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? saturn’s distance from the sun: au

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? saturn’s distance from the sun: au

Answer

Explanation:

Step1: Recall Kepler's third - law

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

Step2: Rearrange the formula for $R$

Given $T^{2}=R^{3}$ (since $k = 1$), we can solve for $R$ as $R=T^{\frac{2}{3}}$.

Step3: Substitute the value of $T$

We know that $T = 29.5$ 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, $\sqrt[3]{870.25}\approx9.55$.

Answer:

$9.55$