Final answer:
Long-period comets come directly from the Oort cloud, which is a vast collection of frozen chunks located on the distant fringes of the solar system. The characteristic that suggests their origin from the Oort cloud is their highly eccentric orbits with aphelia values near 50,000 AU.
Step-by-step explanation:
Long-period comets, which are comets with orbital periods longer than about a century, are believed to come directly from the Oort cloud. The Oort cloud is a vast collection of frozen chunks located on the distant fringes of the solar system. The characteristic of long-period comets that suggest their origin from the Oort cloud is their highly eccentric orbits. These comets have aphelia (points farthest from the Sun) with values near 50,000 AU, which is more than a thousand times farther than Pluto. By following their orbits backward, astronomers can calculate the initial distances from which these comets come.