Question

if astronomers discovered a new planet and found its period of rotation around the sun to be 105 years, how long would its semi - major axis length be as it orbited the sun in au? (1 point)
1.84 au
105 au
4.7 au
22.3 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 (in AU). Given \(T = 105\) years.

Step2: Solve for \(a\)

From \(T^{2}=a^{3}\), we can express \(a=\sqrt[3]{T^{2}}\). Substitute \(T = 105\) into the formula: \(a=\sqrt[3]{105^{2}}=\sqrt[3]{11025}\approx22.3\)

Answer:

22.3 AU