Final answer:
Planet X's likely orbit around the Sun can be described as an ellipse, with the Sun at one focus of the ellipse. Kepler's laws of planetary motion provide the basis for understanding the characteristics of this orbit, including the relationship between orbital period and mean distance from the Sun.
Step-by-step explanation:
Planet X's likely orbit around the Sun can be described as an ellipse, with the Sun at one focus of the ellipse, according to Kepler's first law of planetary motion. Since Planet X is located at an average distance of 15 AU from the Sun, which is approximately midway between Saturn (9.5 AU) and Uranus (19.2 AU), it would have an elliptical orbit with the Sun at one focus.
Kepler's third law of planetary motion states that the ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun. This law relates the orbital period (in years) to the cube of the mean distance (in AU) from the Sun. By calculating and plotting the expected Keplerian period for mean distances from 0.1 to 32 AU, we can see the relationship between planet distance and orbital period.
However, without specific information about the orbital period of Planet X, we cannot provide an exact calculation or plot for its orbit. Nonetheless, based on Kepler's laws and the given information, we can conclude that Planet X's likely orbit would be an elliptical path, with the Sun at one of the foci.