Grigoriy S. answered • 12/04/21

AP Physics / Math Expert Teacher With 40 Years of Proven Success

We know that in most cases, planetary motion differs little from purely circular motion. Hence we can treat the semi-major axis length as an average distance of the planet from the Sun.

Kepler's third law was published 10 years after he published the previous ones. His *final law relates the average orbital distance of a planet from the Sun to its sidereal period.*

**Kepler's Third Law** *The Harmonic Law * * P*^{2}* = a*^{3 }, where

P is the orbital period of the planet, measured in years,

a - the average distance of the planet from the Sun in astronomical units.

*An astronomical unit (AU) is the average distance between the Earth and the Sun 1.496 x 10*^{11}** m**.

So in case of the Venus we have

P^{2} = (0.72)^{3}

If we find at firs the cube of .72 and then take the square root of it, we will get the answer.

Hence, it takes Venus ** 0.61 year** to orbit the Sun. The right answer

**(A)**.