Hi I'm a newbie myself. 75 years into my first game. I started out with 3 comets in the Sol system. 2 outside of Pluto and one way way outside of Pluto. Comets do have hi accessibility. Pluto is 6 billion km, Comet 1 and 3 are 8 and 9 billion km out. Comet 2 is 48 billion km out. The F9 page - System generation and Display shows the values for comets. Comets are listed at the end of the list. The Atmospheric Composition column will list the Aphelion distance for any comet. The next column lists the Current Orbital Distance. On the system map page F3, the All Bodies tab does not list comets ( possibly an oversight), but if you are able to click on a comet, Body info will give you some other info about that comet. primarily the bodies year, in the case of my comet 2, 2526 years.
I thought like you do that the comet would be long gone. but 75 years in the life of a 2500+ year comet is miniscule. Either way, I found that you don't really need to absolutely know the orbital period for some good mining. Some additional tips:
I made my cargo ship with 5 holds and enough fuel to get out to Comet 1 and 3. The cargo fleet consisted of 6 ships. 1 mass driver and 5 automines. I ran out of fuel
. Also I didn't invest research into hyper capable engines. Mod 3 ships are hyper capable engines. Set a waypoint just outside the hyper limit of the system and one near the comet. Normal run out to the first WP, turn on hyper, move to the 2nd WP, turn off Hyper, drop off the stuff on the comet and reverse. The fleet zooms out there.
Out of the next 47 systems, only 2 had comets, one with 1 comet and one with 2 comets. The 48th had 12.
. Now I don't have any colonies in those 2 sytems with comets, so I built Asteroid Miner ships. These have Asteroid Mining Modules and Cargo holds and Hyper capable. Sent them to the comet and they mine it. The minerals are still on the comet and I periodically give the load all minerals command. ( cycling the Load All Minerals orders doesn't work after the first time.)