Question

Venus orbits the Sun with a period of 0.6152 years. What is its average distance (in AU) from the Sun? (Round your answer to at least four significant figures.)

Answer 1

T = time period of orbit of venus around sun = 0.6152 years = 0.6152 x 365 days = 0.6152 x 365 x 24 hours = 0.6152 x 365 x 24 x 3600 sec = 1.94 x 10⁷ sec

r = average distance of venus from sun = radius of the orbit

M = mass of sun = 1.989 x 10³⁰ kg

using kepler's third law

T² = 4$\pi$² r³/(GM)

inserting the values

(1.94 x 10⁷)² = 4(3.14)² r³/((6.67 x 10^-11)(1.989 x 10³⁰))

r = 1.0818 x 10¹¹ m

we know that

1 AU = 1.5 x 10¹¹ m

hence

r = (1.0818 x 10¹¹ m) (1 AU/(1.5 x 10¹¹ m))

r = 0.7212 AU