Suppose, a planet covers dA area in dt time, areal speed \(\frac{d A}{d t}\) = constant. As shown in the figure (6.19) the time taken by the planet to cover the distance from B to A is same as the time taken to cover the distance from B’ to A’. Hence, area SAB = area SA’ B’. Since, both the areas are same hence the orbital speed of the planet changes. When the planet moves away from the Sun, the speed decreases and when it comes closer it increases. Hence, writing areal speed in terms of angular momentum, the angular momentum of the moving planet remains constant; i.e;
\(\frac{d A}{d t}=\frac{L}{2 m}\)
where L is angular momentum and m is the mass of the planet.
Third Law or law of periods : The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the Sun.
T2 ∝ r3
or T2 = Kr3
where K is a constant and r is the average distance between the planet and the Sun.
Therefore, it is clear that farther the planet from the Sun its time period will be more. This is the reason that the time period of Mercury is very less and that of Neptune maximum.