Early Ideas About Comets

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The ancient peoples paid special attention to whatever occurred in the heavens, noting on one side the regularity of several celestial phenomena, such as the rise and the setting of the Sun, Moon and stars, and the phases of the Moon, and on the other side the irruption of unexpected transient events, like eclipses, comets, novae and meteors, that broke such a regularity. Since the heavenly bodies were associated to divinities with influence on terrestrial affairs, the unexpected events caused concern and were regarded as portents of upcoming disasters.

Comets in particular were received with a mixture of woe and fascination, owing to their sudden and sometimes spectacular apparitions. The traditional use of the word "apparition", rather than a more sober one such as "appearance" or "passage", is itself a reminiscence of the old view that regarded comets as ghosts rather than natural objects. Very often the occasional witnesses looked at comets with fear, believing that they were forerunners of wars, pestilence and death. The ancient civilizations seem to have paid special attention to the observation of these bodies and other transient phenomena like fireballs and meteor showers, basically owing to their desire to predict future events rather than by mere scientific curiosity.

The ancient Greeks went beyond the mere contemplation to develop several theories about the nature of comets, though they presumably inspired on previous ideas held by the Chaldeans and the Egyptians. The word comet itself comes from the Greek word kometes that means "long-haired" star, alluding to their main distinctive features: a head or coma and a long tail or tails more or less directed in the antisolar direction (Fig. 1.1). The comet lore through history is a curious blend of scientific thought with superstitious tales that forms part of the rich cultural heritage of mankind. A detailed description of early ideas about comets can be found in the two excellent books by Bailey et al. (1990) and Yeomans (1991).

Figure 1.1. CCD image of comet C/2000 WM1 (LINEAR) observed with the 46-cm Centurion telescope of the Observatorio Astronómico Los Molinos (OALM) by Raul Salvo and Santiago Roland. The field of view of the image is 1/2° x 1/2°, i.e. similar to that occupied by the Moon (Courtesy OALM).

1.1. Early records of comet apparitions

The Chinese were the most prolific observers whose meticulous observations of comets and other phenomena like novae, meteors, aurorae, eclipses and sunspots, have been preserved until now. Theirs is by far the most important source of reliable astronomical data covering a period from about 1100 BC to about 1700 AD. Besides the Chinese, the Koreans and Japanese also contributed with a significant number of observations during portions of the previously quoted time span (a comprehensive compilation of ancient observations from these Asian civilizations was done by Ho Peng Yoke (1962)). It is also possible that the Babylonians kept a good record of comet apparitions, though very little has reached us from them. The same can be said from the Mesoamerican civilizations (Mayans, Aztecs, and other peoples) from which very few documents have survived until present, though from the sketchy information available it seems that they also regarded comets as portents of impending calamities. Very few records of comet apparitions could also be recovered from the Hellenic civilization (which comprised Greece and surrounding areas around the Mediterranean Sea, including Alexandria), despite the attention paid by its philosophers to these bodies. Presumably, Greek philosophers were not so prolific and systematic observers as their Chinese counterparts, which explains the scarcity of references to observed comets. One of the few Hellenic sources of comet observations during the V-VI centuries BC is Aristotle's treatise Meteorologica written in 329 BC. There are some references to comet apparitions from Roman scholars, in particular Pliny the Elder and Lucius Annaeus Seneca (both from the first century AD). However, Roman accounts of comet apparitions are in general very vague, included incidentally within descriptions of historical events as bad omens. During the Middle Ages, Arab astronomers do not seem to have paid much attention to comets either, and their legacy in this matter is very scarce.

The number of recorded comet apparitions is very scant before the second century BC, and then it sharply raises to an average of above 25 comets per century, where it stays more or less constant until the eighth century AD (Fig. 1.2). In the following centuries the average rate raises somewhat to about 40-50 per century. The most ancient available references to comet apparitions date back to the 12th or 13th century BC, though they are extremely vague. The first reliable document describing a comet apparition in 674 BC was uncovered in a Babylonian stone tablet (Kronk 1999). Most comets cataloged until the fifteenth century rely heavily on Chinese and, in a lesser degree, Korean and Japanese reports. The Chinese referred to comets as broom stars, or sparkling stars, or later also as long-tailed stars. They also used the name guest star, but it is very likely that it usually referred to novae rather than comets. In some cases it is not clear that the recorded object is a comet, and it might have as well been a nova or a meteor.

Most of the recorded positions of ancient comets are unprecise and do not allow to compute a reliable orbit. In fact, most of the orbits computed before the 15th century correspond to periodic comets

discovery year

Figure 1.2. Record of comet discoveries per century before 1700 AD as presented by Kronk (1999) (thin histogram), and that corresponding to those apparitions whose observations allowed a reliable orbit determination as presented in Marsden and Williams (2003) Catalogue of Cometary Orbits (gray thick histogram).

discovery year

Figure 1.2. Record of comet discoveries per century before 1700 AD as presented by Kronk (1999) (thin histogram), and that corresponding to those apparitions whose observations allowed a reliable orbit determination as presented in Marsden and Williams (2003) Catalogue of Cometary Orbits (gray thick histogram).

lP/Halley, 109P/Swift-Tuttle and 55P/Tempel-Tuttle, for which the accurate computation of their orbits backward in time allowed to link the computed ephemerides of previous passages with ancient reports of their apparitions. From the fifteenth century, European observers began to play an ever increasing role in the discovery record. The Florentine physician and astronomer Paolo Toscanelli (1397 - 1482) observed accurately several comets, among them Halley in its 1456 apparition, and plotted their positions in the sky on charts which permitted the determination of their orbits by later workers. The fraction of recorded apparitions that allow an orbit determination shows a steady increase since the fourteenth century (Fig. 1.2). Stanislaus de Lubienietz produced one of the first comprehensive catalogues of Western observations of comets, titled Historia Cometarum (1666). which reports comet apparitions since the deluge time to the time of his book. It contains magnificent illustrations of comets on the heavens, one of them is shown below in Fig. 1.4.

As can be seen in Fig. 1.2, the number of recorded apparitions that led to reliable orbit determination, as presented in Marsden and Williams (2003) Catalogue of Cometary Orbits, constitute a small fraction of the total sample during most of the considered period. The fraction started to increase significantly in the fourteenth century following a better record of comet positions with better instrumentation like quadrants. The telescope was introduced for comet observation in 1618 by the Swiss Jesuit Johann Baptist Cysat (ca. 1586 - 1657) and the English astronomer John Bainbridge (1582 - 1643). But the first comet to be discovered telescopically was that of 1680 (now designed as C/1680 V1) by the German astronomer Gottfried Kirsch (1639 - 1710). It marks a turning point between the previous naked-eye discovery regime, and the posterior regime in which the telescope played an ever increasing role in the detection and follow-up of comets. As we shall see in the next chapter, one of the consequences of the telescope revolution was the dramatic growth of comet statistics in quantity as well as in quality. The time around 1700 also witnessed the rapid decline of the Chinese as predominant source of comet apparitions in favor of the Europeans.

1.2. Heavenly bodies or atmospheric phenomena?

The history of cometary thought began as a discussion on whether comets were celestial bodies or atmospheric phenomena. The Pythagoreans in the sixth century BC and Hippocrates of Chios (ca. 440 BC) are credited with the idea that comets were planets that appeared infrequently close to the horizon like Mercury. Anaxagoras of Clazomenae (ca. 500 - 428 BC) and the atomist Democritus of Abdera (ca. 460 - 370 BC) believed that each comet was produced by the close approach or conjunction of two planets giving the appearence of a single elongated object. Anaxagoras argued that both the Sun and comets were made up of burning stones. This peculiar interpretation of their physical nature was probably rooted in the observation of a bright comet followed by a meteorite fall in 467 BC whose bright trail in the sky was seen in daytime. This is the first reference to an association between comets and meteors.

Yet, other Greek thinkers regarded comets as phenomena much closer to the Earth. According to Xenophanes of Colophon (ca. 570 -470 BC) comets were dry exhalations from the Earth in a similar manner that clouds were condensations of moisture raised from the sea. This idea was induced on early thinkers because comets bright enough to become observable with the unaided eye are generally close to the Sun. Therefore, they can only be observed in the early morning or early evening, and having the tail pointing toward the antisolar direction, they appear indeed to raise from the horizon. Aristotle (384 - 322 BC), one of the leading intellectuals of the ancient world, was to have a lasting influence on the ideas on comet's nature. He regarded comets, shooting stars and even the Milky Way as meteorological phenomena, and this is the reason why he included them in his treatise Meteorologica which dealt with the sublunar world. He ruled out the planetary nature of comets by asserting that they had been seen outside the zodiac. He also rejected the conjunction of planets or coalescence of stars, arguing that many comets had been observed to fade away without leaving behind one or more stars.

In Aristotle's view the sublunar world was composed of four concentric spheres ordered according to their density. The first densest sphere was the earth, followed by the watery, the airy and the fiery sphere on the top. The supralunar world populated by the heavenly bodies was composed by a fifth element or quintessence. He adopted the view, attributed to the Pythagoreans, that all celestial bodies moved in circles, considered to be the perfect curve. Irregular and vertical motions, like those attributed to comets, were only possible within the sublunar region. Following Xenophanes, Aristotle argued that comets formed from warm and dry exhalations that rose up from the earth when it was heated by the Sun. These exhalations ascended to the airy sphere and at the border with the fiery sphere they ignited by friction producing comets which were carried about the Earth by the circular motion of the heavens. Aristotle thus provided a physical explanation of why comets should foreshadow droughts, avoiding any kind of supranatural explanation of these bodies as portents or omens. Yet, supersticious fears were going to surround any comet apparition for another two thousand years.

Aristotle's view on comets as meteorological phenomena was mostly unchallenged for the following two millenia. A few dissenters, like Apollonius of Myndus (around the third century BC) still supported that comets were distinctive heavenly bodies, just as the Sun or the Moon, and attributed the changing brightness of a comet to its varying distance to the Earth, while Zeno of Citium on the island of Cyprus (circa 336 - 264 BC) considered that stars united their rays to create the image of an elongated star. Posidonius (135 - 51 BC) followed Aristotle's ideas about comets and added the interesting observation of a comet that became visible during a total solar eclipse, although it was previously concealed by the proximity of the Sun. This observation led him to conclude that comets should be much more numerous than usually observed, because some of them are lost in the glare of the Sun. In line with Aristotle's thought, Posidonius believed that comets burn as long as find nourishment in the aethereal region and that their appearance coincides with drought and their disappearance with heavy rains.

The Roman philosopher Lucius Annaeus Seneca (4 BC - 65 AD) noted in his Quaestiones naturales that comets could not be sudden fires that last at most for a few hours, but permanent creations of nature moving perhaps in close orbits. Seneca expressed genuine admiration for these bodies, being confident that "Men will some day be able to undestand their nature and paths in the heavens". Pliny the Elder (23 - 79 AD) discussed in his Natural History a classification of comets into 10 types according to their shapes and observed features. Pliny strongly supported the idea that comets were portents and that their shapes and the direction in which they dart their beams and what stars are nearby had influence on human affairs. Claudius Ptolemaeus or Ptolemy (ca. 100 - 175 AD) adopted Aristotle's view of comets as atmospheric phenomena, and for this reason they were not included in his masterwork the Almagest that dealt will all the heavenly bodies known at that time. Yet, Ptolemy described comets in his book Tetra-biblos, devoted to astrology, which shows that his main concern was to describe the ill effects brought by comet apparitions.

During the Middle Ages and in the Renaissance comets continued to be regarded in dual terms, as harbingers of disaster on one hand and as meteorological phenomena on the other, under the influence of the unquestioned authority of Aristotle and Ptolemy. Until the fifteenth century, no new original ideas or observations were added to the knowledge of comets, which were relegated to supertitious beliefs. Yet, the interest in these celestial bodies never subsided, which is illustrated in many drawings and paintings, either with the intention to describe their morphology or to reflect the awe their caused to the occasional witnesses (Fig. 1.3).

Colophon Comet
Figure 1.3. Comet drawings through history. (a) Comet types as they appeared in the Chinese Han tomb silk book (ca. 168 BC). (b) The 1066 AD apparition of Halley's comet as depicted in the Bayeux tapestry.

1.3. The confirmation of their celestial nature

From the eleventh century Western Europe started to recover very slowly from the state of ruin, disintegration and cultural darkness that followed the fall of the Roman Empire. There was a renewed interest in the works of the ancient Greek philosophers that reached Western Europe through the Arabs. Against this backdrop the interest in natural phenomena increased, in particular in comets. By the end of the middle ages, a new stimulating environment for scientific enquiry and discussion started to emerge, and with it the first attacks on the astrological signification of comets. Henry of Hesse (1325 - 1397) rejected the widely accepted thought that comets were prognosis of future events. Following Aristotle, he thought that comets were meteorological phenomena, and that pestilence often follows comets because they are produced by the exhalation from the Earth of pestilential vapor.

In 1456, the Viennese astronomer Georg von Peurbach (1423 - 1461) tried to determine the parallax of a comet (later known to correspond to one of the passages of Halley's comet). Some years later, Johannes Muller (1436 - 1476), known by his Latin name of Regiomontanus. attempted to measure the parallax of the great comet observed in 1472, though his derived value of 6° was highly erroneous. The most important legacy of Regiomontanus was to encourage scientific observations of comets with the aim to determine their distances to the Earth, their diameters and lengths of their tails. Girolamo Fracastoro (ca. 1478 -1553) and Peter Apian (1495 - 1552) showed independently that comet tails always point away from the Sun, in fact a property already known by Chinese astronomers at least seven centuries before, and even Seneca wrote in his Quaestiones naturales that "the tails of comets fly from the Sun's rays", so in this point as in others the Renaissance scholars were just rediscovering phenomena already known by the ancients.

During the sixteenth century most astronomers were interested in determining the parallax of a comet in order to settle the debate on whether these bodies belonged to the sublunar world (and were thus atmospheric phenomena), or they belonged to the supralunar world and were thus celestial in nature. The mathematician Girolamo Cardano (1501 - 1576) noted that a comet seen in 1532 had an apparent speed smaller than that of the Moon, thus suggesting a greater distance which would place the comet in the supralunar world. But it was the bright comet of 1577 that gave astronomers all around Europe their great opportunity to measure its parallax (Fig. 1.4). Tycho Brahe (1546 -1601) was among the observers that could successfully obtain a parallax, which placed the comet at least four times farther away than the Moon. Tycho also measured the apparent diameter of the comet's head and found it to be 8' which, according to its estimated distance, gave a diameter of nearly one fourth of the Earth's. Several other great astronomers of the time, as Michael Maestlin (1550-1631) and Helisaeus Roeslin (1544 - 1616) also find distances that put the comet in the supralunar world. As in many other cases in history of science, results can be controversial, mainly when the experiments or observations are pushed to the limits of the capabilities available at the moment. The comet of 1577 was one of these cases, and some respected scholars, among them the foremost astronomer of Eastern Europe Thaddaeus Hagecius (ca. 1525 - 1600), found for the comet a large parallax that placed it below the Moon (Hagecius rectified later his early estimate and recognized the comet to be supralunar). An interesting and well-

Figure 1.4. The motion on the heavens of the great comet of 1577 as illustrated by Stanislaus de Lubienietz in his book Historia Cometarum (1666) (courtesy of John McFarland, Armagh Observatory).

documented account about the comet of 1577 and the comet ideas about that time was presented by Hellman (1944).

Tycho suggested that comets moved around the Sun on circular orbits, like Venus and Mercury. In Tycho's system, the Sun itself, Mars, Jupiter, Saturn and the fixed stars moved around the Earth. Tycho even suggested that the orbit of the comet could be somewhat oblong, being the first time that somebody suggested that a celestial body might move on an orbit different from a circle. Johannes Kepler (1571 -1630) believed that comets were ephemeral bodies that formed out of impurities in the celestial aether and moved along straight, rectilinear paths. He confirmed that tails pointed toward the antisolar direction and put forward the hypothesis that the sunlight passed through the comet's head and took with it some of the matter away from the Sun, leading eventually to its final consumption.

Even though the idea that comets were heavenly bodies had received a growing acceptance during the sixteenth and early seventeenth centuries, there was still a firm opposition from some highly respected scholars. Thus, Nicholas Copernicus (1473 - 1543) still believed that comets were terrestrial objects, and Galileo Galilei (1564 - 1642) went on to affirm that comets were vapors that move vertically upward and were made visible when sunlight reflected on the cloud of vapors. The absence of parallax was then explained by the reason that comets were insubstantial, as mere lights reflected on vapors.

The heavenly nature of comets reached finally wide acceptance by the end of the seventeenth century. Some of the main thinkers of the time discussed the place in heavens were comets originated. Thus, Rene Descartes (1596 - 1649) believed that comets formed together with planets around the Sun and other stars on vortices. For our own solar system comets were found at the outer edge, at the distance of Saturn.

Despite the advance in the understanding of the celestial nature of comets during the sixteenth and seventeenth centuries, and the discussion of their motion with scientific arguments, the supertitious fears unleashed by their apparitions did not subside. Such fears were shared by some of the most respected scholars of the time, like Tycho Brahe, Kepler and Michael Maestlin. Martin Luther (1483 - 1546) referred to comets as harlot stars and works of the devil.

1.4. The determination of their trajectories

Once the heavenly nature of comets was accepted by the majority of astronomers, the next step consisted in determining the kind of trajectory they followed. We have seen before that a wide range of opinions were compiting at that time, going from straight, rectilinear paths, as proposed by Kepler, to circular orbits as proposed by Tycho. The Italian-French astronomer Jean Dominique Cassini (1625 - 1712), one of the last great supporters of the geocentric system, considered that comets, like planets and the Sun, moved around the Earth but in highly eccentric orbits. The Polish astronomer Johannes Hevelius (1611 - 1687), author of the well-known treatise Cometographia (1668), after careful observations of several comets concluded that they moved on paths slightly curved toward the Sun, on either a hyperbola or a parabola. This was corroborated by the German astronomer Georg Dorffel (1643 - 1688), a student of Hevelius, who was able to fit a parabola, with the Sun at its focus, to the motion of the bright comet observed in 1680.

The debate on comet's trajectories could have continued for a long time, were Newton's theory of universal gravitation not ready. Fortunately, at the very same time as the first attempts to fit parabolas or hyperbolas to cometary paths were carried out, Isaac Newton (1642 -1727) had almost completed his theory that predicted elliptic orbits for the planets moving around the Sun, which would occupy one of the focus. It was obvious that his theory should also apply to the case of comets. At the beginning Newton was reluctant with this possibility but, with time, he became convinced that planets and comets should obey the same laws, and developed a method to fit a parabola to the comet's motion given three observations more or less evenly spaced in time. This method was later included in his masterwork Principia (1687).

Newton's countryman Edmond Halley (1656 - 1742) was the first to fully exploit the new theory of gravitation to the case of comets. Halley computed parabolas for a sample of 24 well observed comets and noted that those comets observed in 1456, 1531 and 1607, shared parabolas of similar characteristics as those of the comet of 1682 observed by himself. This observation led Halley to conclude that these were different passages of the same comet and predicted that it would return again in 1758. The comet was recovered by the German farmer and amateur astronomer Georg Palitzsch (1723 - 1788) on Christmas evening of that year. Halley's prediction was corroborated and he had as a posthumous homage the comet named after him. The recovery of Halley's comet symbolizes the end of the era of discussion on the comet's motion: since then there was agreed that comets moved on parabolic, nearly parabolic, or slightly hyperbolic orbits, though a few of them, like Halley, had orbits elliptic enough to record several returns on historic times. Even though Halley was the first to successfully predict a comet return, he was not the first to look into this problem. Pierre Petit (ca. 1594 - 1677) and Adrien Auzout (1622 - 1691) firmly believed that comets were permanent celestial bodies moving in close paths, thus subject to return. Petit went further to claim that the comets observed in 1618 and 1664 were the same object, so its next return was due in 1710. Unfortunately, he was wrong.

The expected return of comet Halley for 1758-59 triggered a feverish computing activity aimed at predicting a more accurate date of perihelion passage, that involved some of the best mathematicians of the time. Leonhard Euler (1707 - 1783), noting the decrease in the period of comet Halley between 1531-1607 and 1607-1682, assumed that it was due to a drag force by the interplanetary aether. On the other hand, Alexis-Claude Clairaut (1713 - 1765) dismissed the drag effects of the aether but understood that a good orbital solution could be obtained only if the perturbations of Jupiter and Saturn were taken into account.

Newton's law of gravitation gave rise to the development of celestial mechanics whose goal is the study of the motion of celestial bodies under their mutual gravitational attraction. As the determination of cometary orbits became routine, it was deemed necessary to dispose of more manageable computing methods. Pierre-Simon Marquis de Laplace (1749 - 1827) developed a method that relaxed the stringent condition of Newton's method of having the observations more or less evenly spaced in time. Wilhelm Olbers (1758 - 1840) developed another simple method for determining the five elements needed for a parabolic orbit solution which was later widely used (description of these methods can be found in standard Celestial Mechanics textbooks like Roy (1982)).

1.5. Interstellar visitors or members of the solar system?

The motion of comets, that depart so markedly from that of planets, led to the idea that they might not be members of our solar system. Indeed, not only their orbits are quite different in shape and size but, while the planets moved all close to the ecliptic plane, most comets moved instead on orbits randomly oriented. Already Kepler believed that comets came from interstellar space, but it was Laplace who developed a complete theory of interstellar origin, becoming identified with it. Laplace argued that comets were condensations in an interstellar cloud, which attained their observed orbits as the result of the gravitational attraction of the Sun. He did not consider the motion of the Sun, but assumed that it was at rest immersed in an interstellar field of comets distributed uniformly and with all possible velocities between zero and infinity. Consequently, comets could be gravitationally attracted by the Sun from different directions which would explain the random orientation of their orbital planes. It is clear that bodies attracted from interstellar distances with very low relative velocities will move on paths very close to parabolas. Laplace explained the cases of comets in elliptical orbits, like Halley, as being captured by one of the planets after a close encounter.

Later, Giovanni Schiaparelli (1835 - 1910) pointed out the necessity to include the proper motion of the Sun relative to the cometary cloud. William Herschel had already found in 1783 that the Sun had a proper motion with respect to nearby stars, moving toward a point termed the solar apex. Therefore, if comets shared the interstellar space with stars, it was natural to think that the Sun would have likewise a proper motion with respect to the interstellar comet cloud. Being the velocity of the Sun toward the Apex of about 20 km s_1, it would be extremely unlikely to find interstellar comets with relative velocities smaller than a few km s_1. This would give an excess of hyperbolic comets far greater than Laplace had estimated. Furthermore, such comets would arrive preferentially from the direction towards which the Sun is moving. Since such a concentration of aphelion points in the apex direction was not observed, Schiaparelli concluded that the comet cloud should be comoving with the Sun.

To illustrate the previous situation, let us assume that the Sun moves with respect to a comet cloud with a velocity u (we neglect any random comet motion). A given comet will be attracted toward the Sun along a hyperbolic path of perihelion distance q and semimajor axis (negative) a (Fig. 1.5). If D is the "target radius" (i.e. the distance of closest

Figure 1.5. Geometry of the encounter of a comet with the Sun with a velocity at infinity u and a target radius D.

approach of the comet to the Sun, if it moved unperturbed along the asymptote), from conservation of angular momentum we have where vq is the orbital velocity of the comet at perihelion. We should bear in mind that in a heliocentric system, —u will correspond to the velocity at infinity of the comet. For a Keplerian hyperbolic motion we have where ^ = GM0, G is the gravitational constant, and M& is the Sun's mass. By substituting these two expressions into eq. (1.1), we can obtain a relation between the perihelion distance and the velocity at infinity:

As shown in Fig. 1.6, for relative velocities greater than a few km/s it is impossible to get comets within a given "observable" region where they become potentially detectable (say, for perihelion distances q < 2 AU where most comets have so far been discovered), unless that the impact parameter D < 10 AU. An interstellar comet will enter the observable region if the encounter velocity u form an angle ft < D/rx radians with the solar direction, where r^ is the Sun-comet distance at the moment of capture. If before capture the comet was at 105 AU (that according to Laplace corresponded to the radius of the Sun's sphere of influence), the angle ft should be at most ~ 10"4 radians or about 20 arcsec. This shows that under the capture hypothesis, only those comets pointing toward or very near the Sun will enter the observable region and in all cases in clearly hyperbolic orbits. The probability that a comet with a randomly oriented velocity vector u will have it pointing to less than 10~4 radians to the Sun is p ~ 10~8/4 = 2.5 x 10~9, so only one comet in 4 x 108 could reach the observable region.

In 1929 Nicholas Bobrovnikoff concluded from the analysis of the lifetimes of 94 comets that these could not be older than one Myr, and that within this time the Sun must have therefore passed through an interstellar cloud from which it captured the comets. Nolke (1936) argued that condensations within the cloud could only become incorporated

Figure 1.6. The perihelion distance reached by an interstellar comet captured along a hyperbolic path as a function of the velocity at infinity u and for the target radii shown beside each plot. The dashed line indicates a somewhat arbitrary "observable" boundary below which a comet would be potentially detected from Earth.

Figure 1.6. The perihelion distance reached by an interstellar comet captured along a hyperbolic path as a function of the velocity at infinity u and for the target radii shown beside each plot. The dashed line indicates a somewhat arbitrary "observable" boundary below which a comet would be potentially detected from Earth.

within the solar system if their motion was taking place in a resisting medium, which he associated to interstellar material composed of dust and gas (a more detailed description of these early works can be found in Richter 1963).

The theories postulating an interstellar origin for comets described before regarded the condensations within the interstellar cloud already formed when the Sun encountered them. On the other hand, in a series of papers published between 1948 - 1958, Raymond Lyttleton proposed that such condensations originated as a byproduct of the process of capture itself. Lyttleton considered Bondi and Hoyle's (1944) theory of accretion, according to which interstellar dust particles are gravi-tationally focused toward the antapex direction where they collide to each other. The collision zone will lie behind the Sun in a range of distances going from a few AU to about 103 AU, depending on the relative velocity of the dust particles at infinity. The dust particles lose kinetic energy via the inelastic collisions, so they will be transferred from the original hyperbolic orbits to elliptic orbits, moving around the Sun in discrete clouds that Lyttleton identified with comets (see Lyttleton 1951). Lyttleton's theory not only proposed an origin for comets, but also provided a physical model for its nucleus as an assemblage of interstellar dust particles. We will discuss further this model in Chapter 3.

At about the same time as Laplace presented his theory of interstellar comet origin, Joseph Louis Lagrange (1736 - 1813) proposed a theory of comet origin within the solar system. According to Lagrange, comets might originate from gigantic eruptions from one of the larger planets (like Jupiter or Saturn). Theories involving the occurrence of catastrophic events of gigantic proportions were not uncommon at that time. Olbers had previously proposed that the asteroids arose from the disruption of a parent planet located between Mars and Jupiter. Even though Lagrange's theory had the appeal of readily explaining the origin of the short-period comet family, whose concentration of aphelion points around Jupiter's orbit might suggest an origin in such a planet, it did not enjoy the favor of many astronomers. A variant of La-grange's theory was presented in 1930 by the Soviet astronomer Sergei Vsekhsvyatskii (1905 - 1984) who argued that comets were formed from volcanic eruptions from the satellites of Jupiter and Saturn. This enabled him to overcome the difficulty of explaining the large velocities required to eject matter from Jupiter and Saturn (about 60 and 35 km s"1 respectively) to a mere few km/s, typical of the largest moons of Jupiter and Saturn. The interest in the planetary explosion theory for the origin of comets waned with time, given the formidable difficulties to explain the physics and the dynamics of the generated comets.

Around 1950 the debate on whether comets were interstellar objects or members of the solar system was still unsettled, as it was their physical and chemical nature. At that time there were a series of fundamental theoretical developments that were going to turn the tide of comet thought toward an origin in the solar system, and set the foundations of the "modern" comet science. So we shall stop here the review of the early ideas on comets and leave the "modern" ones for the following chapters.

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