For this task we need to use Kepler's third law:
T = 2*pi*[tex] \sqrt{ \frac{ r^{3}}{G*M} } [/tex]
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
[tex] \frac{Te}{Tv} = \sqrt{ \frac{ Re^{3} }{ Rv^{3} } } [/tex]
From the text we know that Re/Rv = 1/0.723
Which means that:
[tex]Tv = \sqrt{0.723^3} * Te[/tex]
Tv = 0.614 Te
