This is because the material is not left behind by the comet, but blow away from the comet by the solar wind which exerts pressure on the dust particles and gases that depart from the nucleus. Cometary Orbits Like the Earth, comets are in orbit around the sun. They are members of our solar system. Most of them are in parabolic orbits around the sun, although a few of them are hyperboloid. This is different from the Earth and other planets which are in an elliptical orbits around the sun.
Comets approach the sun briefly - closest approach to the sun of all objects is called parahelion.
When objects are at their farthest distance it is called aphelion. Thus we see comets when they are close to the sun. The comet with the shortest known period is comet Encke, it returns to the sun every 3.3 years. The comet with the longest period we have established is comet Rigollet which orbits in 151 years. The most famous periodic comet is comet Halley, one of the few comets not known by the name of it's discoverer, but by the astronomer who first noted its periodosity and calculated its return.