Question

if a planet had a semi - major axis length of 2.3 au as it orbits the sun, what would be its period in years? (1 point)
1.74 years
2.3 years
3.49 years
12.2 years

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 astronomical units (AU)). Given \(a = 2.3\) AU.

Step2: Calculate \(T\)

We have \(T=\sqrt{a^{3}}\). Substitute \(a = 2.3\) into the formula: \(a^{3}=(2.3)^{3}=2.3\times2.3\times2.3 = 12.167\). Then \(T=\sqrt{12.167}\approx3.49\)

Answer:

3.49 years