suppose that your data shows that saturn orbi...
suppose that your data shows that saturn orbits every 29.5 years. to the nearest hundredth of an au, how far is saturn from the sun? saturns distance from the sun: 9.54 au retry
Answer
# Explanation:
## Step1: Recall Kepler's third - law
Kepler's third - law is $T^{2}=a^{3}$, where $T$ is the orbital period in years and $a$ is the semi - major axis (distance from the Sun) in astronomical units (au).
## Step2: Substitute the given period
We know that $T = 29.5$ years. Substituting into the formula $T^{2}=a^{3}$, we get $(29.5)^{2}=a^{3}$.
## Step3: Calculate $(29.5)^{2}$
$(29.5)^{2}=870.25$. So, $a^{3}=870.25$.
## Step4: Solve for $a$
$a=\sqrt[3]{870.25}$. Using a calculator, $a\approx9.54$ au.
# Answer:
$9.54$