The Origin of the Short-Period Comets
The next group of objects whose origin we must explain are the comets. They consist of relatively small objects, like the asteroids, and therefore probably represent planetesimals that for some reason did not end up inside the planets or their satellites. Unlike the asteroids, they appear to be made mostly of icy materials, and so we assume that they must have originated in the outer solar system, near or beyond the orbit of Jupiter.
The problem of cometary origin can be divided into several parts. The first part is the problem of the short-period comets. These are comets which have orbital sizes of only a few tens of AUs, and therefore have orbital periods of 200 years or less. Just like all other comets, when they are at the far end of their orbits, they will be just small, dirty snowballs, but when they come in close to the Sun, near perihelion, the ices will be vaporized, and the gases that result will escape from their surfaces, and gradually drift into interplanetary space, forming the head and tail of the comet. Each time that these comets pass perihelion they must lose some mass of ice, and whatever dust or soot was embedded in the ice. As a result, they cannot go around the Sun more than a few dozen or hundred times (depending on their perihelion distance) before they have lost virtually all their original mass, and disintegrated, or at least disappeared from view. But since they take less than 200 years to go once around, this means that they cannot be visible for more than a few thousand years. Even Halley's Comet, the brightest and most famous of these comets, seems to be only about half as bright as it was 2000 years ago.
Since the few thousand years that the short period comets can last is just an instant in the 4.5 billion years since the solar system was formed, we either need to suppose that some special event has just created them, or that there is some mechanism which can continually create new ones. Scientists don't like to suppose that special events are required without definite proof that they actually occurred, so we prefer some mechanism of continual creation.
In this case, the creation of the short-period comets is explained by looking at their orbits. Although there are many different orbits involved, there are two very large "families" of orbits which seem to be associated with Jupiter and Saturn. We believe that these comets were somehow "captured" into their present orbits when, at some time in the past, they happened to pass very close to one of these large planets.
When an object, such as a comet, passes close to a large planet, the orbit of the object around the Sun is changed somewhat. If the comet passes on one side of the planet, it may be speeded up by its encounter, but if it passes on the other side of the planet, it would probably be slowed down. In the first case, the comet might well be given so much extra speed that the Sun could no longer hold on to it gravitationally, and the comet would move permanently out of the solar system, along a hyperbolic orbit. In fact, we have observed several comets in the last few hundred years which were in such hyperbolic orbits, and in every case a calculation back along the orbit shows that the orbit was caused by this sort of interaction with a planet which the comet had just passed by. If the comet is slowed down, however, then it not only will not be thrown out of the solar system, but will not even be able to get back to the same distance from the Sun that its orbit originally allowed. In this way, a comet which originally had a very large orbit could become trapped in a small orbit.
We can therefore explain the short-period comets by looking at the long period comets. These comets, with huge orbits, hundreds, or even thousands of AUs or more in size, come into the inner solar system only once in a great while. But if, while there, one happens to pass close to a major planet, it could be captured into a small orbit, and become a short-period comet. The observation of such comets which were thrown into hyperbolic orbits suggests that there must also have been some which were captured into small orbits, and the numbers of long-period comets are so large that this mechanism seems quite adequate to explain all known short-period comets.
The Origin of the Long-Period Comets: The Oort Cloud
The long-period comets mostly have very large orbits (semi-major axes of the order of 10000 AU), and very long orbital periods (of the order of a million years). Because of this, a hundred orbits can take 100 million years or longer. At one time, this was comparable to estimates of the age of the solar system, and we could assume that such comets had been orbiting as they currently do since the beginning of the solar system, but we now know that the solar system is 4.5 billion years old, almost 50 times older than the time that such comets could survive in their current orbits, and so their orbits must also be of relatively recent origin. If they had been orbiting as they are since the origin of the solar system, they would have "burned out" billions of years ago. So where have they been in the past, and why are they here now?
The current theoretical solution to this problem was first proposed by Jan Oort, and his suggestion is referred to as the Oort Cloud theory. Each year a few dozen long-period comets are noted entering the inner solar system, but since these comets take a million years or so to go around the Sun, only about a millionth of the comets currently orbiting in this way are actually seen in any given year. Correcting for the small fraction that we actually get to see, we find that there must actually be several million dozens of comets scattered along their huge orbits.
What Oort noted is that the larger the orbits of the comets, the more of them there are, so that in very large orbits, there might be a vast "reservoir" lying on the outer fringes of the solar system. In the region from a few thousand to a few tens of thousands of AUs from the Sun, there might be as many as several tens or hundreds of billions of comets, each orbiting in its own particular orbital path, just as the planets do in the inner solar system.
However, while the planets have regularly spaced, nearly circular orbits, all in nearly the same orbital plane, the orbits of the comets are quite different. We observe long-period comets coming towards us from all directions in space, with some going around the Sun in one direction or orbital inclination, and others moving in a completely different direction. To explain this, Oort proposed that in this cloud of comets, all possible inclinations or directions, and orbital shapes or eccentricities must occur, probably at random. Some comets would have nearly circular orbits, with eccentricities close to 0.0 or 0.1, but just as many would have orbital eccentricities close to 0.2 or 0.3, or even 0.9 or 1.0, and have very elongated orbits.
With such large orbits, if a comet had an eccentricity of 0.99 or less, its perihelion distance would be well outside the orbit of Pluto, and it would not have a chance to gravitationally interact with the planets, or to be seen by us. But if it had an eccentricity above 0.999, it would "fall" into the planetary system when at the near end of its orbit, and be one of the long-period comets that we see.
Of course, if the orbital eccentricities were "random", then the chance of having an orbital eccentricity of about 0.999 would only be one in a thousand, so that for us to observe dozens of millions of such comets (over their entire orbital period), there would have to be thousands of dozens of millions of other comets, forever unobservable to us, out in the Oort Cloud itself. That is why this theory requires that there be tens of billions of comets in the Cloud, as stated earlier.
The nice thing about this theory is that with so many comets in the Cloud, using up the current crop of long-period comets doesn't really do much to the total number of comets. The observable comets are only a tenth of a percent of the actual pool of comets, so even when they are gone, there will still be plenty of comets left, and the fact that we still observe comets, billions of years after the origin of the solar system, isn't that strange.
However, it won't do us any good if there are still lots of comets in the Cloud, because they are too far away for us to observe them, unless we can somehow turn comet orbits which stay safely away From the Sun into orbits which fall into the inner solar system, almost running into the Sun. Normally, this is not possible. The Sun's gravity, acting on the motion of an object, completely determines how it should move through space. Its pull causes the natural motion to be an ellipse or hyperbola, instead of a straight line, but once that path is determined by the combined effects of the Sun's gravity and whatever motion the object originally had, the Sun cannot change it, as its pull is what causes that particular motion in the first place. Only some other object, such as a planet, can change the orbit, as in the discussion of the origin of the short-period comets. So how can we change the orbits in the Oort Cloud?
Normally, in talking about the solar system, we can completely ignore the stars (other than the Sun), because they are at such vast distances (at least 300,000 AU, even for the closest stars) that they can have no effect on objects in our solar system. But the comets in the Oort cloud can be as much as 20 or 30 thousand AUs from the Sun (perhaps even 50 thousand, in some cases, but that is more speculative), which is of the order of 10% of the way from the Sun to the nearby stars. As a result, when the comets are in the outer parts of their orbits, they can feel gravitational tugs from the other stars which are a few tenths of a percent of the Sun's pull.
As stars "pass by" the solar system, even at several hundred thousand AUs distance, the weak tugs that they exert on the comets on their side of the Oort Cloud slightly "mess up" their orbital motions. If the comets are heading in the same direction as a passing star, they are speeded up just a little bit, while if they are headed in the opposite direction, they are slowed down just a little bit. These small speed changes slightly change the size and shape of the orbit. Over time, small changes can add up to produce substantial ones, so that comets which had orbital eccentricities of .999 might end up with eccentricities of .8 or less, while those with eccentricities of .8 or less might end up with eccentricities of .999 or more. This provides a continual supply of very eccentric comet orbits to replace the ones which we can currently observe. Since, in this theory, the current supply of very eccentric comet orbits is only a tenth of a percent of the original supply, even replacing the current supply 50 times, as would have been necessary during the 4.5 billion years since the origin of the solar system, would only use up 5 percent of the original supply, leaving plenty of comets for us to observe for many billions of years longer.
Although the Oort Cloud theory is now widely accepted, there are some problems that need to be solved before we can consider it a "proven" theory. First, we can't possibly observe comets at the huge distances proposed in this theory, so how can we tell whether they actually exist? Second, how could this Cloud have been created in the first place? And if it does exist, can we find any evidence that comet orbits could be disturbed by passing stars in the proposed way?
In the case of the last problem, fortunately, there are theoretical calculations which show that this would indeed work, and, in addition, some weak observational evidence. If passing stars are the cause of changes in the orbital motions of comets in the Oort Cloud, then if a star passes closer than normal, as would occasionally happen during our motion around the Galaxy, it would cause a much greater than normal change in the cometary orbits, which might allow us to see a pattern in the orbits of the observable comets. In fact, we do find that in some cases there appear to be "families" of cometary orbits which are more-or-less aligned along a line in space. Whether these alignments are real effects or random alignments is not yet clear, but if this is borne out by further study it may prove to be an important piece of evidence.
The Origin of the Oort Cloud: The Kuiper Disk
Although the Oort Cloud theory is an attractive way to explain the origin of the long-period comets, it suffers from the problem that it predicts that most cometary bodies normally lie so far from the Sun that they could never be observed from the Earth. So how could we tell if the Cloud exists at all? And how could such a cloud of cometary nuclei be created in the first place?
For the first question, there is no answer, except for how well the Cloud theory explains the origin of the long-period comets. Despite many efforts, we cannot think of any other way to provide lots of comets for long periods of time without making our current period of time somehow special or exceptional. As a result, as long as the theory has no other significant problems, it is likely to remain the accepted theory of cometary origin, although it would be much nicer if there were more direct, observational evidence of the existence of the Oort Cloud.
For the second question, the best answer appears to be the theory of the Kuiper Disk (named after Gerard Kuiper, who proposed the idea). At the end of the formation of the planets, there must still have been a lot of rubble left over, as indicated by the large numbers of craters on the surfaces of objects, like Mercury and the Moon, which have no atmospheres to weather and erode their surfaces. These craters point to a time, shortly after the formation of these bodies, when many small bodies, such as asteroids, were still running into them, and making lots of large holes in their surfaces. The numbers of such craters are so large that, on the older parts of their surfaces, these objects are totally, completely covered with craters.
Presumably, even after the planets had formed, melted, differentiated, and then resolidified, there was a small fraction of one percent of their mass left between them as rubble. As they ran around and swept up this rubble, it cratered their surfaces, and if they have no atmospheres, we can still see the effects, even though it is now billions of years later.
As discussed above, if a comet were to pass near a planet, but not run into it, the gravity of the planet could change the orbit of the comet. In the inner solar system, because the planets are small, and the Sun is close, the amount by which the orbit can be changed is fairly small, unless the comet comes so close to the planet that it will probably run into it anyway, but in the outer solar system, the Jovian planets are huge, and the Sun is far away, so the comet orbits can be substantially altered, perhaps even throwing them out of the solar system, never to return.
The Kuiper Disk theory proposes that, at the time that the planets were sweeping up the debris left over from their formation, some of the material ejected from the area near the Jovian planets might not have completely escaped from the solar system. In fact, numerical simulations show that, if the orbits of the ejected material are more-or-less random, then a fairly large amount of material could end up in orbits which are a few hundred to a few thousands of AUs in size. Because all of the objects involved in this discussion, both the planets and the debris, are originally going around the Sun in the same plane and direction of motion as the solar nebula, the objects thrown out of the solar system would preferentially end up in a flattened disk, just like the solar nebula, but much, much larger. This large flattened disk of cometary (and smaller) debris is called the Kuiper Disk.
The problem with this theory, as a proposed origin for the Oort Cloud, is that the Oort Cloud is presumably tens of thousands of AUs in size, while the Kuiper Disk is only thousands of AUs in size, and the Oort Cloud is roughly spherical, while the Kuiper Disk is a relatively flat structure. Despite this, in recent years, we have uncovered evidence that this probably is the way in which the Oort Cloud is originally created. For one thing, we have found that a number of relatively young, hot stars have disks of glowing dust surrounding them (if the stars weren't young and hot, the disks wouldn't be glowing brightly enough to see). The glowing dust consists primarily of very small particles, but much larger objects could also be embedded in the glowing disks. For another thing, we have realized that most, if not all, stars are created in clusters of stars, which would provide a way to convert the flattened disk into a more spherical structure.
The Sun is not in a cluster of stars, but most clusters do not have enough stars in them to hold together gravitationally for more than a few hundred million years after their formation, so even if we are not in such a cluster now, we could have been when the solar system was first formed. In fact, to explain the melting and differentiation of the asteroids, we have to assume that the early solar system had "large" amounts of short-lived radioactive materials, which were created in supernovae explosions which were close to the solar system at the time that it was forming (in fact, the explosions may have helped provide the "push" which caused the cloud of gas which became the Sun to collapse in the first place). These explosions would have been caused by massive "siblings" of the Sun, formed in the same cluster as the Sun, which because of their large mass could form, live out their lives, and die, blowing themselves to bits, while the cloud of gas which ended up as the Sun and solar system was still just a cloud of gas.
If this is correct, then when the Jovian planets threw cometary debris out into the Kuiper Disk, the nearest stars would not have been hundreds of thousands of AUs away, as they are nowadays, but only tens of thousands of AUs away, as is more typical in clusters of stars. As a result, even though the Kuiper Disk would have been only a few thousands of AUs in size, objects in the disk would, as in the theory of the Oort Cloud, have been subjected to small tugs from passing stars which could mess up their orbits, gradually making them more and more randomized. Within a few tens of millions of years, most of the Kuiper Disk objects would have become scattered over a larger, more spherical region, just like the Oort Cloud, and as the cluster in which our Sun was formed fell apart, and the distances to the nearby stars increased, the spherical region would have gradually grown as well, so that the most distant objects in the proto-Oort Cloud would always be around 10 to 15 percent of the way from the Sun to the closest stars.
This gradual evolution, from a flattened disk to a spherical cloud, adds an extra layer of complexity to the theory, but it has a nice side effect. If this theory is correct, then the objects in the inner part of the Kuiper Disk, since they are closer to the Sun, would be less likely to be affected by other stars, and could still be running around the Sun in a relatively flattened, fairly small region. It would only be the objects in the outer part of the Kuiper Disk which would have been substantially affected by the nearby stars, and gradually transformed into an Oort Cloud-like structure.
But if this is true, then we can have some hope of being able to actually observe some of these nearby objects, providing they are large enough to observe at distances of several hundred to a few thousand AUs. The Oort Cloud, being tens of thousands of AUs in size, is too large for us to ever hope to observe objects in it, but the Kuiper Disk, being much smaller, could conceivably be directly observed. Of course, even at the distance of the Kuiper Disk, comets would have to be hundreds of miles in diameter for us to observe them in the faint light of the far-distant Sun, but if, as in the case of asteroids, there are a few large comets, then a lot of middling size comets, and finally a huge number of very small comets, then since the small comets must number in the tens of billions, there might well be enough large ones so that we could hope to observe at least some of them. And, as it turns out, in the last few years, we have observed several dozens of objects which are probably cometary bodies, tens or hundreds of miles in diameter, in orbits a few hundreds of AUs in size, so it is beginning to look like the Kuiper Disk does indeed exist as predicted! (Note: although the Kuiper Disk has a disk-shaped structure, since we, near the Sun, would be near the center of the Disk, we would see it, from our "central" position, as a more or less circular band, more or less centered on the Ecliptic, the path that all inner Solar System objects tend to follow. Because of this appearance, objects seen in this area are referred to as Kuiper Belt Objects, or KBOs, the "belt" referring to the band-shaped appearance of the structure, as seen from our point of view.)
To summarize the origin of the comets: Short-period comets are derived from long-period comets through gravitational perturbations caused when they pass by large planets. Long-period comets are derived from a spherical reservoir, the Oort Cloud, when distant stars perturb the orbits of objects in that cloud. The Oort Cloud was derived from a flattened disk, the Kuiper Disk (also created by planetary perturbations) through perturbations caused by nearby stars (in the cluster that the Sun was born in).