THE EXISTENCE OF AN ULTRA-NEPTUNIAN 



PLANET. 



By PHILIP H. LING, M.Sc. 



Thk discoveries of the planets Uranus and Neptune 

 were the first two steps in the outward extension of 

 our knowledge of the solar system. The third 

 step — the discovery of a planet still more distant — 

 is yet to be made. There is, however, a consider- 

 able amount of evidence for the existence of such a 

 planet, and in the present article it is proposed to 

 give a short discussion of the arguments which have 

 been brought forward. 



It should be remarked at the outset, that visual 

 observation will play no part in the argument ; for it 

 is almost certain that no planet exists of sufficiently 

 large dimensions. We, therefore, have recourse to 

 indirect methods by studying the effects which the 

 hypothetical planet may be supposed to produce in 

 bodies which are themselves capable of being 

 observed. ' 



(1) The most obvious way of doing this is by- 

 examining the perturbations of Neptune. Now the 

 latter has a period of one hundred and sixty-five 

 years and has only been under continuous observa- 

 tion since 1846 — that is, for less than one half of its 

 orbit. It is obvious that no certain conclusions can 

 as yet be drawn from so small a portion of Neptune's 

 path ; and while the method may be useful centuries 

 hence, it is at present too precarious. 



(2) A more hopeful plan is to study the perturba- 

 tions of Uranus. These are not completely explained 

 by the attraction of Neptune, and have recently been 

 examined almost simultaneously by Pickering* and 

 by Gaillot,+ working independently. They agree in 

 the mean distance of the unknown planet, which is 

 given as about fifty-two astronomical units ; but 

 Pickering finds the mass to be twice the mass of the 

 earth, while Gaillot makes it five times : the latter 

 also suggests a still more distant planet to be 

 required. The smallness of the mass militates 

 heavily against the correctness of the arguments 

 since the effects produced must be infinitesimal. 



(3) The best method of all is that derived from 

 the orbits of comets. If we compile as complete a 

 list as possible of the periodic comets, arranged in 



ascending order of period, a very striking fact 

 becomes apparent. They are seen to fall into 

 groups, the first of which contains those with periods 

 ranging from 3-3 to nine years, the second those of 

 period about thirteen, the third about thirty-three, 

 the fourth about seventy-three, while there seems to 

 be a fifth with period about one hundred and 

 twenty-one years. Now each of these groups 

 contains comets whose aphelia are approximately at 

 the same distance as one of the planets Jupiter, 

 Saturn, Uranus, and Neptune, while the fifth group 

 seems to correspond to a hitherto unknown planet. 

 There is, therefore, apparently some connection 

 between these groups of comets and the correspond- 

 ing planet, and before basing any argument on it, it 

 is necessary to inquire more closely into the nature 

 of the relation. 



Now the most obvious explanation of the relation 

 between comets and planets, is that known as the 

 " capture " theory. ^According to this, at some 

 previous era the comet approached so closely to the 

 planet, that the gravitational attraction of the latter 

 was sufficient to overpower that of the sun, but not 

 large enough to transform the comet into a satellite. 

 The orbit thus became a long ellipse, with one focus 

 in the sun and the other in the position temporarily 

 occupied by the planet ; and this orbit would remain 

 permanent in the absence of commensurability 

 between the periods. 



This appears to afford an explanation ; but two 

 difficulties, mentioned by NewcombL arise. In the 

 first place, Encke's comet has its orbit completely 

 within that of Jupiter, and no close approach occurs; 

 but we know that this comet probably passes through 

 a resisting medium, which is altering the major axis, 

 and it has been shown by Backlund§ that " capture " 

 within the last five thousand seven hundred years is 

 not by any means impossible. 



The second difficulty is extremely serious. The 

 planets all move nearly in the same plane ; the 

 orbits of comets, however, are inclined to this plane 

 at all angles, and, as a result, though the statement 



:;: See Nature, June 17th and August 26th, 1909. 



I Comptes Rendu*, March, 1909. See Nature, July Sth, 1909. 



[ "Encyclopaedia Britannica," 11th edition, Art. "Comet." 



>' Royal Astronomical Society, Monthly Notices, LXX, 5, (March, 1910). 



171 



