The actual icy core of the comet, called its nucleus, can be anywhere from a mile across to 50 miles across for the rare 'super comets' like Hale-Bopp. By the time they enter the inner solar system and their ices begin to turn to gas, they billow like clouds into objects with cores thousands of miles across and tails that can stretch 10s of MILLIONS of miles as the ices in the nucleus are heated and give off gas and dust clouds and streamers.
Here is the close-up image of a comet body, Wild-2, taken by the Stardust spacecraft during its January 2, 2004 fly-by.
Comet Wild 2 is shown in this image taken by the Stardust navigation camera during the spacecraft's closest approach to the comet on January 2. The image was taken within a distance of 500 kilometers (about 311 miles) of the comet's nucleus with a 10-millisecond exposure. You can see it is a very pitted surface. In other images, you can also see the plumes of faint gas leaving the surface.
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