Question

Given the equation P2 = A3, what is the orbital period, in years, for the planet Saturn? (Saturn is located 9.5 AU from the sun.)

Answer 1

\[P^2 = a^3 \]
is valid for any object orbiting the sun, where P is the orbital period (in years), and a is the length of the semimajor axis (ie the average distance from the sun). We are given a=9.5 AU, so we make P by itself:
\[P=\sqrt{a^3}=\sqrt{9.5^3}\approx29.28097\ yr\]
Where the negative answer is unphysical (negative time? What?!). Of course, we were only given two significant figures in the question, so must only give back two significant figures: P=29 yr

Answer 2

thank you