Final answer:
The orbital period of a planet with a semi-major axis of 35 AU is approximately 206.231 years.
Step-by-step explanation:
The orbital period of a planet can be determined using Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. For a planet with a semi-major axis of 35 AU, we can calculate the orbital period as follows:
Period^2 = Semi-Major Axis^3
Period^2 = (35 AU)^3
Period^2 = 42,875 AU^2
Period = sqrt(42,875) AU
Using a calculator, we can find the square root of 42,875 as approximately 206.231 AU. Therefore, the orbital period of the planet is approximately 206.231 years.