Comet Encke or Encke's Comet (official designation: 2P/Encke) is a periodic comet that completes an orbit of the Sun

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 once every three years — the shortest period of any known comet. It was first recorded by Pierre Méchain

Pierre Méchain

Pierre François André Méchain was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep sky objects and comets.-Life:...

 in 1786, but it was not recognized as a periodic comet until 1819 when its orbit was computed by Johann Franz Encke

Johann Franz Encke

Johann Franz Encke was a German astronomer. Among his activities, he worked on the calculation of the periods of comets and asteroids, measured the distance from the earth to the sun, and made observations on the planet Saturn.-Biography:Encke was born in Hamburg, where his father was a...

; like Halley's Comet, it is unusual in being named after the calculator of its orbit rather than its discoverer.
As its official designation implies, Encke's Comet was the first periodic comet discovered after Halley's Comet (designated 1P/Halley).