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: Use Kepler's third - law

Kepler's third - law is $T^{2}=k\cdot a^{3}$, where $T$ is the orbital period, $a$ is the semi - major axis (distance from the Sun for a nearly circular orbit), and for objects in our solar system $k = 1$ when $T$ is in years and $a$ is in astronomical units (au). We are given $T = 29.5$ years. Substituting into the formula $T^{2}=a^{3}$, we get $a^{3}=T^{2}$.

Step2: Calculate $a^{3}$

$a^{3}=(29.5)^{2}=870.25$.

Step3: Solve for $a$

$a=\sqrt[3]{870.25}$. Using a calculator, $a\approx9.55$ au.

Answer:

$9.55$