Answer
The period of Mars is about 2.8 times the period of Venus.
Work Step by Step
$T^2 = c~r^3$, where $c$ is a constant
$T = \sqrt{c~r^3}$
We can write an expression for the period of Mars:
$T_m = \sqrt{c~r_m^3}$
We can write an expression for the period of Venus:
$T_v = \sqrt{c~r_v^3}$
We can divide the period of Mars by the period of Venus:
$\frac{T_m}{T_v} = \sqrt{\frac{c~r_m^3}{c~r_v^3}}$
$\frac{T_m}{T_v} = \sqrt{\frac{(2~r_v)^3}{r_v^3}}$
$\frac{T_m}{T_v} = \sqrt{8}$
$\frac{T_m}{T_v} = 2.8$
The period of Mars is about 2.8 times the period of Venus.
