orbit .
It is called an orbit. A comet has an eccentric or parabolic orbit.
chiken tenders
Comets in space have an orbit path.
An orbit
asteroid belt
An orbit
The solar system
The first person to calculate a comet's elliptical path and predict its return date was Edmond Halley, who did so for the comet now known as Halley's Comet. He predicted its return after observing it in 1682, and it returned as predicted in 1758.
Halley's Comet is following its long orbital path. It is currently a little past the orbit of Neptune, and is not visible.
A comet is often described by Astronomers as a 'Dirty Snowball'. This is because a comet comprises of Ice, from frozen gases mixed with dust and other particulate matter, collected on its orbital path.
Tracking the wayward path of a comet is no easy matter.
The path of a comet around the sun would depend on its mass, speed, and trajectory. It a comet enters the sun's gravitational field at the correct trajectory and speed, it would fall into a roughly circular orbit.