September, 1906.] 



KNOWLEDGE & SCIENTIFIC NEWS. 



535 



The New Planet TG. 



By A. C. D. Crommelin. 

 The zone of asteroids has certainly attracted more 

 attention from astronomers since the discovery of Eros 

 in 1898. There was a natural expectation that further 

 sensational orbits might be discovered, and after a 

 lapse of eight years this expectation has been realised. 

 The planet TG is indeed of less practical importance 

 than Eros, which has already proved so useful in 

 measuring the Sun's distance, but its theoretical 

 interest is nearly, if not quite, as high. Tlie new planet 

 is remarkable for its very large mean distance, which is 

 practically identical with that of Jupiter; and as it has a 

 considerable eccentricity, its aphelion lies far outside 

 Jupiter's orbit, so that the family of asteroids, as now 

 known, ranges from distance i.i (perihelion of Eros) to 

 distance 6.1 (aphelion of TG). Tliey have in fact burst 

 their bounds in each direction, going far inside the orbit 

 of IMars and far outside that of Jupiter. It is probable 

 that the disturbing action of these two planets has 

 brought Eros and TG into their present orbits. Herr 

 Dziewulski, of Cracow, has recently published some 

 researches on the motion of Eros, in which he takes 

 account of the modification of its orbit produced by the 

 action of the other planets, and finds that about B.C. 

 7,400 its orbit intersected that of Mars, so that very 

 close approaches of the two planets would be likely to 

 occur. It is, in fact, very probable that the orbit of Eros 

 was deflected into its present position by such an en- 

 counter or series of encounters with Mars. Its orbit 

 even now cannot be looked on as perfectly stable, for 

 about A.D. 8,800 it will again intersect that of Mars, 

 and further notable changes are likely to occur, whose 

 exact character it is at present impossible to determine. 

 It would at first sight appear that TG was in still 

 greater danger of destructive changes in its orbit than 

 Eros, for its troublesome neighbour is not the small 

 and feeble Mars, but the giant planet Jupiter, notorious 

 for the mighty disturbances which he produces in the 

 orbits of heavenly bodies so* unfortunate as to^ pass near 

 him. However, Professor C. V. L. Charlier (in Astr. 

 Nac/ir/c/iieii, No. 4,094) indicates a possible way of 

 escape for TG from such destructive chang^es, which 

 will at the same time afford a most interesting illustra- 

 tion of a principle which had already been recogni.sed as 

 theoretically possible, although no actual case was 

 known. The "Problem of Tliree Bodies" or the 

 attempt tO' arrive at expressions which will give their 

 mutual positions at any time we may desire, is probably 

 insoluble in the general ca.sc, though the results of lunar 

 and planetary theory have been arrived at thanks to the 

 circumstance that in these cases one of the attracting 

 bodies is greatly superior to the others in its action, 

 and a soUition by successive approximation is thus ren- 

 dered possible. There are, however, a few simple cases 

 where a rigorous solution of the problem has been 

 arrived at. One is when the three bodies are in a 

 straight line and also moving in that line. In this case 

 elementary methods suffice for a solution (at least so 

 long as no collision takes place; if such happens a know- 

 ledge of the elasticity of the bodies is rec|uired, before 

 we can predict their sub.sequent behaviour). A more 

 interesting case is the one which Dr. Charlier considers 

 may very probably be exemplified by the Sun, Jupiter 

 and iX;. Lagrange showed that if three bodies 

 arc placed at the angles of an equilateral triangle and 

 projected with appropriate spcxids in the proper direc- 

 tions, they will continue to form an equilateral triangle 



unless disturbed by some extraneous force such as a 

 fourth body, a resisting medium, etc. Dr. Charlier 

 himself continued the investigation in " Publications of 

 the Lund Observatory," No. 18, and showed that the 

 system might still be stable, even if the triangle were 

 not accurately equilateral to start with; we should in 

 this ca.se get oscillatory motion, never deviating very 

 widely from the synmietrical form. There are two 

 reasons for thinking that the three bodies named above 

 form a system of this kind : (x) The period found for 

 TCi by Dr. Berberich (viz., 12.02 years) is almost 

 exactly the same as that of Jupiter (11.86 years). As 

 the planet has only been under observation for three 

 months it is quite possible that Dr. Berberich's period 

 is in error by this trifling amount (about tw'o months), 

 and that the periods are really exactly equal. We shall 

 probably have to wait till next year before this point is 

 certainly known. (2) The angle subtended at the Sun 

 between Jupiter and TG does not differ greatly from 60" 

 It was in fact 55" 31' on February 22 last, which is 

 quite within the possible range of oscillation about a 

 mean value of 60°. 



Assuming that the period of TG is really 11. 86 

 years, Dr. Charlier finds that its motion can be approxi- 

 mately pictured as follows : (i) Consider a point 

 travelling in an ellipse about the Sun with the period 

 11.86 years, but with the perihelion point advancing 

 so that the period from the perihelion passage to 

 the next is 11.90 years. (2) Consider TG as moving in 

 a small ellipse round this point in a period of 148 years. 

 The size of the ellipse will be deducible when the 

 elements of TG are better determined, but it may be 

 large enough to produce a very noticeable shift in the 

 position of TG. Dr. Charlier has considered the case 

 of a small planet whose orbit plane coincides with that 

 of Jupiter. The plane of TG deviates very notably 

 from this, and there will, I suppose, be similar perturba- 

 tions in latitude, viz., one with a period of about twelve 

 years, which is practically the principal term in latitude, 

 and another with a much longer period. Of course TG 

 will be liable in addition to perturbations by the other 

 planets, of which Saturn will play by far the greater 

 ro/e. These, howe\er, w ill be of an oscillatory charac- 

 ter, and will probably not tend to derlinge permanently 

 the balance of the system. It is to be hoped that Di 

 Charlier's expectations may be verified, and that I'G 

 may indeed prove to exemplify a type of motion so 

 wonderfully anticipated by the great Lagrange more 

 than a century ago. To strengthen his case he states 

 as a conjecture that Jupiter would probably compel a 

 planet that had a jjeriod nearly the same as his to take 

 up this exact period, since otherwise its motion would 

 seem to be unstable. He makes the suggestion that 

 the regions 60" distant from Jupiter on each side should 

 be diligently swept for other bodies of the same type, 

 and even extends the suggestion to the ca.se of Saturn, 

 though the pros[>ects here are not very encouraging. 



TG must be a fairly large asteroid; judging from its 

 brightness its diameter can scarcely fall below 100 miles, 

 which far exceeds the estimates for most of the recent 

 discoveries. Professor Barnard deduced that Ceres 

 headed the list with 480 miles, X'esta, although brighter, 

 being only 240 miles in diameter. Dr. Berberich's 

 elements follow; it will not be difficult with their aid lo 

 insert the orbit in a diagram of the Solar System. 



Epoch. 19C6. Feb. 22. Berlin. Midnight. 

 Mean Longitude . . .. 4S'' 57' 

 Longitude of Perihelion 76' o' 

 ,, .-\sc. Node 315"" 34' 

 Inclination to Ecliptic 10' 21' 

 Eccentricity .. .. o'i676 



Perioil i;o; years. 

 Mean distance from Sun 5 248 

 Least ,. ,, 4369 



Greatest ,, ,, 6127 



