As Venus orbits the sun, it’s semi-major axis length is 0.72 AU. how long does it take Venus to orbit the sun in years?

Question

A) 0.61 years

B) 0.37 years

C) 0.80 years

D) 0.72 years

Answer 1

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 P² = a³ , 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 10¹¹m.

So in case of the Venus we have

P² = (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).