Kepler’s laws of Planetary Motion
Hey student’s here we are going to deal with the very essential part of gravitation. Sir Johannes Kepler studied the motion of planet and gives his illustration in the form of the three laws. The Kepler’s law are not exactly agreed to Newton’s statement about the circular orbit of the planet around sun but gives more detailed illustration of the gravitational force. Kepler proposed three laws to explain to put his opinion. So let’s learn the laws as follows.
I) Law of orbit: Every planet revolves around the sun in an elliptical orbit, with sun acts as one of the foci of ellipse.
This law describes the path followed by planets around the sun. Practically its verified that, orbits of all planets is elliptical.
The long axis of ellipse is known as major axis; where as short axis is known as minor axis. Ellipse has two foci, sun acts as one of them.
The longest distance between sun an planets is known as perihelion and shortest distance is known as aphelion.
II) Law of equal areas: Line joining planet and sun sweeps out equal areas in equal intervals of time OR the areal velocity of planet is constant.
Imagine the planet takes time ‘t’ to move from point A to point B along its orbit, the area of sector traced by line joining the planet and sun is A1. Now let planer moves from point C to point D in same time ‘t’ as shown in fig below.
Area traced during this is say A2. Then according to Kepler’s law the area swept by planets in two different position but in same interval of time is always same, hence we can say, A1= A2
III) Law of period: Square of period of rotation of planet around the sun is directly proportional to cube of mean distance of planet from the sun.
Time required to complete one rotation/revolution is known as period.
According to Kepler’s 3rd law
For detailed illustration consider the following examples.
Eg: Initial distance between the planet and sun is 1010 km, and period of planet is 4 hours. If the distance between the planet is changed to 1012 km, what will be new period of revolution of the planet.
Eg: Ratio of periods of two planets is 2√2:5√5. Find the ratio of distance of planet
Ans: T1/T2 =(2√2)/(5√5)
r1/r2 =?
By Kepler’s 3rd law, we can write,
hence the ratio of distance of planet will be 2:5