Question

pluto behaves like a planet when we consider its period and the semi - major axis length of its orbit around the sun. pluto has a semi - major axis length of 39.5 au as it orbits the sun. what is its period of rotation around the sun? (1 point) 248 years 39.5 years 61,629 years 11.6 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 \( a = 39.5\ AU \).

Step2: Calculate \( T \)

Substitute \( a = 39.5\) into \( T^{2}=a^{3}\).
\( T^{2}=(39.5)^{3}=39.5\times39.5\times39.5 = 61629.875\)
Then \( T=\sqrt{61629.875}\approx248\)

Answer:

248 years