best notes ever on Kepler's law
The planetary motion had been observed by astronomers since ancient times. Before
Galileo, all observations of the planet’s positions were made with naked eyes. By the 16th
century a lot of data were available about planetary positions and motion. Johannes
Kepler, studied these data. He noticed that the motion of planets follows certain laws. He
stated three laws describing planetary motion. These are known as Kepler’s laws which
are given below.
1.Kepler's 1st law-:the orbit of a planet is an ellipse with the sun at one of the foci.
the figure shows the elliptical orbit of a planet revolving around the sun. the position of sun indicated by s.
2. Kepler's 2nd law-:the line joining the planet and the sun sweeps equal areas in equal intervals of time. AB and CD are distances covered by the planet in equal time. after equal intervals of time , the position of the planet starting from A and C are shown by B and D respectively.
the straight lines AS and CS sweep equal area in equal interval of time. area ASB and CSD are equal.
3.Kepler's 3rd law-:the square of its period of revolution around the sun directly proportional to the cube of a mean distance of the planet from the sun.
thus, if r is the average distance of the planet from the sun and t is its period of revolution then,
T2
an r3 T2
r3 = constant = K ............. (1)
Kepler obtained these laws simply from the study of the positions of planets obtained
by regular observations. He had no explanation as to why planets obey these laws.
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