Part 5 (1/2)

CHAPTER XV

AFTER NEWTON

We have said that practically all the motions in the solar system have been accounted for by the Newtonian law of gravitation. It will be of interest to inquire into the instances that lead to qualification of this absolute statement.

One relates to the planet Mercury, whose orbit or path round the sun is the most elliptical of all the planetary orbits. This will be explained a little later.

The moon has given the mathematical astronomers more trouble than any other of the celestial bodies, for one reason because it is nearest to us and very minute deviations in its motion are therefore detectible.

Halley it was who ascertained two centuries ago that the moon's motion round the earth was not uniform, but subject to a slight acceleration which greatly puzzled Lagrange and Laplace, because they had proved exactly this sort of thing to be impossible, unless indeed the body in question should be acted on by some other force than gravitation. But Laplace finally traced the cause to the secular or very slow reduction in the eccentricity of the earth's own orbit. The sun's action on the moon was indeed progressively changing from century to century in such manner as to accelerate the moon's own motion in its...o...b..t round the earth.

Adams, the eminent English astronomer, revised the calculations of Laplace, and found the effect in question only half as great as Laplace had done; and for years a great mathematical battle was on between the greatest of astronomical experts in this field of research. Adams, in conjunction with Delaunay, the greatest of the French mathematicians a half century ago, won the battle in so far as the mathematical calculations were concerned; but the moon continues to the present day her slight and perplexing deviation, as if perhaps our standard time-keeper, the earth, by its rotation round its axis, were itself subject to variation. Although many investigations have been made of the uniformity of the earth's rotation, no such irregularity has been detected, and this unexplained variation of the moon's motion is one of the unsolved problems of the gravitational astronomer of to-day.

But we are pa.s.sing over the most impressive of all the earlier researches of Lagrange and Laplace, which concerned the exceedingly slow changes, technically called the secular variations of the elements of the planetary orbits. These elements are geometrical relations which indicate the form of the orbit, the size of the orbit, and its position in s.p.a.ce; and it was found that none of these relations or quant.i.ties are constant in amount or direction, but that all, with but one exception, are subject to very slow, or secular, change, or oscillation.

This question a.s.sumed an alarming significance at an early day, particularly as it affected the eccentricity of the earth's...o...b..t round the sun. Should it be possible for this element to go on increasing for indefinite ages, clearly the earth's...o...b..t would become more and more elliptical, and the sun would come nearer and nearer at perihelion, and the earth would drift farther and farther from the sun at aphelion, until the extremes of temperature would bring all forms of life on the earth to an end. The refined and powerful a.n.a.lysis of Lagrange, however, soon allayed the fears of humanity by accounting for these slow progressive changes as merely part of the regular system of mere oscillations, in entire accord with the operation of the law of gravitation; and extending throughout the entire planetary system.

Indeed, the periods of these oscillations were so vast that none of them were shorter than 50,000 years, while they ranged up to two million years in length--”great clocks of eternity which beat ages as ours beat seconds.”

About a century ago, an eminent lecturer on astronomy told his audience that the problem of weighing the planets might readily be one that would seem wholly impossible to solve. To measure their sizes and distances might well be done, but actually to ascertain how many tons they weigh--never!

Yet if a planet is fortunate enough to have one satellite or more, the astronomer's method of weighing the planet is exceedingly simple; and all the major planets have satellites except the two interior ones, Mercury and Venus. As the satellite travels round its primary, just as the moon does round the earth, two elements of its...o...b..t need to be ascertained, and only two. First, the mean distance of the satellite from its primary, and second the time of revolution round it.

Now it is simply a case of applying Kepler's third law. First take the cube of the satellite's distance and divide it by the square of the time of revolution. Similarly take the cube of the planet's distance from the sun and divide by the square of the planet's time of revolution round him. The proportion, then, of the first quotient to the second shows the relation of the ma.s.s (that is the weight) of the planet to that of the sun. In the case of Jupiter, we should find it to be 1,050, in that of Saturn 3,500, and so on.

The range of planetary ma.s.ses, in fact, is very curious, and is doubtless of much significance in the cosmogony, with which we deal later. If we consider the sun and his eight planets, the ma.s.s or weight of each of the nine bodies far exceeds the combined ma.s.s of all the others which are lighter than itself.

To ill.u.s.trate: suppose we take as our unit of weight the one-billionth part of the sun's weight; then the planets in the order of their ma.s.ses will be Mercury, Mars, Venus, Earth, Ura.n.u.s, Neptune, Saturn, and Jupiter. According to their relative ma.s.ses, then, Mercury being a five-millionth part the weight of the sun will be represented by 200; similarly Venus, a four hundred and twenty-five thousandth part by 2,350, and so on. Then we have

Mercury 200 Mars 340 ------ Sum of weights of Mercury and Mars 540 Venus 2,350 ------ Sum of weights of Mercury, Mars, and Venus 2,890 The Earth 3,060 ------ Sum of weights of four inner planets 5,950

Ura.n.u.s 44,250 ------ Sum of weights of five planets 50,200 Neptune 51,600 ------- Sum of weights of six planets 101,800 Saturn 285,580 --------- Sum of weights of seven planets 387,380 Jupiter 954,300 --------- Sum of weights of all the planets 1,341,680 Ma.s.s or weight of the sun 1,000,000,000

Curious and interesting it is that Saturn is nearly three times as heavy as the six lighter planets taken together, Jupiter between two and three times heavier than all the other planets combined, while the sun's ma.s.s is 750 times that of all the great planets of his system rolled into one.

All the foregoing ma.s.ses, except those of Mercury and Venus, are pretty accurately known because they were found by the satellite method just indicated. Mercury's ma.s.s is found by its disturbing effects on Encke's comet whenever it approaches very near. The ma.s.s of Venus is ascertained by the perturbations in the orbital motion of the earth. In such cases the Newtonian law of gravitation forms the basis of the intricate and tedious calculations necessary to find out the ma.s.s by this indirect method.

Its inferiority to the satellite method was strikingly shown at the Observatory in Was.h.i.+ngton soon after the satellites of Mars were discovered in 1877. The inaccurate ma.s.s of that planet, as previously known by months of computation based upon years and years of observation, was immediately discarded in favor of the new ma.s.s derived from the distance and period of the outer satellite by only a few minutes' calculation.

In weighing the planets, astronomers always use the sun as the unit.

What then is the sun's own weight? Obviously the law of gravitation answers this question, if we compare the sun's attraction with the earth's at equal distances. First we conceive of the sun's ma.s.s as if all compressed into a globe the size of the earth, and calculate how far a body at the surface of this globe would fall in one second. The relation of this number to 16.1 feet, the distance a body falls in one second on the actual earth, is about 330,000, which is therefore the number of times the sun's weight exceeds that of the earth.

A word may be added regarding the force of gravitation and what it really is. As a matter of fact Newton did not concern himself in the least with this inquiry, and says so very definitely. What he did was to discover the law according to which gravitation acts everywhere throughout the solar system. And although many physicists have endeavored to find out what gravitation really is, its cause is not yet known. In some manner as yet mysterious it acts instantaneously over distances great and small alike, and no substance has been found which, if we interpose it between two bodies, has in any degree the effect of interrupting their gravitational tendency toward each other.

While the Newtonian law of gravitation has been accepted as true because it explained and accounted for all the motions of the heavenly bodies, even including such motions of the stars as have been subjected to observation, astronomers have for a long time recognized that quite possibly the law might not be absolutely exact in a mathematical sense, and that deviations from it would surely make their appearance in time.

A crude instance of this was suggested about a century ago, when the planet Ura.n.u.s was found to be deviating from the path marked out for it by Bouvard's tables based on the Newtonian law; and the theory was advocated by many astronomers that this law, while operant at the medium distances from the sun where the planets within Jupiter and Saturn travel, could not be expected to hold absolutely true at the vast distance of Ura.n.u.s and beyond. The discovery of Neptune in 1846, however, put an end to all such speculation, and has universally been regarded as an extraordinary verification of the law, as indeed it is.

When, however, Le Verrier investigated the orbit of Mercury he found an excess of motion in the perihelion point of the planet's...o...b..t which neither he nor subsequent investigators have been able to account for by Newtonian gravitation, pure and simple. If Newton's theory is absolutely true, the excess motion of Mercury's perihelion remains a mystery.