If a tenth planet (tentatively predicted to exist on the basis of perturbations in the orbits of Uranus and Neptune)were to be discovered with a sidereal period of 125 years,what would be the radius of its orbit (assumed to be circular)?
A) 8.55 AU
B) 125 AU
C) 1 AU
D) 25 AU

Question

Quizplus · Accepted Answer

The period, P, of an object in circular orbit around the sun can be related to the radius, r, of its orbit using Kepler's third law: P^2 = 4π^2r^3/GM, where G is the gravitational constant and M is the mass of the sun. Solving for r gives r = (P^2GM/4π^2)^(1/3). 
Substituting P = 125 years and using the values G = 6.674 × 10^-11 m^3/kg s^2 and M = 1.989 × 10^30 kg for the gravitational constant and mass of the sun, respectively, we get r ≈ 25 AU. Therefore, the correct answer is D, 25 AU.

If a Tenth Planet (Tentatively Predicted to Exist on the Basis