The motion of a comet
Keplerís Laws were shown by Newton to explain the motion of comets. They orbit the Sun in highly elliptical orbits coming close to the Sun for a while and then moving off to the outer reaches of the Solar System to return many years later.
We only see a comet for a short time because they move fast when they are close to the Sun but very slowly in the outer parts of their orbit, see Keplerís second law. One of the most famous comets, Halleyís comet returns every 75 years.
1. The planets move in ellipses with the Sun at one focus
2. A line drawn from the planet to the Sun sweeps out equal areas in equal times
3. The ratio of the square of the period (T) of the planet about the Sun to the cube of the mean orbit radius (r) is a constant or T2/r3 = constant. (Notice that r3/T2 is also constant)