If a hypothetical planet in our Solar System had a sidereal period of 11.1 Earth years and a circular orbit, how far from the Sun in Astronomical Units would it be? Enter your answer to the nearest 0.01 AU.
Using convenient units of 1 AU for earth orbit and mass of sun=1, and P=1 earth year, you know that
R^3 = P^2
using 11.1P,
(11.1P)^2 = 123.21P^2 = (4.976R)^3
So, the distance is 4.967 AU