Question

Kepler's third law of planetary motion states that :(Symbols have their usual meaning)
A \[{{v}_{0}}=\sqrt{Rg}\]
B \[{{F}_{12}}=-{{F}_{21}}\]
C\[{{r}^{2}}\alpha {{T}^{3}}\]
D\[{{r}^{3}}\alpha {{T}^{2}}\]

Answer 1

Hint: Kepler gave three laws that describe how planets and other heavenly bodies orbit around the earth. There are three laws and each law gives a description of the motions of the planets around the sun. They were given in 17 th century.

Complete step by step answer:
Kepler third law is also known as the law of the orbits. It states that the square of the time taken by the planet to complete one revolution around the sun is proportional to the cube of the semi major axes of their orbits. Stating it mathematically, \[{{r}^{3}}\alpha {{T}^{2}}\].

So, the correct option is (D).

Additional information:
The first law of Kepler states that the orbit of the planets around the sun is elliptical in shape. The sun is located at one of the foci always and the planet to Sun distance is constantly changing as the planet goes around its orbit.
The second law of Kepler states that there exists an imaginary line joining the planet with the sun and it sweeps out equal areas of space during equal time intervals as the planet orbits.

Note:As to check the validity of the third law we can see it states that period increases with the radius of the orbit. So, opposite of that must also, hold. Mercury which is closest to the sun takes 88 days to complete one revolution and earth which is far away as compared to the mercury takes 365 days to complete one revolution.