A comet is a loose collection of ices and grit weakly held together by its own gravity. Our idea of what it is is best grasped by imagining a loose pile of snowflakes and frost, mixed with dirt. There may be larger blocks of stone in the mass as well. By "ices" is meant not only water ice but all manner of things that are not ice here on earth: methane, ammonia, carbon monoxide and dioxide, cyanide, nitrogen, etc. This is important because it is the evaporation of these into gas that produces all of the phenomena we see in comets: The coma is essentially a temporary "atmosphere" erupted by this evaporating body, filled with dust that was propelled out along with the vapor. The tail in turn is an extension of the coma blown back by the solar wind. The "pile of snowflakes and dirt" is called the nucleus of the comet and is so tiny (less than10 km in diameter usually and 1-3 km for Comet Hyakutake, the Great Comet of 1996) that it is rarely observed, being invisible within its coma. The nucleus of Comet Hale-Bopp may be 40 miles in diameter - enormous for a comet. Therefore, what we call a comet is actually just the cloud surrounding the important object, which is the nucleus. The coma varies is greatly size from comet to comet and from time to time. Hyakutake's was about 300,000 miles in diameter - greater than the distance from the Earth to the moon, and the tail is many millions of miles long. The coma of Hale-Bopp is now over 2 million miles in diameter, making it one of the largest visible objects in the Solar System. One of the famous trivia about comets is that all of this volume contains much less actual material than a small lake, but against the blackness of space it shows very brightly.

Birth of solar systems: protoplanetary disks against the backdrop of the Orion Nebula (HST WFPC2 Images)
It is this origin that makes comets interesting to astronomers (beyond the shear magnificence of a great comet). It is becoming more and more accepted that the oceans and the atmosphere - and the material of which most living things on Earth are made - had their origin in comets that rained down on the Earth early in its history. To see one or a piece of one is to see tho original stuff of which the planets are made, and everything on them, including us. To see one blown into coma and tail is to see the process in microcosm that ocurred en masse when the Sun first ignited. We who study this know that the proto-Earth's "first dawns", if we can call them such, were lit by the light of the newborn sun and of myriads of comets.
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