My classroom lecture on comets consisted of a discussion similar to the text immediately below, illustrated by the pictures following the text, so students who missed the lecture could get a basic idea of what they missed by reading this page in its entirety.

 Comets are basically dirty snowballs, sometimes hard and icy, sometimes soft and fluffy, originally formed in the outer Solar System, at or beyond the orbit of Jupiter, then flung to the outer edges of the Solar System during the period of heavy bombardment more than 4 billion years ago, which have recently had their orbits changed by passing stars or collisions with other cometary objects, so that they can once again enter the planetary regions.
 The 'snow' in comets is a mixture of various ices -- materials that we are used to as liquids or gases, but which are frozen at the low temperatures in the outer Solar System -- such as water, methane, ammonia, carbon dioxide, hydrogen cyanide, and various hydrocarbon coumpounds. When the comet is far from the Sun, all these materials are frozen solid, and the 'comet' is a mere speck in the sky, a dot too small and faint to even notice as an apparent starlike object. But when the comet nears the orbits of the outer planets, the more volatile (more easily vaporized) ices begin to evaporate, and escape the comet, into interplanetary space.
 As long as the comet is far from the Sun, the amount of gas lost in this way is negligible, and although we might be able to see the pinprick of light reflected by the solid nucleus (as the actual body of the comet is called), we wouldn't notice the gas itself. But as the comet gets closer to the Sun, and more gas boils off of it, we may start to see a small 'fuzzball', slowly moving among the stars.
 Analysis of the light given off by the 'fuzz', or glowing gas surrounding the nucleus, tells us that this 'head' or coma is usually made of pieces of molecules which were broken down by the absorption of high-energy radiation (ultraviolet radiation and blue and violet light). These pieces are often electrically charged, as their breakdown may not uniformly distribute the electrons between the original atoms of the molecule; if so, they are referred to as ions, and we can refer to the gas as an ionized gas, or if most of the gas particles are ionized, as a plasma.
 To a certain extent the gas escaping from the comet will move outwards in all directions, giving it a more or less spherical shape, so the coma or head usually appears more or less round. But as it moves outward it begins to encounter the Solar Wind, a thin gas streaming away from the Sun at hundreds of miles per second.
 Normally, there aren't any direct encounters between the particles in the Solar Wind (mostly pieces of hydrogen atoms -- bare atomic nuclei, or protons, and free electrons), and those in the head of the comet, because the gas in the head is extremely rarefied (low density). In fact, it is often said that a comet (meaning the gas escaping from the nucleus) is as close to nothing as something can get and still be something, because it is typically billions or trillions of times thinner than the gases at the surface of the Earth. And if that aphorism were true then the Solar Wind would be so close to nothing that it really was nothing, as it is billions or trillions of times thinner yet; and with so few particles in either the Solar Wind or the coma, the Solar Wind essentially blows right through the coma without even noticing that it is there, and vice versa.
 However, there is an interaction between the two gases, thin as they are, because the Solar Wind, like the coma, is made almost entirely of charged particles; and as it streams away from the Sun, it carries a small part of the Solar magnetic field out into space, forming the interplanetary magnetic field. The strength of the field is very low in any given place -- typically tens of thousands of times weaker than the magnetic field of the Earth -- but it is strong enough that as it is pulled through the head of the comet, it can interact with the charged particles in the coma, and start dragging them outwards, away from the Sun, just as it is being dragged outward by the Solar Wind. In other words, although the Solar Wind cannot directly influence the gas in the coma, its interaction with the interplanetary magnetic field allows it to transfer some of its outward momentum to the coma, and after a while, the gas in the coma is no longer streaming outward in every direction, but moving more and more outward, away from the Sun faster and faster, until it is flowing outward at tens of miles per second, never to return to either the comet that created it, or the star that the comet continues to orbit.
 Strictly speaking, the gas in the tail, as it is called, streams outward for tens of billions of miles, in a more or less contained stream, due to its interaction with the Solar Wind, and the interplanetary magnetic field. But we only see it while it is still close to the comet and reasonably dense, so that it can absorb and reradiate (as fluorescence) large amounts of light. If the cometary nucleus is very large, and the comet gets close to the Sun, so that thousands of tons of gas are lost every day, the gas tail may be visible for as much as a hundred million miles, stretching outward as far as the semi-major axis of the Earth's orbit. Usually, however, the gas isn't as abundant, and the tail isn't visible for more than a few tens of thousands of miles; and of course, while the comet is still far from the Sun, and even the head is too faint to notice, the tail is completely unobservable as well.
 Since the gas in the coma and tail consists primarily of ionized particles, the gas tail may be referred to by that name, or as the 'ion tail' or 'plasma tail'. These different names do not refer to different tails, but to the same tail, simply taking into account the fact that the gas particles are mostly ions, and a gas made mostly of ions is called a plasma. Whatever the tail is called, it stretches outward, directly away from the Sun, because that is the direction the Solar Wind is going, and the direction that it drags the interplanetary magnetic field outward, from the Sun.
 In addition to the ice in comets, however, there is 'dirt', which may consist of rocky materials (silica dusts and the like), or more often, numerous hydrocarbon compounds, such as soots. This dust, or dirt, is mostly in the form of microscopic bits, but can include pieces of substantially larger size, depending upon the force with which the gas erupted from the nucleus, when the ices evaporated.
 nbsp;   Unlike the gas, the dust particles are essentially electrically neutral, and whatever charge they may have is insignificant in comparison with their mass, which ranges from hundreds of millions or trillions of times greater than that of the gas molecules for microscopic bits of dust, to billions of trillions of times greater, for bits large enough to see without a microscope, such as sand or pebble-sized chunks of material. The large mass and relatively low charge of the dust particles make it impossible for the Solar Wind to give them any effective outward push, so as they slowly drift away from the comet, they should tend to form a roughly spherical distribution, much the same shape as the coma. And they do just that for a while; but after a while, they also begin to drift more outward, than in other directions, because of a very unlikely force -- namely, the outward push of the light which reflects off of them.
 Since light has no mass, we often think of it as being completely insubstantial, but it does carry energy and momentum, as it streams into space, and when light reflects off the cometary dust, it gives them a very tiny nudge outwards. Any given photon (the smallest piece of light, for a given wavelength or color) gives a particular dust grain an almost inconceivably small nudge; but as one photon after another bounces off the particle -- that is, as light reflects off it, day after day -- the particle slowly moves a little outward, compared to the path it would have followed in the absence of the photons' push.
 The outward motion that the dust grains, sand grains and pebbles receive in this way is completely insignificant in comparison with the orbital velocity of the comet, which the dust essentially retains even as it slowly spreads outward, away from its parent body. So the dust continues to orbit the Sun, relatively close to the comet, but gradually a little further and further out, compared to the comet's distance from the Sun. This effect is greater for smaller particles, so the smallest particles spread outwards the most, and the larger particles the least, but all of them eventually move outwards by as much as several tens or hundreds of thousands of miles (a large distance by our standards, but nothing at all compared to the size of the Solar System). So in addition to the comet itself, there is a huge cloud of debris of various sizes following the comet's orbit, though mostly a little further out than the original orbit.
 You may recall that according to Kepler's Third Law of Planetary Motion, larger orbits require slower orbital velocities and longer orbital periods; and since the slowly spreading dust tail is further out from the Sun than the nucleus, the particles in the tail, as they move outward must gradually lose part of their orbital speed and fall behind the nucleus more and more, because they are now following a larger path, at a slower orbital velocity. In other words, the dust tail also streams outward from the Sun -- just not as fast or in quite the same way as the gas tail. Whereas the gas tail streams directly away from the Sun at tens of miles per second, never to return to the inner Solar System, the dust tail continues to follow the cometary orbit, but in a curved arc that heads outward, away from the Sun, and backwards, along the path of the comet.
 For those comets whose perihelion distance is less than the size of our orbit, it is not unusual for us to approach some point in their orbit, at some point in our orbit around the Sun. And given the broad swath of material lost by the comet each time it goes round the Sun, it would hardly be surprising if some of the material lost by the comet might pass even closer to our orbit than the comet, and that it might even run into our atmosphere, causing a streak of light in the sky, called a meteor. And in fact, over 90% of meteor trails are caused by debris lost by comets in the last few decades or centuries, which is still following more or less the same path as the comet which lost the material. As a result, when you see a 'shooting star' or 'falling star', what you are normally seeing is the heat and light radiated by air heated by the passage of a small piece of a comet, and the gas produced by the vaporization of that piece, as it passes through our upper atmosphere at speeds of tens of thousands of miles per hour.

 A view from the Deep Impact (now EPOXI) spacecraft as it swept past Comet Hartley 2 on November 4, 2010. At that time the spacecraft was just over 400 miles from the 1.2 mile long cometary nucleus, and traveling 27 thousand miles an hour. The comet orbits the Sun every six years, and must have passed perihelion hundreds of times, so it is surprising how active it still is (most short-period comets fade into negligible activity fairly quickly). In this image dozens of jets of (mostly carbon dioxide and hydrogen cyanide) gas are seen spewing out of areas lit by the Sun (which is off to the right), and along the terminator (the region where the Sun is rising or setting, as the comet rotates). One interesting feature of the comet is its appearance, which is strongly reminiscent of asteroid Itokawa 2 -- rugged ends covered with rubble-like chunks tens of yards in size and (in this case a quarter-mile wide) smooth neck, presumably covered with much finer material. (The rock sticking up out of the right edge of the neck, into the sunlight, is about 100 yards high.) The image shown here, though the most detailed of the early flyby images, was taken with the spacecraft's medium resolution camera; higher-resolution images will be posted as soon as available.

 A member of the Kreutz sungrazer family of comets passed the and was pulled apart and vaporized in early January of 2010. The Kreutz family is named after a 19th century German astronomer, Heinrich Kreutz, who showed that a number of comets with exceptionally small perihelion distances had similar orbits, and must consist of the remnants of a great comet which passed close to the Sun in 1106. Many of the great comets of the last few centuries were Kreutz sungrazers, such as 1965's Ikeya-Seki (shown below) -- which was perhaps the brightest comet in the last thousand years -- and many more such comets are expected to be observed in centuries to come. Since the launch of the SOHO satellite, which allows observations of relatively faint sungrazers, hundreds of small members of the family have been seen nearing the Sun, only to be destroyed by its heat and tidal forces. (LASCO, SOHO Consortium, NRL, ESA, NASA, apod100116)

 The brightest comet in modern history, Ikeya-Seki was visible in full daylight when nearest the Sun. Like many other great comets of the last few centuries, Ikeya-Seki was a Kreutz sungrazer, passing less than 300,000 miles above the surface of the Sun on October 21, 1965. This image was taken early the following year (note that the tail, blown outward by the solar wind, is streaming away from the Sun, and therefore ahead of the comet's motion). Like other Kreutz sungrazers, Ikeya-Seki's aphelion distance is around 200 AUs, so it will be about a millennium before it returns to the inner solar system.
 The tremendous brightness of comets such as Ikeya-Seki is due to their near approach to the Sun. When further, they are much fainter, so the image shown here gives little indication of its far more spectacular appearance a few months earlier. In fact, the comet was only a very faint telescopic object when it was discovered, less than five weeks before its greatest brilliance. Given that, and an uncertainty of nearly two hundred years in its orbital period, the next approach of Ikeya-Seki may well be as great a surprise as the last one. (Roger Lynds/AURA/NSF/NOAO)

 Comet McNaught observed in evening twilight, on January 3, 2007. At that time, the comet was second magnitude and rapidly brightening, as it approached the Sun. On January 12 it passed perihelion, only 16 million miles from the Sun (about half Mercury's perihelion distance), and reached temperatures well in excess of a thousand degrees, causing it to give off prodigious amounts of gas (and dust mixed with the vaporized ices). (Michael Jager, Gerald Rhemann, apod070105)

 Comet McNaught observed in full daylight, on January 13, 2007 (one day after perihelion passage). A polarizing filter was used to darken the sky for this 1/200th of a second exposure, but the comet was still remarkably easy to see for those who knew where and how to look. (Stefan Seip, apod070119)

 Comet McNaught as observed by its discoverer in evening twilight on January 19, 2007. By this time the comet had passed perihelion, and was receding from the Sun; but it was still brighter than Sirius, and more than half as bright as Venus. Only visible from the southern hemisphere during the rest of its visit to the inner Solar System, it will rapidly fade as it moves away from the Sun, disappearing into the vastness of the outer Solar System, and eventually, the Oort Cloud. When it returns, a million or so years from now, will any humans still exist to observe its passage, or any record remain of its present visit?
 The exceptionally curved tail of the comet is caused by its rapid movement around the Sun (approximately 55 miles per second, or three times the Earth's orbital speed, at perihelion). Material in various parts of the tail is being pushed away from the Sun, but from the position the comet was in at the time it lost that material. As the comet swung around the Sun, the direction the "newer" material was being pushed changed relative to the direction that the "older" material was still being pushed, creating a "garden-hose" effect in the shape of the tail.
 The "Great Comet of 2007" was one of the brightest comets observed in decades, and was even visible in daylight (by blocking out the light of the Sun) during the days that it was closest to perihelion. (Robert A. McNaught, apod070122)

 Discovered in early 2006, this comet is fairly typical in appearance. A fuzzball, the coma, or head, surrounds the unseen object, a dirty snowball called the nucleus, which creates the coma by the release of gases from ice vaporized by the heat of the Sun. The gas is blown away from the head by the solar wind, which is streaming away from the Sun (which is off to the right, but below the horizon, in this image) at velocities of a few hundred miles per second. The resulting tail is what gives comets their name, which is based on a Greek phrase meaning "hairy star". The name of this particular comet refers to its discoverer (Grzegorz Pojmanski, of the Warsaw University Observatory), and to when it was discovered. The estimated orbit of the comet is very elongated, with an eccentricity of 0.99978, which would place its aphelion nearly 10,000 AUs from the Sun, while its perihelion distance is only about half an AU. Comets with relatively small orbits, and periods of less than 200 years, replace the C/ in their name with a P/, to indicate that they return to our part of the solar system on a periodic basis. Comets with large orbits, and hence large periods, such as Pojmanski, which would take the best part of 300,000 years for one trip around the Sun, retain the C/ beginning. (Adam Block (Caelum Observatory), R. Jay GaBany (Cosmotography.com), apod060311)

 A time-lapse animation showing the motion of Comet Ikeya-Zhang relative to the stars, and movements of gases in its tail, created by combining ten images taken during a half-hour period on March 11, 2002. The comet is moving upward relative to the stars, as shown by the short dashes which represent their positions (caused by guiding on the comet, during each exposure), and the downward movement of those dashes relative to the comet (caused by placing the comet in the same position in each "frame" of the image, despite its upward movement). The sun is down to the right, as indicated by the position of the gas tail, which points up to the left, which is opposite the direction of the Sun. The motion of gas from the comet, up to the left, away from the Sun, is caused by an interaction between the Solar Wind, blowing away from the Sun, and charged particles in the gaseous coma or head of the comet. This interaction does not involve direct physical collision of the particles, because the cometary gases are very close to being a vacuum, and the Solar Wind is even closer. Instead, as the Solar Wind blows away from the Sun, it pulls part of the Sun's magnetic field out into space, creating the interplanetary magnetic field. As the field is pulled past the comet by the Solar Wind, it interacts with the charged particles (ions) in the cometary gases, pulling them outwards as well. The speed attained by the gases is greater than the escape velocity of the Solar System, so they go outward into space until they reach the boundary of the Solar magnetic field (the heliopause), a hundred or more AUs from the Sun. (Michael Karrer, apod020515)

 The motion of Comet P73/Schwassmann-Wachmann 3 over a period of sixty-seven minutes on May 16, 2006 (or more accurately, of fragment B of that comet, after the comet's breakup into dozens of pieces, earlier that year). Usually, comets are so far away that they seem to move very slowly against the background of stars; but at the time that the eighty-three images which comprise this animation were taken, the cometary fragment was only a little over six million miles from the Earth, one of the closest passages of a comet in historic times, and its motion could easily be observed to move against the starry background even with binoculars (presuming, of course, a location where the sky was dark enough for binoculars to reveal such a faint object). It should be noted, in light of the many hoaxes about collisions of fragments of this comet with the Earth, that even at its closest distance, it was 25 times further from the Earth than the orbit of the Moon. Debris lost by the comet over previous centuries has gradually drifted away from its orbit, and microscopic and pebble-sized pieces of the comet may produce a meteor shower around mid-May, but none of those small pieces have any chance of penetrating our atmosphere, and will all be vaporized more than fifty miles above the surface of the Earth.
 There is a possibility of a far closer approach of Halley's Comet, in 2138. If the comet passes our orbit on exactly the same day that the Earth passes closest to the orbit of the comet, it would pass only two million miles below the south pole of the Earth -- still 8 times the distance of the Moon, but close enough that it would be a spectacular sight in southern skies, and fragments lost by it in the past might well fill the skies with meteors. However, the path of any comet is very slightly affected by the gas 'jets' which it emits as it loses mass, and the perihelion date can vary by as much as a week, even for short-period comets like Halley's Comet; and since we move a million and a half miles in a day, even a day or two error in when the Comet returns in 2138 would double its distance, and substantially reduce its apparent brightness and size. (Thad V'Soske (Cosmotions.com), apod060523)

 Just as Comet Shoemaker-Levy 9 was torn to pieces by Jupiter's gravity, Comet P73/Schwassmann-Wachmann 3 recently broke into several dozen pieces in 2006 (for reasons unknown, since it was hundreds of millions of miles away from any object of substantial mass). This is not the first time that the comet has fallen apart. It split into several large pieces during its perihelion passage in 1995. Some comets may, as they lose mass, simply become piles of sooty rubble, unable to generate a head or tail, due to their lack of ice; but many, if not most, are such fragile conglomerates of ice, soot and dust, that they simply fall to pieces. As it happens, the pieces of Schwassmann-Wachmann passed only a few million miles from the Earth in May 2006, but since they are so small, they were impossible to see in bright skies, and difficult to see even in dark skies without binoculars or telescopes. In the image above, taken in late April 2006, Fragment B of the comet is shown on the left, as it passed the 5th magnitude star χ (Chi) Böotis; and much fainter fragment G is barely visible at far top right. (For a collection of images of Comet P73, see The 2006 Breakup of Comet P73/Schwassmann-Wachmann 3.) (Mike Holloway, spaceweather.com)

Comet Halley as photographed by the Giotto spacecraft in 1986. An extremely dark surface is broken by gas jets streaming from the comet. The nucleus is about 10 miles across, and loses about 20 feet of material at each perihelion passage. The dusty debris left in its path is responsible for the Orionid meteor shower in October, and the Eta (η) Aquarid meteor shower in May. (Halley Multicolor Camera Team, Giotto Project, ESA, (Copyright: MPAE), apod000805)

Another version of the Giotto image of Comet Halley, emphasizing the gas and dust streaming away from the nucleus, into the coma. The coma is thousands of times larger than the area shown here, so by the time the gas and dust have spread out to "fill it", they are very rarefied, and their distribution is hardly affected by the way in which they first left the comet. (Halley Multicolor Camera Team, Giotto Project, ESA, (© MPAE), apod100104)

Comet Halley in March of 2003, when it was 28 AUs (2.6 billion miles) from the Sun. It will be 35 AUs from the Sun at aphelion, in 2023, and return to the Sun in 2061. (O. Hainaut (ESO-Chile) et al., VLT Project, European Southern Observatory, apod031003)

The five-mile long nucleus of Comet Borrelly, photographed from about 2000 miles away by Deep Space 1, in 2001. (Deep Space 1 Team, JPL, NASA, apod010926)

Comet Tempel 1, thirteen seconds after being struck by the impact portion of the Deep Impact spacecraft. (U. Md., JPL-Caltech, NASA, apod050705)

 Composite of Comet Tempel 1 created by combining images of varying resolution taken as the Deep Impact spacecraft approached the comet. The sharpest appearing region, near the left side of the image, is where the impact occurred. The comet displays a large number of sharp-walled craters, indicating a long history of natural impacts. (Univ. Maryland, JPL-Caltech, NASA, apod050915)