Question

The table below shows the average distances of Venus and Earth from the sun. -Name of Planet -Distance from the sun (in AU) Venus 0.72 Earth 1.0 What is the difference between the orbital periods of Venus and Earth? a. 1.72 years b. 1.62 years c. 0.62 years d. 0.28 years

Answer 1

Venus goes around faster than Earth, so its period must be less than Earths 1.0 years. That eliminates the first two answers. My recollection is that T^2 = k r^3, relating period of orbit to radius, so T should be (0.72/1.00)^3/2 = 0.61 of the Earths period, so 0.62 is ans. 

Answer 2

Answer: 0.39 years (Venus orbits the Sun in 0.62 Earth years)

Explanation:

The orbital period is related to the distance of the planet from the star as:

T² = R³

where T is in years and R is in AU.

Orbital period of Venus:

T² = (0.72)³

⇒ T = 0.62 years

Orbital period of Earth

T² = (1.0)³

⇒T = 1 year

The difference between the orbital periods of Venus and Earth is: (1 -0.62) = 0.38 years. Venus orbits the Sun in 0.62 Earth years.