Q:  Suppose one comet's orbit has a semi-major axis of size 30,000 AU.
          How long does it take to make one full revolution?


            Using Kepler's Third Law,

                   P^2    =   a^3   

                  
                   P      =   a^(3/2)

            So, plugging in the numbers,

                   P      =  (30,000)^(3/2)  =  5.2 million years



  Q:  The comet spends almost all of that time at the very farthest
          reaches of its elliptical orbit, and very little time
          flying past Jupiter, Mars, Earth, and so forth.

          Why?  Is there some scientific justification for moving
          very slowly when very far from the Sun?


             Yes, there is.  Newton's Law of Universal Gravitation
             states that the gravitational forces on an object so far
             from the Sun will be very small.  Therefore, the acceleration
             of a comet when it is far from the Sun will be tiny.
             That means that its velocity will change very, very slowly,
             so it will take a long time to turn around and come back.

             Kepler's Second Law implies the same thing: the speed of an
             object orbiting the Sun will be fast when it is close,
             but very slow when far away.