Question

Given the equation p2 = a3, what is the orbital period, in days, for the planet venus? (venus is located 0.72 au from the sun?)

Answer 1

Hello,
P=0.72^(3/2)=0.610940...years=223.1398...days

Answer 2

Answer: 223 days

Explanation:

From Kepler's third law, the orbital period of planet around the sun is related with the semi-major axis of the orbit as:

p² = a³

where p is the orbital period in years and a is the semi-major axis/ distance to the star in AU.

It is given for Venus, a = 0.72 AU, then

p = √(0.72 AU)³ = 0.61 years

1 year = 365 days 222.9 days ≈ 223 days