ASTRONOMY. 



[PERTURBATIONS. 



Attraction on the Utter body involve* an error compara- 

 tively insignificant. 



" It U true, that when observation* are earned to a 

 high degree of precision, and when each planet U traced 

 through many successive revolutions, and it* history 

 carried back, by the aid of calculations founded on these 

 data, we learn to regard the laws of Kepler as only .tint 

 approximation* to ilia much more complicated ones which 

 actually prevail ; and that to bring remote observations 

 into rigorous mathematical accordance with each other, 

 and at the same time to retain the extremely convenient 

 nomenclature and relations of the ELLIPTIC SYSTKM, it 

 becomes necessary to modify, to a certain extent, our 

 il expression of the laws, and to regard the numeri- 

 cal data or elliptic fitments of the planetary orbits as not 

 absolutely permanent, but subject to a series of extremely 

 alow and almost imperceptible changes. These changes 

 may be neglected when we consider only a few revo- 

 lutions ; but going on from century to century, and 

 continually accumulating, they at length produce con- 

 siderable departures in the orbits from their original 

 tate." Henchel. 



From the principle of universal gravitation, the third 

 law of Kepler, from which the law of attractive force 

 has been deduced above, requires to be modified as 

 follows : The cubes of the mean distances of the planets 

 from the sun are us the products of the squares of the 

 ] e i'xlic times, by the sum of the masses of the attracting 

 an 1 attracted bodies. In the original enunciation of the 

 law, the mass of the attracted body was neglected ; the 

 trifling amount of error thus introduced seeing that 

 even Jupiter, the largest of the planets, has less than a 

 thousandth part of the matter contained in the sun is 

 evidently such as to render the departure from strict 

 accuracy too minute to be detected, except by delicate 

 observations extended over a long period of time. 



PERTURBATIONS OF THE PLANETARY. MOTIONS. In 

 consequence of the law of universal gravitation, each 

 planet exercises an influence over every other planet ; 

 these mutual disturbances necessarily modify, in a slight 

 degree, as just noticed, the orbits of all, and occasion 

 what are called perturbations and inequalities. But all 

 these are fully accounted for, and satisfactorily explained, 

 by referring them to Newton's great principle. Calcula- 

 tions founded upon this principle, enable us to predict 

 the position of a planet at any future time with a degree 

 of accuracy that appears little short of marvellous, when 

 we consider the complication involved in the mutal actions 

 of the sun and all the planets on one another. " The 

 motion of Jupiter, for instance, U so perfectly calculated, 

 that astronomers have computed, ten years before hand, 

 the time at which it will pass the meridian of any sprri- 

 fied place ; and we find the prediction correct within half 

 ft second." Airy. 



No physical law has ever been enunciated which long 

 ftnd careful observation more completely verifies than 

 Newton's law of universal gravitation. The distances 

 and masses of the planets being known, the effect of the 

 attractions of all, in modifying the path of each, can be 

 correctly ascertained, though only by aid of investigations 

 of the mcut difficult and recondite character ; but one of 

 the most remarkable attestations to the truth of this 

 universal principle, is that which has been furnished in 

 oar own day by Mr. Adams, of Cambridge. K nowing that 

 there were certain small perturbations of the orbit of 

 L'ranus that the combined attractions of all the other 

 planets of the system were insufficient to account for, 

 and fully confiding in the competency of Newton's law 

 to explain every movement of the heavenly bodies, he 

 had the boldness to pronounce that a yet unseen planet ; 

 existed beyond the bounds of what had till th.-n been 

 rewarded as the remotest p'.anet in our system ; and 

 taxing the unaccounted-for ]>eitiirl>ations of Uranus as 

 data, he had science enough to assign the place where, 

 t ft specified time, the new planet would be foun I An 

 eminent French mathematician, Loverrier, had in.l"- 

 )u<lently, and but a short time afterwards, arrived at a 

 >r conclusion ; an<l ii|.on transmitting the neoesxary 

 instruction* to a German astronomer, O.illc, the pre- 



dicted planet, Neptune, was revealed to his telescope on 

 the evening of the day that the communication reached 

 lam. 



( >ne of the most important results to which tho various 

 researches into the planetary perturbations have con- 

 ducted is, that the major axes of tho variable elliptic 

 orbits always preserve the same value*. The disturb- 

 ance* to which each planet is subjected, by the action of . 

 the others, affect all the element* of ita elliptic path, 

 except it* major axis, which throughout every other 

 change continues itself invariable ; this invariability 

 insure* at the same time the invariability of the period 

 of revolution, agreeably to the third law of Kepler. 

 And thus the stability of tin- system is secmvl. We are 

 indebted for this great truth to the genius and researches 

 of Lagrange. 



MASSES or THE PLANETS AB COMPARED WITH THE Si \. 

 The mass of a planet is ascertained by observing the 

 disturbances which its attraction produces in tho orbits 

 of other planets, or, if it have a satellite, by determining 

 the force exerted upon that satellite. The mas* of the 

 sun being represented by unit, the masses of the planets 

 have been estimated as in the following table.* 



It must bo understood that the mass of a body is not 

 the same thing as its bulk or volume. The mas-t is esti- 

 mated by volume and density ; if one body have only half 

 the volume of another, but be twice as douse, their 

 masses are equal. If a planetary body be so minute in 

 volume, or so feeble in density, as to render its attractive 

 energy too small to perturb sensibly the motions of the 

 other planets, the mass of tliat body cannot be deter- 

 mined. On these accounts there is still some uncertainty 

 as to the mass of Mercury ; and respecting the masses of 

 tho small planets between Mars and Jupiter asteroids, 

 as they have been called we know nothing. In like 

 manner, as respects the comets, all we know is, that their 

 masses must be exceedingly small ; that is, that they 

 contain but a very small quantity of matter, as they pro- 

 duce no appreciable disturbance of the planetary move- 

 ments. It has happened that a comet has crossed among 

 the satellites of Jupiter without occasioning any observ- 

 able disturbance even in the motions of these compara- 

 tively small bodies. 



Before concluding this section on the principle of 

 universal gravitation, we must devote a short article to 

 one of the most noticeable effects of that principle on our 

 own planet the phenomena of the tides. 



THE TIDES. The principal physical cause of those 

 periodical oscillations of the surface of the ocean called 

 tides, is the attraction of the moon ; the sun contribute* 

 to the general results, but in a far less degree. 



Suppose the earth were entirely covered with water : 

 from the mutual attraction of all its ji.-irts, its surface 

 would assume an exactly spherical form. Its rotation 

 on it* axis, however, would cause the equatorial parts to 

 recede from the centre, and to bulge out. 



'1'h in receding from the centre, of the equatorial regions 

 of tin- earth, is caused by a now force. opjx>sed to th 

 Hi:n nation, Iwing brought into operation by the plan, t's 

 n. It is called the (v/,--i/./,if force, from its im- 

 parting a tendency in the outer particles of the rotating 

 nia^s to fly off or recede from the centre. Just such a 

 tendency would be excited if the earth were at rest, and 

 See Note, anli, p. B2A. 



