Final answer:
The object should be classified as a long-period comet because of its highly eccentric orbit and rare appearances near Mars's orbit, which suggest an origin from the distant Oort cloud.
Step-by-step explanation:
Based on the description of an object with a highly eccentric orbit that is only visible from near the orbit of Mars every 400 years or so and has a faint jet of volatile compounds, the classification of this object would be a long-period comet. This category of comets comes from a distant reservoir of icy objects called the Oort cloud, which surrounds the Sun. These comets are considered primitive bodies that have been preserved unchanged for billions of years. The object’s long visibility interval of several hundreds of years indicates it is not a short-period comet, which tend to have orbits that bring them back into the inner solar system on a timescale that is less than a couple of centuries.