Answer
Icarus' average distance from the Sun is $ 1.62\times 10^8 ~km$
Work Step by Step
$(\frac{s_I}{s_E})^3 = (\frac{T_I}{T_E})^2$
$(\frac{s_I}{s_E}) = (\frac{T_I}{T_E})^{2/3}$
We know that $T_I=410d$ and $T_E=365d$:
$(\frac{s_I}{s_E}) = (\frac{410 ~d}{365 ~d})^{2/3}$
$(\frac{s_I}{s_E}) = (1.12)^{2/3}$
$(\frac{s_I}{s_E}) = 1.08$
$s_I = 1.08\times s_E$
$s_I = (1.08)(1.50\times 10^8 ~km)$
$s_I = 1.62\times 10^8 ~km$
Therefore, Icarus' average distance from the Sun is $ 1.62\times 10^8 ~km$
