Hypothetical Planetsby Paul Schlyter (firstname.lastname@example.org)
Vulcan, the intra-Mercurial planet, 1860-1916, 1971
The French mathematician Urbain Le Verrier, co-predictor with J.C. Adams of the position of Neptune before it was seen, in a lecture at 2 Jan 1860 announced that the problem of observed deviations of the motion of Mercury could be solved by assuming an intra-Mercurial planet, or possibly a second asteroid belt inside Mercury's orbit. The only possible way to observe this intra-Mercurial planet or asteroids was if/when they transited the Sun, or during total solar eclipses. Prof. Wolf at the Zurich sunspot data center, found a number of suspicious "dots" on the Sun, and another astronomer found some more. A total of two dozen spots seemed to fit the pattern of two intra-Mercurial orbits, one with a period of 26 days and the other of 38 days.
In 1859, Le Verrier received a letter from the amateur astronomer Lescarbault, who reported having seen a round black spot on the Sun on March 26 1859, looking like a planet transiting the Sun. He had seen the spot one hour and a quarter, when it moved a quarter of the solar diameter. Lescarbault estimated the orbital inclination to between 5.3 and 7.3 degrees, its longitude of node about 183 deg, its eccentricity "enormous", and its transit time across the solar disk 4 hours 30 minutes. Le Verrier investigated this observation, and computed an orbit from it: period 19 days 7 hours, mean distance from Sun 0.1427 a.u., inclination 12# 10', ascending node at 12# 59' The diameter was considerably smaller than Mercury's and its mass was estimated at 1/17 of Mercury's mass. This was too small to account for the deviations of Mercury's orbit, but perhaps this was the largest member of that intra-Mercurial asteroid belt? Le Verrier fell in love with the planet, and named it Vulcan.
In 1860 there was a total eclipse of the Sun. Le Verrier mobilized all French and some other astronomers to find Vulcan - nobody did. Wolf's suspicious 'sunspots' now revived Le Verrier's interest, and just before Le Verrier's death in 1877 some more 'evidence' found its way into print. On April 4 1875, a German astronomer, H. Weber, saw a round spot on the Sun. Le Verrier's orbit indicated a possible transit at April 3 that year, and Wolf noticed that his 38-day orbit also could have performed a transit at about that time. That 'round dot' was also photographed at Greenwich and in Madrid.
There was one more flurry after the total solar eclipse at July 29 1878, where two observers claimed to have seen in the vicinity of the Sun small illuminated disks which could only be small planets inside Mercury's orbit: J.C Watson (professor of astronomy at the Univ. of Michigan) believed he'd found TWO intra-Mercurial planets! Lewis Swift (co-discoverer of Comet Swift-Tuttle, which returned 1992), also saw a 'star' he believed to be Vulcan -- but at a different position than either of Watson's two 'intra-Mercurials'. In addition, neither Watson's nor Swift's Vulcans could be reconciled with Le Verrier's or Lescarbault's Vulcan.
After this, nobody ever saw Vulcan again, in spite of several searches at different total solar eclipses. And in 1916, Albert Einstein published his General Theory of Relativity, which explained the deviations in the motions of Mercury without the need to invoke an unknown intra-Mercurial planet. In May 1929 Erwin Freundlich, Potsdam, photographed the total solar eclipse in Sumatra, and later carefully examined the plates which showed a profusion of star images. Comparison plates were taken six months later. No unknown object brighter than 9th magnitude was found near the Sun.
But what did these people really see? Lescarbault had no reason to tell a fairy tale, and even Le Verrier believed him. It is possible that Lescarbault happened to see a small asteroid passing very close to the Earth, just inside Earth's orbit. Such asteroids were unknown at that time, so Lescarbault's only idea was that he saw an intra-Mercurial planet. Swift and Watson could, during the hurry to obtain observations during totality, have misidentified some stars, believing they had seen Vulcan.
"Vulcan" was briefly revived around 1970-1971, when a few researchers thought they had detected several faint objects close to the Sun during a total solar eclipse. These objects might have been faint comets, and later comets have been observed that later did pass close enough to the Sun to collide with it.
Mercury's Moon, 1974
Two days before the 29 March 1974 Mariner 10 flyby past Mercury, one instrument began registering bright emissions in the extreme UV that had "no right to be there". The next day it was gone. Three days later it reappeared, and the "object" appeared to detach itself from Mercury. The astronomers first thought they had seen a star. But they had seen it in two quite different directions, and every astronomer knew that these extreme UV wavelengths couldn't penetrate very far through the interstellar medium, suggesting that the object must be close. Did Mercury have a moon?
After a hectic Friday, when the "object" had been computed to move at 4 km/s, a speed consistent with that of a moon, JPL managers were called in. They turned the then-dying spacecraft over full time to the UV team, and everyone started worrying about a press conference scheduled for later that Saturday. Should the suspected moon be announced? But the press already knew. Some papers -- the bigger, more respectable ones -- played it straight; many others ran excited stories about Mercury's new moon.
And the "moon" itself? It headed straight on out from Mercury, and was eventually identified as a hot star, 31 Crateris. What the original emissions came from, the ones spotted on the approach to the planet, remains a mystery. So ends the story of Mercury's moon but at the same time a new chapter in astronomy began: extreme UV turned out not to be so completely absorbed by the interstellar medium as formerly believed. Already the Gum nebula has turned out to be a quite strong emitter in the extreme UV, and spreads across 140 degrees of the night sky at 540 angstroms. Astronomers had discovered a new window through which to observe the heavens.
Neith, the Moon of Venus, 1672-1892
In 1672, Giovanni Domenico Cassini, one of the prominent astronomers of the time, noticed a small companion close to Venus. Did Venus have a satellite? Cassini decided not to announce his observation, but 14 years later, in 1686, he saw the object again, and then entered it in his journal. The object was estimated to have about 1/4 the diameter of Venus, and it showed the same phase as Venus. Later, the object was seen by other astronomers as well: by James Short in 1740, Andreas Mayer in 1759, J. L. Lagrange in 1761 (Lagrange announced that the orbital plane of the satellite was perpendicular to the ecliptic). During 1761 the object was seen a total of 18 times by five observers. The observations of Scheuten on June 6 1761 was especially interesting: he saw Venus in transit across the Sun's disk, accompanied by a smaller dark spot on one side, which followed Venus in its transit. However, Samuel Dunn at Chelsea, England, who also watched that transit, did not see that additional spot. In 1764 there were 8 observations by two observers. Other observers tried to see the satellite but failed to find it.
Now the astronomical world was faced with a controversy: several observers had reported seeing the satellite while several others had failed to find it in spite of determined efforts. In 1766, the director of the Vienna observatory, Father Hell (!), published a treatise where he declared that all observations of the satellite were optical illusions -- the image of Venus is so bright that it is reflected in the eye, back into the telescope, creating a secondary image at a smaller scale. Others published treatises declaring that the observations were real. J. H. Lambert of Germany published orbital elements of the satellite in Berliner Astronomischer Jahrbuch 1777: mean distance 66.5 Venus radii, orbital period 11 days 3 hours, inclination to ecliptic 64 degrees. It was hoped that the satellite could be seen during the transit of Venus in front of the Sun June 1 1777 (it is self evident that Lambert made a mistake in calculating these orbital elements: at 66.5 Venus radii, the distance from Venus is about the same as our Moon's distance from the Earth. This fits very badly with the orbital period of 11 days or only somewhat more than 1/3 of the orbital period of our Moon. The mass of Venus is a little smaller than the mass of the Earth).
In 1768 there was one more observation of the satellite, by Christian Horrebow in Copenhagen. There were also three searches, one made by one of the greatest astronomers of all time, William Herschel -- all three of them failed to find any satellite. Quite late in the game, F. Schorr from Germany tried to make a case for the satellite in a book published in 1875.
In 1884, M. Hozeau, former director of the Royal Observatory of Brussels, suggested a different hypothesis. By analysing available observations Hozeau concluded that the Venus moon appeared close to Venus approximately every 2.96 years or 1080 days. Hozeau suggested that it wasn't a moon of Venus, but a planet of its own, orbiting the sun once every 283 days and thus being in conjunction with Venus once every 1080 days. Hozeau also named it Neith, after the mysterious goddess of Sais, whose veil no mortal raised.
In 1887, three years after the "moon of Venus" had been revived by Hozeau, the Belgian Academy of Sciences published a long paper where each and every reported observation was investigated in detail. Several observations of the satellite were really stars seen in the vicinity of Venus. Roedkier's observations "checked out" especially well -- he had been fooled, in succession, by Chi Orionis, M Tauri, 71 Orionis, and Nu Geminorum! James Short had really seen a star somewhat fainter than 8th magnitude. All observations by Le Verrier and Montaigne could be similarly explained. Lambert's orbital calculations were demolished. The very last observation, by Horrebow in 1768, could be ascribed to Theta Librae.
After this paper was published, only one more observation was reported, by a man who had earlier made a search for the satellite of Venus but failed to find it: on Aug 13 1892, E. E. Barnard recorded a 7th magnitude object near Venus. There is no star in the position recorded by Barnard, and Barnard's eyesight was notoriously excellent. We still don't know what he saw. Was it an asteroid that hadn't been charted? Or was it a short-lived nova that nobody else happened to see?
The Earth's Second Moon, 1846-present
In 1846, Frederic Petit, director of the observatory of Toulouse, stated that a second moon of the Earth had been discovered. It had been seen by two observers, Lebon and Dassier, at Toulouse and by a third, Lariviere, at Artenac, during the early evening of March 21 1846. Petit found that the orbit was elliptical, with a period of 2 hours 44 minutes 59 seconds, an apogee at 3570 km above the Earth's surface and perigee at just 11.4 km (!) above the Earth's surface. Le Verrier, who was in the audience, grumbled that one needed to take air resistance into account, something nobody could do at that time. Petit became obsessed with this idea of a second moon, and 15 years later announced that he had made calculations about a small moon of Earth which caused some then-unexplained peculiarities in the motion of our main Moon. Astronomers generally ignored this, and the idea would have been forgotten if not a young French writer, Jules Verne, had not read an abstract. In Verne's novel "From the Earth to the Moon", Verne lets a small object pass close to the traveller's space capsule, causing it to travel around the Moon instead of smashing into it:
"It is", said Barbicane, "a simple meteorite but an enormous one, retained as a satellite by the attraction of the Earth."Jules Verne was read by millions of people, but not until 1942 did anybody notice the discrepancies in Verne's text:
Nevertheless, Jules Verne made Petit's second moon known all over the world. Amateur astronomers jumped to the conclusion that here was opportunity for fame -- anybody discovering this second moon would have his name inscribed in the annals of science. No major observatory ever checked the problem of the Earth's second moon, or if they did they kept quiet. German amateurs were chasing what they called Kleinchen ("little bit") -- of course they never found Kleinchen.
W. H. Pickering devoted his attention to the theory of the subject: if the satellite orbited 320 km above the surface and if its diameter was 0.3 meters, with the same reflecting power as the Moon, it should be visible in a 3-inch telescope. A 3 meter satellite would be a unaided-eye object of magnitude 5. Though Pickering did not look for the Petit object, he did carry on a search for a secondary moon -- a satellite of our Moon ("On a photographic search for a satellite of the Moon", Popular Astronomy, 1903). The result was negative and Pickering concluded that any satellite of our Moon must be smaller than about 3 meters.
Pickering's article on the possibility of a tiny second moon of Earth, "A Meteoritic Satellite", appeared in Popular Astronomy in 1922 and caused another short flurry among amateur astronomers, since it contained a virtual request: "A 3-5-inch telescope with a low-power eyepiece would be the likeliest mean to find it. It is an opportunity for the amateur." But again, all searches remained fruitless.
The original idea was that the gravitational field of the second moon should account for the then inexplicable minor deviations of the motion of our big Moon. That meant an object at least several miles large -- but if such a large second moon really existed, it would have been seen by the Babylonians. Even if it was too small to show a disk, its comparative nearness would have made it move fast and therefore be conspicuous, as today's watchers of artificial satellites and even airplanes know. On the other hand, nobody was much interested in moonlets too small to be seen.
There have been other proposals for additional natural satellites of the Earth. In 1898 Dr Georg Waltemath from Hamburg claimed to have discovered not only a second moon but a whole system of midget moons. Waltemath gave orbital elements for one of these moons: distance from Earth 1.03 million km, diameter 700 km, orbital period 119 days, synodic period 177 days. "Sometimes", says Waltemath, "it shines at night like the Sun" and he thinks this moon was seen in Greenland on 24 October 1881 by Lieut Greely, ten days after the Sun had set for the winter. Public interest was aroused when Waltemath predicted his second moon would pass in front of the Sun on the 2nd, 3rd or 4th of February 1898. On the 4th February, 12 persons at the post office of Greifswald (Herr Postdirektor Ziegel, members of his family, and postal employees) observed the Sun with their unaided eye, without protection of the glare. It is easy to imagine a faintly preposterous scene: an imposing-looking Prussian civil servant pointing skyward through his office window, while he reads Waltemath's prediction aloud to a knot of respectful subordinates. On being interviewed, these witnesses spoke of a dark object having one fifth the Sun's apparent diameter, and which took from 1:10 to 2:10 Berlin time to traverse the solar disk. It was soon proven to be a mistake, because during that very hour the Sun was being scrutinized by two experienced astronomers, W. Winkler in Jena and Baron Ivo von Benko from Pola, Austria. They both reported that only a few ordinary sunspots were on the disk. The failure of this and later forecasts did not discourage Waltemath, who continued to issue predictions and ask for verifications. Contemporary astronomers were pretty irritated over and over again having to answer questions from the public like "Oh, by the way, what about all these new moons?". But astrologers caught on -- in 1918 the astrologer Sepharial named this moon Lilith. He considered it to be black enough to be invisible most of the time, being visible only close to opposition or when in transit across the solar disk. Sepharial constructed an ephemeris of Lilith, based on several of Waltemath's claimed observations. He considered Lilith to have about the same mass as the Moon, apparently happily unaware that any such satellite would, even if invisible, show its existence by perturbing the motion of the Earth. And even to this day, "the dark moon" Lilith is used by some astrologers in their horoscopes.
From time to time other "additional moons" were reported from observers. The German astronomical magazine "Die Sterne" reported that a German amateur astronomer named W. Spill had observed a second moon cross our first moon's disc on May 24, 1926.
Around 1950, when artificial satellites began to be discussed in earnest, everybody expected them to be just burned-out upper stages of multistage rockets, carrying no radio transmitters but being tracked by radar from the Earth. In such cases a bunch of small nearby natural satellites would have been most annoying, reflecting radar beams meant for the artificial satellites. The method to search for such natural satellites was developed by Clyde Tombaugh: the motion of a satellite at e.g. 5000 km height is computed. Then a camera platform is constructed that scans the sky at precisely that rate. Stars, planets etc will then appear as lines on the photographs taken by this camera, while any satellite at the correct altitude will appear as a dot. If the satellite was at a somewhat different altitude, it would produce a short line.
Observations began in 1953 at the Lowell Observatory and actually invaded virgin territory: with the exception of the Germans searching for "Kleinchen" nobody had ever paid attention to the space between the Moon and the Earth! By the fall of 1954, weekly journals and daily newspapers of high reputation stated that the search had brought its first results: one small natural satellite at 700 km altitude, another one 1000 km out. One general is said to have asked: "Is he sure they're natural?". Nobody seems to know how these reports originated -- the searches were completely negative. When the first artificial satellites were launched in 1957 and 1958, the cameras tracked those satellites instead.
But strangely enough, this does not mean that the Earth only has one natural satellite. The Earth can have a very near satellite for a short time. Meteoroids passing the Earth and skimming through the upper atmosphere can lose enough velocity to go into a satellite orbit around the Earth. But since they pass the upper atmosphere at each perigee, they will not last long, maybe only one or two, possibly a hundred revolutions (about 150 hours). There are some indications that such "ephemeral satellites" have been seen; it is even possible that Petit's observers did see one. (see also)
In addition to ephemeral satellites there are two more possibilities. One is that the Moon had a satellite of its own -- but despite several searches none has been found (in addition it's now known that the gravity field of the Moon is uneven or "lumpy" enough for any lunar satellite orbit to be unstable -- any lunar satellite will therefore crash into the Moon after a fairly short time, a few years or possibly a decade). The other possibility is that there might be Trojan satellites, i.e. secondary satellites in the lunar orbit, travelling 60 degrees ahead of or behind the Moon.
Such "Trojan satellites" were first reported by the Polish astronomer Kordylewski of Krakow observatory. He started his search in 1951, visually with a good telescope. He was hoping for reasonably large bodies in the lunar orbit, 60 degrees away from the Moon. The search was negative, but in 1956 his compatriot and colleague, Wilkowski, suggested that there may be many tiny bodies, too small to be seen individually but many enough to appear as a cloud of dust particles. In such a case, they would be best visible without a telescope i.e. with the unaided eye! Using a telescope would "magnify it out of existence". Dr Kordylewski was willing to try. A dark night with clear skies, and the Moon being below the horizon, was required.
In October 1956, Kordylewski saw, for the first time, a fairly bright patch in one of the two positions. It was not small, subtending an angle of 2 degrees (i.e. about 4 times larger than the Moon itself), and was very faint, only about half as bright as the notoriously difficult Gegenschein (counterglow -- a bright patch in the zodiacal light, directly opposite to the Sun). In March and April 1961, Kordylewski succeeded in photographing two clouds near the expected positions. They seem to vary in extent, but that may be due to changing illumination. J. Roach detected these cloud satellites in 1975 with the OSO (Orbiting Solar Observatory) 6 spacecraft. In 1990 they were again photographed, this time by the Polish astronomer Winiarski, who found that they were a few degrees in apparent diameter, that they "wandered" up to ten degrees away from the "trojan" point, and that they were somewhat redder than the zodiacal light.
So the century-long search for a second moon of the Earth seems to have succeeded, after all, even though this 'second moon' turned out to be entirely different from anything anybody had ever expected. They are very hard to detect and to distinguish from the zodiacal light, in particular the Gegenschein.
But people are still proposing additional natural satellites of the Earth. Between 1966 and 1969 John Bargby, an American scientist, claimed to have observed at least ten small natural satellites of the Earth, visible only in a telescope. Bargby found elliptical orbits for all the objects: eccentricity 0.498, semimajor axis 14065 km, which yields perigee and apogee heights of 680 and 14700 km. Bargby considered them to be fragments of a larger body which broke up in December 1955. He based much of his suggested satellites on supposed perturbations of artificial satellites. Bargby used artificial satellite data from Goddard Satellite Situation Report, unaware that the values in this publication are only approximate and sometimes grossly in error and can therefore not be used for any precise scientific analysis. In addition, from Bargby's own claimed observations it can be deduced that when at perigee Bargby's satellites ought to be visible at first magnitude and thus be easily visible to the unaided eye, yet no-one has seen them as such.
In 1997, Paul Wiegert (et al) discovered that the near-Earth asteroid 3753 Cruithne has a very strange orbit and can be considered a companion to Earth, though it certainly does not orbit the Earth directly. 2002 AA29 also has a special relationship with Earth.
The Moons of Mars, 1610, 1643, 1727, 1747, 1750, 1877-present
In 1643, the Capuchin monk Anton Maria Shyrl claimed to really have seen the moons of Mars. We now know that would be impossible with the telescopes of that time -- probably Shyrl got deceived by a star nearby Mars.
In 1727, Jonathan Swift in "Gulliver's Travels" wrote about two small moons orbiting Mars, known to the Laputian astronomers. Their periods of revolution were 10 and 21.5 hours. These 'moons' were in 1750 adopted by Voltaire in his novel "Micromegas", the story of a giant from Sirius visiting our solar system.
In 1747 a German captain, Kindermann, had claimed to have seen the moon (just one!) of Mars, on 10 July 1744. Kindermann reported the orbital period of this martian moon as 59 hours 50 minutes and 6 seconds (!)
In 1877, Asaph Hall finally discovered Phobos and Deimos, the two small moons of Mars. Their orbital periods are 7 hours 39 minutes and 30 hours 18 minutes, quite close to the periods guessed by Jonathan Swift 150 years earlier!
The 14th Moon of Jupiter, 1975-1980
In 1975, Charles Kowal at Palomar (discoverer of Comet 95 P/Chiron) photographed an object thought to be a new satellite of Jupiter. It was seen several times, but not enough to determine an orbit, then lost. It used to show up as a footnote in texts of the late 70s.
And then in 2000 it was found again by S. S. Sheppard et al!
Saturn's Ninth and Tenth Moons, 1861, 1905-1960, 1966-1980
In April 1861 Hermann Goldschmidt announced the discovery of a 9th moon of Saturn, which orbited the planet between Titan and Hyperion. He named that moon Chiron (!). However the discovery was never confirmed -- nobody else ever saw this satellite "Chiron". Later, Pickering discovered what's now considered Saturn's 9th moon, Phoebe, in 1898. This was the first time a satellite of another planet was discovered by photographical observations. Phoebe is also Saturn's outermost moon.
In 1905, Pickering though he had discovered a tenth moon, which he named Themis. According to Pickering, it orbited Saturn between the orbits of Titan and Hyperion in a highly inclined orbit: mean distance from Saturn 1,460,000 km, orbital period 20.85 days, eccentricity 0.23, inclination 39 degrees. Themis was never seen again, but nevertheless appeared in almanacs and astronomy books well into the 1950's and 1960's.
In 1966, A. Dollfus discovered another new moon of Saturn. It was named Janus, and orbited Saturn just outside its rings. It was so faint and close to the rings that the only chance to see it was when the rings of Saturn were seen from the edge, as happened in 1966. Now Janus was Saturn's tenth moon.
In 1980, when Saturns rings again were seen edgewise, a flurry of observations discovered a lot of new satellites close to the rings of Saturn. Close to Janus another satellite was discovered, named Epimetheus. Their orbits are very close to each other, and the most interesting aspect of this satellite pair is that they regularly switch orbits with each other! It turned out that the "Janus" discovered in 1966 really were observations of both of these co-orbital satellites. Thus the 'tenth moon of Saturn' discovered in 1966 really turned out to be two different moons! The spacecraft Voyager 1 and Voyager 2, which travelled past Saturn shortly afterwards, confirmed this.
Six Moons of Uranus, 1787
In 1787, William Herschel announced the discovery of six satellites of Uranus. Herschel here made a mistake -- only two of his six satellites were real (Titania and Oberon, the largest and outermost two satellites), the remaining four were just stars which happened to be nearby (...I think I've heard this story before.... :-)
Planet X, 1841-1992
In 1841, John Couch Adams began investigating the by then quite large residuals in the motion of Uranus. In 1845, Urbain Le Verrier started to investigate them, too. Adams presented two different solutions to the problem, assuming that the deviations were caused by the gravitation from an unknown planet. Adams tried to present his solutions to the Greenwich observatory, but since he was young and unknown, he wasn't taken seriously. Urbain Le Verrier presented his solution in 1846, but France lacked the necessary resources to locate the planet. Le Verrier then instead turned to the Berlin observatory, where Galle and his assistant d'Arrest found Neptune on the evening of Sept 23, 1846. Nowadays, both Adams and Le Verrier share the credit of having predicted the existence and position of Neptune.
Inspired by this success, Le Verrier attacked the problem of the deviations of Mercury's orbit, and suggested the existence of an intra-mercurial planet, Vulcan, which later turned out to be non-existent.)
On 30 Sept 1846, one week after the discovery of Neptune, Le Verrier declared that there may be still another unknown planet out there. On October 10, Neptune's large moon Triton was discovered, which yielded an easy way to determine accurately the mass of Neptune, which turned out to be 2% larger than expected from the perturbations upon Uranus. It seemed as if the deviations in Uranus' motion really was caused by two planets -- in addition the real orbit of Neptune turned out to be significantly different from the orbits predicted by both Adams and Le Verrier.
In 1850 Ferguson was observing the motion of the minor planet Hygeia. One reader of Ferguson's report was Hind, who checked the reference stars used by Ferguson. Hind was unable to find one of Ferguson's reference stars. Maury, at the Naval Observatory, was also unable to find that star. During a few years it was believed that this was an observation of yet another planet, but in 1879 another explanation was offered: Ferguson had made a mistake when recording his observation -- when that mistake was corrected, another star nicely fit his 'missing reference star'.
The first serious attempt to find a trans-Neptunian planet was done in 1877 by David Todd. He used a "graphical method", and despite the inconclusivenesses of the residuals of Uranus, he derived elements for a trans-Neptunian planet: mean distance 52 a.u., period 375 years, magnitude fainter than 13. Its longitude for 1877.84 was given 170 degrees with an uncertainty of 10 degrees. The inclination was 1.40 degrees and the longitude of the ascending node 103 degrees.
In 1879, Camille Flammarion added another hint as to the existence of a planet beyond Neptune: the aphelia of periodic comets tend to cluster around the orbits of major planets. Jupiter has the greatest share of such comets, and Saturn, Uranus and Neptune also have a few each. Flammarion found two comets, 1862 III with a period of 120 years and aphelion at 47.6 a.u., and 1889 II, with a somewhat longer period and aphelion at 49.8 a.u. Flammarion suggested that the hypothetical planet probably moved at 45 a.u.
One year later, in 1880, professor Forbes published a memoir concerning the aphelia of comets and their association with planetary orbits. By about 1900 five comets were known with aphelia outside Neptune's orbit, and then Forbes suggested one trans-Neptunian moved at a distance of about 100 a.u., and another one at 300 a.u., with periods of 1000 and 5000 years.
During the next five years, several astronomers/mathematicians published their own ideas of what might be found in the outer parts of the solar system. Gaillot at Paris Observatory assumed two trans-Neptunian planets at 45 and 60 a.u. Thomas Jefferson Jackson See predicted three trans-Neptunian planets: "Oceanus" at 41.25 a.u. and period 272 years, "trans-Oceanus" at 56 a.u. and period 420 years, and finally another one at 72 a.u. and period 610 years. Dr Theodor Grigull of Munster, Germany, assumed in 1902 a Uranus-sized planet at 50 a.u. and period 360 years, which he called "Hades". Grigull based his work mainly on the orbits of comets with aphelia beyond Neptune's orbit, with a cross check whether the gravitational pull of such a body would produce the observed deviations in Uranus motion. In 1921 Grigull revised the orbital period of "Hades" to 310-330 years, to better fit the observed deviations.
In 1900 Hans-Emil Lau, Copenhagen, published elements of two trans-Neptunian planets at 46.6 and 70.7 a.u. distance, with masses of 9 and 47.2 times the Earth, and a magnitude for the nearer planet around 10-11. The 1900 longitudes of those hypothetical bodies were 274 and 343 degrees, both with the very large uncertainty of 180 degrees.
In 1901, Gabriel Dallet deduced a hypothetical planet at 47 a.u. with a magnitude of 9.5-10.5 and a 1900 longitude of 358 degrees. The same year Theodor Grigull derived a longitude of a trans-Neptunian planet less than 6 degrees away from Dallet's planet, and later brought the difference down to 2.5 degrees. This planet was supposed to be 50.6 a.u. distant.
In 1904, Thomas Jefferson Jackson See suggested three trans-Neptunian planets, at 42.25, 56 and 72 a.u. The inner planet had a period of 272.2 years and a longitude in 1904 of 200 degrees. A Russian general named Alexander Garnowsky suggested four hypothetical planets but failed to supply any details about them.
The two most carefully worked out predictions for the Trans-Neptune were both of American origin: Pickering's "A search for a planet beyond Neptune" (Annals Astron. Obs. Harvard Coll, vol LXI part II 1909), and Percival Lowell's "Memoir on a trans-Neptunian planet" (Lynn, Mass 1915). They were concerned with the same subject but used different approaches and arrived at different results.
Pickering used a graphical analysis and suggested a "Planet O" at 51.9 a.u. with a period of 373.5 years, a mass twice the Earth's and a magnitude of 11.5-14. Pickering suggested eight other trans-Neptunian planets during the forthcoming 24 years. Pickerings results caused Gaillot to revise the distances of his two trans-Neptunians to 44 and 66 a.u., and he gave them masses of 5 and 24 Earth masses.
All in all, from 1908 to 1932, Pickering proposed seven hypothetical planets -- O, P, Q, R, S, T and U. His final elements for O and P define completely different bodies than the original ones, so the total can be set at nine, certainly the record for planetary prognostication. Most of Pickerings predictions are only of passing interest as curiosities. In 1911 Pickering suggested that planet Q had a mass of 20,000 Earths, making it 63 times more massive than Jupiter or about 1/6 the Sun's mass, close to a star of minimal mass. Pickering said planet Q had a highly elliptical orbit.
In later years only planet P seriously occupied his attention. In 1928 he reduced the distance of P from 123 to 67.7 a.u., and its period from 1400 to 556.6 years. He gave P a mass of 20 Earth masses and a magnitude of 11. In 1931, after the discovery of Pluto, he issued another elliptical orbit for P: distance 75.5 a.u., period 656 years, mass 50 Earth masses, eccentricity 0.265, inclination 37 degrees, close to the values given for the 1911 orbit. His Planet S, proposed in 1928 and given elements in 1931, was put at 48.3 a.u. distance (close to Lowell's Planet X at 47.5 a.u.), period 336 years, mass 5 Earths, magnitude 15. In 1929 Pickering proposed planet U, distance 5.79 a.u., period 13.93 years, i.e. barely outside Jupiter's orbit. Its mass was 0.045 Earth masses, eccentricity 0.26. The least of Pickering's planets is planet T, suggested in 1931: distance 32.8 a.u., period 188 years.
Pickering's different elements for planet O were:
Mean dist Period Mass Magnitude Node Incl Longitude 1908 51.9 373.5 y 2 earth's 11.5-13.4 105.13 1919 55.1 409 y 15 100 15 1928 35.23 209.2 y 0.5 earth's 12Percival Lowell, most well known as a proponent for canals on Mars, built a private observatory in Flagstaff, Arizona. Lowell called his hypothetical planet Planet X, and performed several searches for it, without success. Lowell's first search for Planet X came to an end in 1909, but in 1913 he started a second search, with a new prediction of Planet X: epoch 1850-01-01, mean long 11.67 deg, perih. long 186, eccentricity 0.228, mean dist 47.5 a.u. long arc node 110.99 deg, inclination 7.30 deg, mass 1/21000 solar masses. Lowell and others searched in vain for this Planet X in 1913-1915. In 1915, Lowell published his theoretical results of Planet X. It is ironical that this very same year, 1915, two faint images of Pluto was recorded at Lowell observatory, although they were never recognized as such until after the discovery of Pluto (1930). Lowell's failure of finding Planet X was his greatest disappointment in life. He didn't spend much time looking for Planet X during the last two years of his life. Lowell died in 1916. On the nearly 1000 plates exposed in this second search were 515 asteroids, 700 variable stars and 2 images of Pluto!
The third search for Planet X began in April 1927. No progress was made in 1927-1928. In December 1929 a young farmer's boy and amateur astronomer, Clyde Tombaugh from Kansas, was hired to do the search. Tombaugh started his work in April 1929. On January 23 and 29, Tombaugh exposed the pair of plates on which he found Pluto when examining them on February 18. By then Tombaugh had examined hundreds of plate pairs and millions of stars. The search for Planet X had come to an end.
Or had it? The new planet, later named Pluto, turned out to be disappointingly small, perhaps only one Earth mass but probably only about 1/10 Earth masses or smaller (in 1979, when Pluto's satellite Charon was discovered, the mass of the Pluto-Charon pair turned out to be only about 1/400 Earth mass!). Planet X must, if it was causing those perturbations in the orbit of Uranus, be much larger than that! Tombaugh continued his search another 13 years, and examined the sky from the north celestial pole to 50 deg. south declination, down to magnitude 16-17, sometimes even 18. Tombaugh examined some 90 million images of some 30 million stars over more than 30,000 square degrees on the sky. He found one new globular cluster, 5 new open star clusters, one new supercluster of 1800 galaxies and several new small galaxy clusters, one new comet, about 775 new asteroids -- but no new planet except Pluto. Tombaugh concluded that no unknown planet brighter than magnitude 16.5 did exist -- only a planet in an almost polar orbit and situated near the south celestial pole could have escaped his detection. He could have picked up a Neptune-sized planet at seven times the distance of Pluto, or a Pluto-sized planet out to 60 a.u.
The naming of Pluto is a story by itself. Early suggestions of the name of the new planet were: Atlas, Zymal, Artemis, Perseus, Vulcan, Tantalus, Idana, Cronus. The New York Times suggested Minerva, reporters suggested Osiris, Bacchus, Apollo, Erebus. Lowell's widow suggested Zeus, but later changed her mind to Constance. Many people suggested the planet be named Lowell. The staff of the Flagstaff observatory, where Pluto was discovered, suggested Cronus, Minerva, and Pluto. A few months later the planet was officially named Pluto. The name Pluto was originally suggested by Venetia Burney, an 11-year-old schoolgirl in Oxford, England.
The very first orbit computed for Pluto yielded an eccentricity of
0.909 and a period of 3000 years! This cast some doubt whether it
was a planet or not. However, a few months later, considerably
better orbital elements for Pluto were obtained. Below is a
comparison of the orbital elements of Lowell's Planet X, Pickering's
Planet O, and Pluto:
Lowell's X Pickering's O Pluto a (mean dist) 43.0 55.1 39.5 e (eccentricity) 0.202 0.31 0.248 i (inclination) 10 15 17.1 N (long asc node) (not pred) 100 109.4 W (long perihelion) 204.9 280.1 223.4 T (perihelion date) Febr 1991 Jan 2129 Sept 1989 u (mean annual motion) 1.2411 0.880 1.451 P (period, years) 282 409.1 248 T (perihel. date) 1991.2 2129.1 1989.8 E (long 1930.0) 102.7 102.6 108.5 m (mass, Earth=1) 6.6 2.0 0.002 M (magnitude) 12-13 15 15The mass of Pluto was very hard to determine. Several values were given at different times -- the matter wasn't settled until James W. Christy discovered Pluto's moon Charon in June 1978 -- Pluto was then shown to have only 20% of the mass of our Moon! That made Pluto hopelessly inadequate to produce measurable gravitational perturbations on Uranus and Neptune. Pluto could not be Lowell's Planet X -- the planet found was not the planet sought. What seemed to be another triumph of celestial mechanics turned out to be an accident -- or rather a result of the intelligence and thoroughness of Clyde Tombaugh's search.
The mass of Pluto:
Crommelin 1930: 0.11 (Earth masses) Nicholson 1931: 0.94 Wylie, 1942: 0.91 Brouwer, 1949: 0.8-0.9 Kuiper, 1950: 0.10 1965: <0.14 (occultation of faint star by Pluto) Seidelmann, 1968: 0.14 Seidelmann, 1971: 0.11 Cruikshank, 1976: 0.002 Christy, 1978: 0.002 (Charon discovered)Another short-lived trans-Neptunian suspect was reported on April 22 1930 by R.M. Stewart in Ottawa, Canada -- it was reported from plates taken in 1924. Crommelin computed an orbit (dist 39.82 a.u., asc node 280.49 deg, inclination 49.7 deg!). Tombaugh searched for the "Ottawa object" without finding it. Several other searches were made, but nothing was ever found.
Meanwhile Pickering continued to predict new planets (see above).
Others also predicted new planets on theoretical grounds (Lowell
himself had already suggested a second trans-Neptunian at about 75
a.u.). In 1946, Francis M. E. Sevin suggested a trans-Plutonian
planet at 78 a.u. He first derived this from a curious empirical
method where he grouped the planets and the erratic asteroid
Hidalgo, into two groups of inner and outer bodies:
Group I: Mercury Venus Earth Mars Asteroids Jupiter Group II: ? Pluto Neptune Uranus Saturn HidalgoHe then added the logarithms of the periods of each pair of planets, finding a roughly constant sum of about 7.34. Assuming this sum to be valid for Mercury and the trans-Plutonian too, he arrived at a period of about 677 years for "Transpluto". Later Sevin worked out a full set of elements for "Transpluto": dist 77.8 a.u., period 685.8 years, eccentricity 0.3, mass 11.6 Earth masses. His prediction stirred little interest among astronomers.
In 1950, K. Schutte of Munich used data from eight periodic comets to suggest a trans-Plutonian planet at 77 a.u. Four years later, H. H. Kitzinger of Karlsruhe, using the same eight comets, extended and refined the work, finding the supposed planet to be at 65 a.u., with a period of 523.5 years, an orbital inclination of 56 degrees, and an estimated magnitude of 11. In 1957, Kitzinger reworked the problem and arrived at new elements: dist 75.1 a.u., period 650 years, inclination 40 degrees, magnitude around 10. After unsuccessful photographic searches, he re-worked the problem once again in 1959, arriving at a mean dist of 77 a.u., period 675.7 years, inclination 38 degrees, eccentricity 0.07, a planet not unlike Sevin's "Transpluto" and in some ways similar to Pickering's final Planet P. No such planet has ever been found, though.
Halley's Comet has also been used as a "probe" for trans-plutonian planets. In 1942 R. S. Richardson found that an Earth-sized planet at 36.2 a.u., or 1 a.u. beyond Halley's aphelion, would delay Halley's perihelion passage so that it agreed better with observations. A planet at 35.3 a.u. of 0.1 Earth masses would have a similar effect. In 1972, Brady predicted a planet at 59.9 a.u., period 464 years, eccentricity 0.07, inclination 120 degrees (i.e. being in a retrograde orbit), magnitude 13-14, size about Saturn's size. Such a trans-Plutonian planet would reduce the residuals of Halley's Comet significantly back to the 1456 perihelion passage. This gigantic trans-Plutonian planet was also searched for, but never found.
Tom van Flandern examined the positions of Uranus and Neptune in the 1970s. The calculated orbit of Neptune fit observations only for a few years, and then started to drift away. Uranus orbit fit the observations during one revolution but not during the previous revolution. In 1976 Tom van Flandern became convinced that there was a tenth planet. After the discovery of Charon in 1978 showed the mass of Pluto to be much smaller than expected, van Flandern convinced his USNO colleague Robert S. Harrington of the existence of this tenth planet. They started to collaborate by investigate the Neptunian satellite system. Soon their views diverged. van Flandern thought the tenth planet had formed beyond Neptune's orbit, while Harrington believed it had formed between the orbits of Uranus and Neptune. van Flandern thought more data was needed, such as an improved mass for Neptune furnished by Voyager 2. Harrington started to search for the planet by brute force -- he started in 1979, and by 1987 he had still not found any planet. van Flandern and Harrington suggested that the tenth planet might be near aphelion in a highly elliptical orbit. If the planet is dark, it might be as faint as magnitude 16-17, suggests van Flandern.
In 1987, Whitmire and Matese suggested a tenth planet at 80 a.u. with a period of 700 years and an inclination of perhaps 45 degrees, as an alternative to their "Nemesis" hypothesis. However, according to Eugene M. Shoemaker, this planet could not have caused those meteor showers that Whitmire and Matese suggested (see below).
In 1987, John Anderson at JPL examined the motions of the spacecraft Pioneer 10 and Pioneer 11, to see if any deflection due to unknown gravity forces could be found. None was found -- from this Anderson concluded that a tenth planet most likely exists! JPL had excluded observations of Uranus prior to 1910 in their ephemerides, while Anderson had confidence in the earlier observations as well. Anderson concluded that the tenth planet must have a highly elliptical orbit, carrying it far away to be undetectable now but periodically bringing it close enough to leave its disturbing signature on the paths of the outer planets. He suggests a mass of five Earth masses, an orbital period of about 700-1000 years, and a highly inclined orbit. Its perturbations on the outer planets won't be detected again until 2600. Anderson hoped that the two Voyagers would help to pin down the location of this planet.
Conley Powell, from JPL, also analyzed the planetary motions. He also found that the observations of Uranus suddenly did fit the calculations much better after 1910 than before. Powell suggested a planet with 2.9 Earth masses at 60.8 a.u. from the Sun, a period of 494 years, inclination 8.3 degrees and only a small eccentricity. Powell was intrigued that the period was approximately twice Pluto's and three times Neptune's period, suggesting that the planet he thought he saw in the data had an orbit stabilized by mutual resonance with its nearest neighbours despite their vast separation. The solution called for the planet to be in Gemini, and also being brighter than Pluto when it was discovered. A search was performed in 1987 at Lowell Observatory for Powell's planet -- nothing was found. Powell re-examined his solution and revised the elements: 0.87 Earth masses, distance 39.8 a.u., period 251 years, eccentricity 0.26, i.e. an orbit very similar to Pluto's! Currently, Powell's new planet should be in Leo, at magnitude 12, however Powell thinks it's premature to search for it, he needs to examine his data further.
Even if no trans-Plutonian planet ever was found, the interest was focused to the outer parts of the solar system. The erratic asteroid Hidalgo, moving in an orbit between Jupiter and Saturn, has already been mentioned. In 1977-1984 Charles Kowal performed a new systematic search for undiscovered bodies in the solar system, using Palomar Observatory's 48-inch Schmidt telescope. In October 1987 he found the asteroid 1977 UB, later named Chiron, moving at mean distance 13.7 a.u., period 50.7 years, eccentricity 0.3786, inclination 6.923 deg, diameter about 50 km. During his search, Kowal also found 5 comets and 15 asteroids, including Chiron, the most distant asteroid known when it was discovered. Kowal also recovered 4 lost comets and one lost asteroid. Kowal did not find a tenth planet, and concluded that there was no unknown planet brighter than 20th magnitude within 3 degrees of the ecliptic.
Chiron was first announced as a "tenth planet", but was immediately designated as an asteroid. But Kowal suspected it may be very comet-like, and later it has even developed a short cometary tail! In 1995 Chiron was also classified as a comet - it is certainly the largest comet we know about.
In 1992 an even more distant asteroid was found: Pholus. Later in 1992 an asteroid outside Pluto's orbit was found, followed by five additional trans-Plutonian asteroids in 1993 and at least a dozen in 1994!
Meanwhile, the spacecraft Pioneer 10 and 11 and Voyagers 1 and 2 had
travelled outside the solar system, and could also be used as
"probes" for unknown gravitational forces possibly from unknown
planets -- nothing has been found. The Voyagers also yielded more
accurate masses for the outer planets -- when these updated masses
were inserted in the numerical integrations of the solar system, the
residuals in the positions of the outer planets finally disappeared.
It seems like the search for "Planet X" finally has come to an end.
There was no "Planet X" (Pluto doesn't really count), but instead an
asteroid belt outside Neptune/Pluto was found! The asteroids outside
Jupiter's orbit that were known in August 1993 are as follows:
Asteroid a e Incl Node Arg perih Mean an Per Name a.u. deg deg deg deg yr 944 5.79853 .658236 42.5914 21.6567 56.8478 60.1911 14.0 Hidalgo 2060 13.74883 .384822 6.9275 209.3969 339.2884 342.1686 51.0 Chiron 5145 20.44311 .575008 24.6871 119.3877 354.9451 7.1792 92.4 Pholus 5335 11.89073 .866990 61.8583 314.1316 191.3015 23.3556 41.0 Damocles 1992QB1 43.82934 .087611 2.2128 359.4129 44.0135 324.1086 290 1993FW 43.9311 .04066 7.745 187.914 359.501 0.4259 291 Epoch: 1993-08-01.0 TTIn November 1994 these trans-Neptunian asteroids were known:
Object a e incl R Mag Diam Discovery Discoverers a.u. deg km Date 1992 QB1 43.9 0.070 2.2 22.8 283 1992 Aug Jewitt & Luu 1993 FW 43.9 0.047 7.7 22.8 286 1993 Mar Jewitt & Luu 1993 RO 39.3 0.198 3.7 23.2 139 1993 Sep Jewitt & Luu 1993 RP 39.3 0.114 2.6 24.5 96 1993 Sep Jewitt & Luu 1993 SB 39.4 0.321 1.9 22.7 188 1993 Sep Williams et al. 1993 SC 39.5 0.185 5.2 21.7 319 1993 Sep Williams et al. 1994 ES2 45.3 0.012 1.0 24.3 159 1994 Mar Jewitt & Luu 1994 EV3 43.1 0.043 1.6 23.3 267 1994 Mar Jewitt & Luu 1994 GV9 42.2 0.000 0.1 23.1 264 1994 Apr Jewitt & Luu 1994 JQ1 43.3 0.000 3.8 22.4 382 1994 May Irwin et al. 1994 JR1 39.4 0.118 3.8 22.9 238 1994 May Irwin et al. 1994 JS 39.4 0.081 14.6 22.4 263 1994 May Luu & Jewitt 1994 JV 39.5 0.125 16.5 22.4 254 1994 May Jewitt & Luu 1994 TB 31.7 0.000 10.2 21.5 258 1994 Oct Jewitt & Chen 1994 TG 42.3 0.000 6.8 23.0 232 1994 Oct Chen et al. 1994 TG2 41.5 0.000 3.9 24.0 141 1994 Oct Hainaut 1994 TH 40.9 0.000 16.1 23.0 217 1994 Oct Jewitt et al. 1994 VK8 43.5 0.000 1.4 22.5 273 1994 Nov Fitzwilliams et al. Diameter is in km (and is based on the magnitudes and a guess at albedo, and is given to too many significant figures)The trans-Neptunian bodies seem to form two groups. One group, composed of Pluto, 1993 SC, 1993 SB and 1993 RO, have eccentric orbits and a 3:2 resonance with Neptune. The second group, including 1992 QB1 and 1993 FW, is slightly further out and in rather low eccentricity.
Nemesis, the Sun's companion star, 1983-present
Suppose our Sun was not alone but had a companion star. Suppose that this companion star moved in an elliptical orbit, its solar distance varying between 90,000 a.u. (1.4 light years) and 20,000 a.u., with a period of 30 million years. Also suppose this star is dark or at least very faint, and because of that we haven't noticed it yet.
This would mean that once every 30 million years that hypothetical companion star of the Sun would pass through the Oort cloud (a hypothetical cloud of proto-comets at a great distance from the Sun). During such a passage, the proto-comets in the Oort cloud would be stirred around. Some tens of thousands of years later, here on Earth we would notice a dramatic increase in the the number of comets passing the inner solar system. If the number of comets increases dramatically, so does the risk of the Earth colliding with the nucleus of one of those comets.
When examining the Earth's geological record, it appears that about once every 30 million years a mass extinction of life on Earth has occurred. The most well-known of those mass extinctions is of course the dinosaur extinction some 65 million years ago. About 25 million years from now it's time for the next mass extinction, according to this hypothesis.
This hypothetical "death companion" of the Sun was suggested in 1985 by Daniel P. Whitmire and John J. Matese, Univ of Southern Louisiana. It has even received a name: Nemesis. One awkward fact of the Nemesis hypothesis is that there is no evidence whatever of a companion star of the Sun. It need not be very bright or very massive, a star much smaller and dimmer than the Sun would suffice, even a brown or a black dwarf (a planet-like body insufficiently massive to start "burning hydrogen" like a star). It is possible that this star already exists in one of the catalogues of dim stars without anyone having noted something peculiar, namely the enormous apparent motion of that star against the background of more distant stars (i.e. its parallax). If it should be found, few will doubt that it is the primary cause of periodic mass extinctions on Earth.
But this is also a notion of mythical power. If an anthropologist of a previous generation had heard such a story from his informants, the resulting scholarly tome would doubtless use words like 'primitive' or 'pre-scientific'. Consider this story:
There is another Sun in the sky, a Demon Sun we cannot see. Long ago, even before great grandmother's time, the Demon Sun attacked our Sun. Comets fell, and a terrible winter overtook the Earth. Almost all life was destroyed. The Demon Sun has attacked many times before. It will attack again.This is why some scientists thought this Nemesis theory was a joke when they first heard of it -- an invisible Sun attacking the Earth with comets sounds like delusion or myth. It deserves an additional dollop of skepticism for that reason: we are always in danger of deceiving ourselves. But even if the theory is speculative, it's serious and respectable, because its main idea is testable: you find the star and examine its properties.
However, since the examination of the entire sky in the far IR by IRAS with no "Nemesis" found, the existence of "Nemesis" is not very likely.
Willy Ley: "Watcher's of the skies", The Viking Press NY,1963,1966,1969
William Graves Hoyt: "Planet X and Pluto", The University of Arizona Press 1980, ISBN 0-8165-0684-1, 0-8165-0664-7 pbk.
Carl Sagan, Ann Druyan: "Comet", Michael Joseph Ltd, 1985, ISBN 0-7181-2631-9
Mark Littman: "Planets Beyond - discovering the outer solar system", John Wiley 1988, ISBN 0-471-61128-X
Tom van Flandern: "Dark Matter, Missing Planets & New Comets. Paradoxes resolved, origins illuminated", North Atlantic Books 1993, ISBN 1-55643-155-4
Joseph Ashbrook: "The many moons of Dr Waltemath", Sky and Telescope, Vol 28, Oct 1964, p 218, also on page 97-99 of "The Astronomical Scrapbook" by Joseph Ashbrook, SKy Publ. Corp. 1984, ISBN 0-933346-24-7
Delphine Jay: "The Lilith Ephemeris", American Federation of Astrologers 1983, ISBN 0-86690-255-4
William R. Corliss: "Mysterious Universe: A handbook of astronomical anomalies", Sourcebook Project 1979, ISBN 0-915554-05-4, p 45-71 "The intramercurial planet", p 82-84 "Mercury's moon that wasn't", p 136-143 "Neith, the lost satellite of Venus", p 146-157 "Other moons of the Earth", p 423-427 "The Moons of Mars", p 464 "A ring around Jupiter?", p 500-526 "Enigmatic objects"
Richard Baum & William Sheehan: "In Search of Planet Vulcan" Plenum Press, New York, 1997 ISBN 0-306-45567-6 , QB605.2.B38
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