by Paul Schlyter

from TheNineTenPlanets Website

University of Arizona

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 accurately determine 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

• 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)

• 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:

Percival 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 put 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 1/1000 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 was obtained. Below is a comparison of the orbital elements of Lowell’s Planet X, Pickering’s Planet O, and Pluto:
 

The 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:
 

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    Hidalgo

He 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 20^th 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:
 

In November 1994 these trans-Neptunian asteroids were known:
 

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  TT

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.