Halley's comet has nearly reached aphelion right now, which is the most distant point from the Sun of its orbit. Kepler's third law shows how in a very elongated elliptical orbit, as it's typical with periodic comets, the orbital velocity near its aphelion is very low. Hale-Bopp it's moving towards its aphelion which is even farther than Halley's.
So, they're not fixed in its orbits, they're just extremely slow, as you can see if you accelerate time speed 106 times.
Comet tails are the result of dust particles and gases, heated by solar radiation. The amount of energy that those comets receive when they are far from the Sun is not enough to make that tail apparent, in fact we could say that there's a direct correlation between their distance from the Sun and their tail appearance, also depending on the relative composition of the comet.
SpaceEngine depicts that.
"Time is illusion. Lunchtime doubly so". Douglas N. Adams
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