Physics: Orbital Period of an Asteroid

Question

An asteroid is discovered in a nearly circular orbit around the Sun, with an orbital radius that is 1.89 times Earth's. What is the asteroid's orbital period in terms of Earth years?

Answer 1

The period is proportional to the orbital radius to the 3/2 power.

Te = 1 year

T/Te = (r/re)^3/2 = (1.89)^1.5 = 2.60 years