ON NEWTON’S SCALES.

Taranaki Daily News, 20 December 1930, Page 13 (Supplement)

ON NEWTON’S SCALES.

WEIGHT OF THE MOON

(By Rev.

B. Dudley, F.R.A.S.)

We have seen how the weight of the earth, the sphere at our feet, has, by the ingenuity of the mathematician, been determined from (1) the swinging pendulum and; (2) the deviation from the vertical of a plumb line when dravvn aside by the pull of a mass of roek or by a mountain. It should not therefore surprise anyone to learn that the moon also has been placed in balances and weighed; We have seen how the great law of universal gravitation was made use of for the purpose of ascertaining the earth’s weight, this law beijig, indeed, the . only means we have , of getting at a solution of the problem; We shall now see how the moon—the ball that hurtles over- our heads, as it were—-is put ou the scales, and her mass, or weight, determined, t 'A simple account of the process can best be given 1 , perhaps, by describing how Newton forked at, the 'problem. That’ overwhelming genius was gifted in a remarkable degree with the power of grasping essential facts, and seemed, as if by a kind of intuition, to • choose the right method of research out of (several alternatives.’ \rhus was lie led so. often to the true, theory . of things. He possessed, moreover, more than the requisite mathematical ability. In all his investigations, he invariably started with the assumption; that ’simplicity is the keynote, to natural philosophy.' And, .working on that principle now, he arrived (for that is the most appropriate word) at the law of universal gravitation, , the discovery, of which' showed him' to (be'.right in the assumption. . .?■.?. ' ■■ ■.’>■ It is not,likely that Newton .was the first to ask himself why. an apple falls to’ the ground. The idea of the earth attracting bodies to itself was not foreign; even ’to the ancients.; But when the question presented itself to Newton it found a prepared mind. There came to him thesuggestion that possibly it was the earth’s attraction which -gave rise to the moon’s movement and .her steady progress; in her orbit about the earth. If ah apple,' de-, tached h‘y nature from a tree, reaches the earth—why?. ' There must be -a force, residing in the earth, pulling at it, else how should it move earthwards? The moon is »■ a , detached body—a monster apple. :Is it, too, pulled towards us by this attractive energy, onlykept at ,a distance by its motion round the earth? 'The sun, tl}e planets, even the more distent stars, are /these all bound together, yet held apart in the same way ? Here by inference was unfolded the. secret of the universe. Newton sow that tif he could show that the moon’s movement was .the result of the same law of attraction that, governed the fall of the apple, then the old problem was solvable. . ' -’C • ’A further question that confronted the great philosopher just now was to what extent precisely distance operates to modify the attraction which the earth exerts on a body like the apple. He took for granted, for ’the time being, that, as had been announced by others, this attraction varies in a given proportion; .varies, that is'to say, in accordance with what is called the inverse square law, which' need not be defined here. If this law is. correct, then the distance of the moon from ,the.. earth- ought to be about 60 times the. radius of the earth;' in other words. GO ■ times the distance of the earth’s sup face from its (the earth’s) centre. When worked■' out Newton’s results unfortunately did not quite agree with the observed lunar movement. He was but a youth at this time, and it is easy to imagine the keen' ' enthusiasm with which he pursued his calculations, and the great disappointment he,, fqlt on finding that they would not behr out his expectations. Assuming that his' guess was quite wrong, he laid aside his work on this problem indefinitely. As a matter .of factpit was not wrong; and had he been living, in a place affording him access to books of reference, instead of in a remote country place, he would have found merely that he had trusted too 1 much to his memory in the matter of the earth’s radius (or semidiameter), an important element in the calculations. The figure he had used was a trifle too small and thus lie had

been misled. It was not until 1682, sixteen years; later, that he resumed his studies along this line, detected his error, and. found that he had previously been on the right track, after all. Thus he • was successful in establishing the fact that tthe moon does indeed, in her constant journey round the earth, obey' the’.same Jaw as that under, the ■ihipulsioh' of which • the apple falls, at one’s feet when, sitting in an orchard. The movement of the moon is virtually a continuous fall toward her primary, the earth; and she is only kept at bay by the swiftness of her motion, just as a stone swung round on a string by the hand maintains its revolutions by the speed with which >it moves. By this method of inquiry, and others more recent, the mass of the moon in terms of the mass of the earth can be definitely stated, and the findings show that the density of the moon is 3.4 (nearly 31j. 'times that of water. It has been shown that the weight of a body on the surface of the earth depends upon the earth’s mass and the distance of the surface of, the earth from its centre. The weight of a body is directly proportitional to the mass of the earth, and inversely proportional ,to the square of its distance from the centre of the earth. The corresponding thing is true on the moon. Using the mass of the. moon and the size of. it, it is found that an object on the surface of the moon weighs only one-sixth as much as the same object would on the surface of the earth. A body on the moon' therefore weighs only a sixth much as it would weigh here. The same force of projection that would toss it a mile here would on the moon send it up to a height of six miles (this statement takes no notice whatever of the fact that there is no atmospheric friction on the moon,' while there is one of considerable influence here). Volcanic activity on the moon, for example, would throw matter six times as high as the same activity here. And since matter weighs less on the moon, mountains could be piled six times as high before the rocks would crush and break out at their bases. This may explain why lunar mountains are so enormously high and rugged as compared with those of the earth, which, as was shown in the last article, is SO times the weight of the moon.