Final answer:
Among the hypothetical options provided, Planet Y with an orbital period of 145 days is the one that orbits closest to its star. The semi-major axis of an orbit can be determined using Kepler's Third Law, with shorter periods corresponding to smaller semi-major axes, meaning closer orbits.
Step-by-step explanation:
The student has asked which exoplanet orbits closest to its star among a list of given options. To determine which planet is closest, we need to consider the orbital periods of these exoplanets. Orbiting closest to a star generally means the planet has the shortest orbital period due to the gravitational forces involved.
However, the question provided is not specific to any particular exoplanets and instead instructs students to consider an exoplanetary system with two known planets, Planet X and Planet Y. In this hypothetical scenario, Planet Y, which orbits its star in 145 days, is closer to the star than Planet X which has an orbital period of 290 days. This is because shorter orbital periods typically correspond to closer orbits.
For planets orbiting a star with the same mass as the Sun, the semi-major axis of their orbits can be estimated using Kepler's Third Law, which relates the orbital period of a planet to its distance from the star. Without specific calculations, it's clear that Planet Y with the shorter orbital period will have a smaller semi-major axis and thus be closer to the star.