Question

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

Explanation:

Step1: Apply 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). Given \(T = 29.5\) years.

Step2: Solve for \(a\)

We have \(a=\sqrt[3]{T^{2}}\). Substitute \(T = 29.5\) into the formula: \(a=\sqrt[3]{29.5^{2}}\). 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:

\(9.55\)