distance from the sun in 47 years

Question

what would be the average distance from the sun in astronomical units of a comet with a period of 47 years?

Answer 1

So consider the orbital periods of the outer planets. Which planets would this object orbit carry it between? Saturn takes roughly 29 Earth Years to orbit and the next planet out Uranus takes 84 years. So if this object had a similarly round orbit the object would be somewhere between the orbits of the two planets. Kepler's laws of planetary motion work whether an object has a nearly circular orbit or a highly elliptical orbit. The cool thing about the average is this doesn't matter. Sure the object might zip out past Uranus before plunging near the Sun, many comets have a very elliptical orbit, its average distance will be the same as an object in a nearly circular orbit of the same orbital period.