Final answer:
Comets have a broad range of orbital periods due to the vast difference in their original orbits, which are influenced by gravitational interactions with planets and their origins from different regions of the solar system, such as the Oort cloud for long-period comets and the Kuiper belt for some short-period comets.
Step-by-step explanation:
Comets have a broad range of orbital periods because they are influenced by different factors in the solar system. Comets generally have orbits of larger size and greater eccentricity than those of the asteroids, normally with an eccentricity of 0.8 or higher. Given their elongated paths, according to Kepler's second law, comets spend the majority of their orbital period far from the Sun, travelling slowly. As they draw near to perihelion, the closest point to the Sun, their speed increases significantly.
There are two main classes of comets: short-period (less than a century) and long-period comets (thousands of years). Short-period comets, like Comet Halley, often have orbits affected by gravitational interactions with the giant planets, especially Jupiter, forming the so-called Jupiter-family comets. Long-period comets, on the other hand, originate from the distant Oort cloud, a spherical cloud of icy bodies at the fringe of the solar system. Periodic comets may also come from the Kuiper Belt as Centaurs.
The wide variety in the sources and influences (such as planetary gravitation) result in the significant diversity in orbital periods. Additionally, interactions within the solar system can lead to a comet being ejected, impacting a planet, or having its orbit shortened, thus changing its orbital period and potentially making it a short-period comet.