<span>The orbital period will be 5.196 earth years.
The period of an orbit is proportional to the square root of the cube of the semi-major axis. The semi-major axis of earth is 1 AU (actually 1.000001018 AU, but for this problem 1 is close enough). The hypothetical planet will have a semi-major axis of 3 AU. So making the ratios with earth's year being 1, earth's semi-major axis being 1, the planet's year being y, and the planet's semi-major axis being 3, we get the following ratio.
1 / 1^(3/2) = y / 3^(3/2)
Raise the denominators to the 3/2 powers.
1/1 = y/5.196
Multiply both sides by 5.196
5.196 = y
So the orbit period will be 5.196 earth years.</span>
