Given the equation P^2 = A^3, what is the orbital period, in years, for the planet Saturn? (Saturn is located 9.5 AU from the sun.)

5 years
29 years
229 years
500 years

(If you could explain the process on how to get the answer too, that'd be awesome. Thanks.) :)

Question

Given the equation P^2 = A^3, what is the orbital period, in years, for the planet Saturn? (Saturn is located 9.5 AU from the sun.)

5 years
29 years
229 years
500 years

(If you could explain the process on how to get the answer too, that'd be awesome. Thanks.) :)

dape · Answer

We know that earth has a orbital period of 1 year, and that it's 1 AU from the sun by definition. Since saturn is 9.5 times further away, it's orbital period must be 9.5^(3/2)≈29 times longer.

anonymous · Answer

Oh, so it's just 29 years? Also, I'm sorry, but I still don't quite understand how you got to that number.

dape · Answer

You can solve for P in the equation by taking the square root of both sides [P=√A^3]. Then A is just the semi-major axis of the orbit, which is 9.5 AU in this case.

anonymous · Answer

Oh, think I got it. :) Thanks!