111P/Helin–Roman–Crockett
111P/Helin–Roman–Crockett is a periodic comet in the Solar System. It was discovered by Eleanor and Ron Helin on 5 January 1989 from images obtained on the 3rd and 4th of that month. It is a Jupiter family comet known for extremely close approaches to Jupiter being a Quasi-Hilda comet. During these approaches, it actually orbits Jupiter. The last such approach was in 1976, the next will be in 2071. The Jovian orbits are highly elliptical and subject to intense Solar perturbation at apojove which eventually pulls the comet out of Jovian orbit  for the cycle to begin anew. Simulations predict such a cycle is unstable, the object will either be captured into an encounter orbit (e.g. Shoemaker-Levy 9) or expelled into a new orbit which does not have periodic approaches. This implies that 111P's orbit is recent within the past few thousand years. It fits the definition of an Encke-type comet with (T > 3; a < a).