suppose that your data shows that saturn orbits every 29.5 years. to the nearest hundredth of an au, how far…

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: au done

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: au done

Answer

Explanation:

Step1: Recall Kepler's third - law

Kepler's third - law is $T^{2}=kR^{3}$, for objects orbiting the Sun, $k = 1$ (in astronomical units and years), where $T$ is the orbital period in years and $R$ is the average distance from the Sun in astronomical units (au).

Step2: Rearrange the formula for $R$

Given $T^{2}=R^{3}$, we can solve for $R$ as $R = T^{\frac{2}{3}}$.

Step3: Substitute the value of $T$

We know $T = 29.5$ years. So $R=(29.5)^{\frac{2}{3}}$. First, calculate $(29.5)^{2}=870.25$. Then find the cube - root of $870.25$. Using a calculator, $R=\sqrt[3]{870.25}\approx9.54$ au.

Answer:

$9.54$