Question

Venus has an average distance to the sun of 0.723 AU. In two or more complete sentences, explain how to calculate the orbital period of Venus, and then calculate it.

Answer 1

For this task we need to use Kepler's third law:

T = 2*pi*$\sqrt{ \frac{ r^{3}}{G*M} }$

where T is orbital period in seconds, r is Venus's semi-major axis, G is gravitational constant and M is mass of the sun.

Distance from earth to sun is 1AU so if we know earths period and distance from the sun we can calculate Venus period.
Te-earths period
Tv-venus period

$\frac{Te}{Tv} = \sqrt{ \frac{ Re^{3} }{ Rv^{3} } }$

From the text we know that Re/Rv = 1/0.723

Which means that:
$Tv = \sqrt{0.723^3} * Te$

Tv = 0.614 Te