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 200 years, what would be the radius of its orbit (assumed to be circular)?
A) 2828 au
B) 34.2 au
C) 342 au
D) 200 au

Question

Quizplus · Accepted Answer

Using Kepler's third law, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit, $T^2 \propto r^3$, we can compare the unknown planet's orbit to that of Earth's. Given Earth's orbital period is 1 year and its average distance from the Sun is 1 astronomical unit (au), for the unknown planet with a sidereal period of 200 years, the equation can be set up as $(200^2) = r^3$. Solving for r gives approximately 34.2 au, indicating the radius of its orbit.

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