NEW METHODS IN ASTRONOMY 



(AND THEIR APPLICATION TO THE EVOLUTION OF OLR SYSTEM) 



Bv F. W. HEXKFL, B.A.. F.K.A.S. 



During tlie last few \-ears the researches of eminent 

 British and Continental Astronomers ha\-e thrown a 

 flood of light upon some of the most recondite 

 problems of the science. Amongst these ma\' be 

 especialK- mentioned the w ork of Dr. Hill. AL Poincare 

 and Sir George Darwin, and we propose giving a 

 simple account of some of their results, as well as 

 the bearing these have upon theories as to the origin 

 of our system. The Laplacian nebular hypothesis, 

 greatly shaken hv later discoveries and the critical 

 in\estigation of its postulates, seems likely to 

 undergo the fate prophe- 

 sied for it l)v the late Mr. 

 Proctor, founder of 

 "Knowledge," and his 

 words mav be quoted here: 

 " If ever proper cnquir\- 

 is made into Laplace's 

 nebular h\'pothesis, that 

 also will be still more 

 decisively rejected" /Old 

 and A't'ic Astroiioiii Y , 

 p. 638.1 We shall have 

 occasion to allude to 

 some of the alternative 

 hypotheses ; an account 

 of part of Professor See's 

 work has already appeared 

 in " Knowledge " (June 

 1909). 



Newton, in his immortal 

 Principia, has once for 

 all solved the problem of 

 two bodies. " Given two 

 spherical masses acting on 

 one another, according to 

 the law of gravitation, and their position and motions 

 at any time, to find their motions at anv future or 

 past time." The planets move in ellipses closely 

 approximating to circles round the Sun, the comets 

 mostly mo\-e in parabolas, a few in very elongated 

 ellipses, and perhaps a ver\- few in hvperbolas round 

 the same centre of force. This, however, is onl\- an 

 approximation, though very close, to their motion, 

 arising from the fact that the mass of the Sun is so 

 enormously great compared with that of anv of the 

 planets, that the attraction between Sun and planet 

 is the main factor in determining the path of any 

 one of these bodies. Every planet moves in an 

 orbit round the Sun which is ver\- nearh- the same 

 as it would be were no other bodies but itself and 

 the Sun to exist ; the small deviations between the 

 actual motion and this ideal motion are known as 



Figure 1. 



Curves of Zer 



Critical values 



" perturbations." and are due to the disturbing 

 action of the other members of the Solar system, 

 arising from the difference of their attractions upon 

 the Sun and the planet in question in each case. 

 Owing to the fact that, as we have mentioned above, 

 all the planets are much smaller than the Sun, we 

 ma\-, bv a series of approximations, determine these 

 perturbations one after another, and add their 

 results till we obtain a satisfactory agreement between 

 theory and observation. The general problem of 

 three bodies is, however, far be^'ond the capacity of 



our present mathematics 

 to solve, and all that can 

 be done is to take some 

 simple cases and then 

 consider others approxi- 

 mating to them as nearlv 

 as possible. 



The ^Lx)n moves in a 

 path round the earth which 

 is not very different from 

 a circle, but, owing to the 

 disturbing action of the 

 Sun. the form of this path 

 is continualK- undergoing 

 slight variation. In this 

 case, though the disturb- 

 ing bod\- is not small, \e\. 

 on account of its much 

 greater distance, the Sun's 

 disturbing force or its 

 dijfcrciice of action upon 

 Earth and Moon is only 

 a small fraction of the 

 Earth's attraction upon the 

 Moon. Were the Sun to 

 attract Earth and Moon equalh- and along parallel 

 directions there would be no disturbance of their 

 relative motion. In a similar way we may say that 

 anv external force acting equally upon all members of 

 our sx'stem w ill produce no change in the planetary 

 and satellite orbits. Whatever force may be moving 

 our Sun along its mightv path towards " Hercules " 

 (or Vega), is equally drawing its family of planets, 

 satellites, comets and meteors. Even as it is, 

 however, with the comparative simplification intro- 

 duced b\' the smallness of the disturbing force, the 

 "Lunar Theor\- " is one of the most complex 

 branches of applied Mathematics, and though the 

 general agreement between the results of theory and 

 observation affords one of the most complete 

 verifications of the exact truth of Newton's law of 

 gra\itation. there are questions even yet awaiting 



o Velocity (after Darwin), 

 only shown. 



350 



