Biography of Percival Lowell :: CHAPTER XVIIII THE ORIGIN OF THE PLANETS

CHAPTER XVIIII THE ORIGIN OF THE PLANETS

In a paper presented to the American Academy in April, 1913, and printed in their Memoirs[38] Percival explained the “Origin of the Planets” by the same principle of commensurate periods. In addition to what has already been said about the places where these periods occur coming closer and closer together as an object nears the planet, so that it is enabled to draw neighboring small bodies into itself, he points out that in attracting any object outside of its own orbit a planet is acting from the same side as the Sun thereby increasing the Sun’s attraction, accelerating the motion of the particle and making it come sunward. Whereas on a particle inside its orbit the planet is acting against the Sun, thereby diminishing its attraction, slowing the motion of the particle and causing it to move outward. “Thus a body already formed tends to draw surrounding matter to itself by making that matter’s mean motion nearly synchronous with its own.” These two facts, the close—almost continuous—commensurate points, and the effects on the speed of revolution of particles outside and inside its own orbit, assist a nucleus once formed to sweep clear the space so far as its influence is predominant, drawing all matter there to itself, until it has attained its full size. “Any difference of density in a revolving nebula is thus a starting point for accumulation. So soon as two or three particles have gathered together they tend by increased mass to annex their neighbors. An embryo planet is thus formed. By the same principle it grows crescendo through an ever increasing sphere of influence until the commensurate points are too far apart to bridge by their oscillation the space between them.”

So much for the process of forming a planet; but what he was seeking was why the planets formed just where they did. For this purpose he worked out intricate mathematical formulae, based on those already known but more fully and exactly developed. These it is not necessary to follow, for the results may be set forth,—so far as possible in his own words. “Beyond a certain distance from the planet the commensurate-period swings no longer suffice to bridge the intervening space and the planet’s annexing power stops. This happens somewhat before a certain place is reached where three potent periodic ratios succeed each other—1:2, 2:5, 1:3. For here the distances between the periodic points is greatly increased....

“At this distance a new action sets in. Though the character of its occasioning be the same it produces a very different outcome. The greater swing of the particles at these commensurate points together with a temporary massing of some of them near it conduces to collisions and near approaches between them which must end in a certain permanent combining there. A nucleus of consolidation is thus formed. This attracts other particles to it, gaining force by what it feeds on, until out of the once diffused mass a new planet comes into being which in its turn gathers to itself the matter about it.

“A new planet tends to collect here: because the annexing power of the old has here ceased while at the same time the scattered constituents to compose it are here aided to combine by the very potent commensurability perturbations of its already formed neighbor.

“So soon as it has come into being another begins to be beyond it, called up in the same manner. It could not do so earlier because the most important deus ex machina in the matter, the perturbation of its predecessor, was lacking.

“So the process goes on, each planet acting as a sort of elder sister in bringing up the next.

“That such must have been the genesis of the several planets is evident when we consider that had each arisen of itself out of surrounding matter there would have been in celestial mechanics nothing to prevent their being situated in almost any relative positions other than the peculiar one in which they actually stand....

“It will be noticed that the several planets are not quite at the commensurate points. They are in fact all just inside them.... Suppose now a particle or planet close to the commensurable point inside it. The mean motion in consequence of the above perturbation will be permanently increased, and therefore the major axis be permanently decreased. In other words, the particle or planet will be pushed sunward. If it be still where” the effect of the commensurateness is still felt “it will suffer another push, and so on until it has reached a place where the perturbation is no longer sensible.” He then goes on to show from his formulae that if the particle were just within the outer edge of the place where the perturbation began to be effective it would also be pushed sunward, and so across the commensurable point until it joined those previously displaced.

“We thus reach from theory two conclusions:

“1. All the planets were originally forced to form where the important and closely lying commensurable points 1:2, 2:5, or 1:3, and in one case 3:5, existed with their neighbors; which of these points it was being determined by the perturbations themselves.

“2. Each planet was at the same time pushed somewhat sunward by perturbation.”

He then calculates the mutual perturbations of the major axes of the outer planets taken in pairs and of Venus and the Earth.

“From them we note that:

“1. The inner planet is caeteris paribus more potent than the outer.

“2. The greater the mass of the disturber and, in certain cases, the greater the excentricity of either the disturber or the disturbed the greater the effect.”

As he points out, the effect of each component of the pair is masked by the simultaneous action of the other, and refers to the case of Jupiter and the asteroids, where the effect they have upon it is imperceptible, and we can see its effect upon them clearly.

Thus he shows that a new planet would naturally arise near to a point where its orbit would be commensurate with that of the older one next to it. But the particular commensurate fraction in each case is not so certain. In general it would depend upon the ratio of the two pulls to each other, for if “the action of the more potent planet greatly exceeds the other’s it sweeps to itself particles farther away than would otherwise be possible”; if it does not so greatly exceed it would not sweep them from so far and hence allow the other planet to form nearer. Now of the four commensurate ratios mentioned, near which a planet may form its neighbor, that of 3:5 means that the two planets are relatively nearest together, for the inner one makes only five revolutions while the outer makes three, that is the inner one revolves around the Sun less than twice as fast as the outer one. The ratio 1:2 means that the inner one revolves just twice as fast as the outer; while 2:5 means that it revolves twice and a half as fast, and 1:3 that it does so three times as fast. Thus the nearer equal the pulls of any pair of forming planets the larger the fraction and the nearer the relative distance between them. Relative, mind, for as we go away from the Sun all the dimensions increase and the actual distances between the planets among the rest.

Venus is smaller than the Earth, but her interior position gives her an advantage more than enough to make up for this, with the result that the pulls of the two are more nearly equal than those of any other pair, the commensurate ratio being 3:5. The next nearest equality of pull is between Uranus and Neptune, where the commensurate ratio is 1:2; the next between Jupiter and Saturn, and Venus and Mercury, where it is 2:5; the least equality being between Saturn and Uranus, where it is only 1:3. Mars seems exceptional for, as Percival says, from the mutual pulls we should expect its ratio with the Earth to be 1:3 instead of 1:2 as it is, and he suggests as the explanation, “the continued action of the gigantic Jupiter in this territory, or it may be that a second origin of condensation started with the Earth while Jupiter fashioned the outer planets.”

He brings the Memoir to an end with the following summary:

“From the foregoing some interesting deductions are possible:

“1. The planets grew out of scattered material. For had they arisen from already more or less complete nuclei these could not have borne to one another the general comensurate relation of mean motions existent to-day.

“2. Each brought the next one into being by the perturbation it induced in the scattered material at a definite distance from it.

“3. Jupiter was the starting point, certainly as regards the major planets; and is the only one among them that could have had a nucleus at the start, though that, too, may equally have been lacking.

“4. After this was formed Saturn, then Uranus, and then Neptune.” (This he shows from the densities of these planets.)

“5. The asteroids point unmistakably to such a genesis, missed in the making.

“6. The inner planets betray inter se the action of the same law, and dovetail into the major ones through the 2:5 relation between Mars and the asteroids.

“We thus close with the law we enunciated: Each planet has formed the next in the series at one of the adjacent commensurable-period points, corresponding to 1:2, 2:5, 1:3, and in one instance 3:5, of its mean motion, each then displacing the other slightly sunward, thus making of the solar system an articulated whole, an inorganic organism, which not only evolved but evolved in a definite order, the steps of which celestial mechanics enables us to retrace.

“The above planetary law may perhaps be likened to Mendelief’s law for the elements. It, too, admits of prediction. Thus in conclusion I venture to forecast that when the nearest trans-Neptunian planet is detected it will be found to have a major axis of very approximately 47.5 astronomical units, and from its position a mass comparable with that of Neptune, though probably less; while, if it follows a feature of the satellite systems which I have pointed out elsewhere, its excentricity should be considerable, with an inclination to match.”

The last paragraph we shall have reason to recall again.

This paper on the “Origin of the Planets” has been called the most speculative of Percival’s astronomical studies, and so it is; but it fascinated him, and is interesting not more in itself, than as an illustration of the inquiring and imaginative trend of his mind and of the ease with which intricate mathematical work came to the aid of an idea.

Meanwhile his reputation was growing in Europe. At the end of 1909 he is asked to send to the German National Museum in Munich some transparencies of his fundamental work on Mars and other planets with Dr. Slipher’s star spectra, and Dr. Max Wolf of Heidelberg who writes the letter adds: “I believe there is no American astronomer, except yours, [sic] invited till now to do so.” A year later the firm in Jena which had just published a translation of his “Soul of the Far East” wants to do the same for “Mars as the Abode of Life.” In August 1914 he writes to authorize a second French edition of this last book which had been published with the title “Evolution des Mondes.” Every other year, he took a vacation of a few weeks in Europe to visit his astronomic friends, and to speak at their societies. We have seen how he did so after his marriage in 1908. He went with Mrs. Lowell again in the spring of 1910, giving lectures before the SociÉtÉ Astronomique in Paris, and the Royal Institution in London, and once more, two years later, when we find him entertained and speaking before several scientific bodies in both Paris and London. That autumn he was confined to the house by illness; and although he improved and went to Flagstaff in March, he writes of himself in August 1913 as “personally still on the retired list.” In the spring it was thought wise for him to take another vacation abroad; and since his wife was recovering from an operation he went alone. He saw his old friends in France and England and enjoyed their hospitality; but he did not feel well, and save for showing at the Bureau des Longitudes “some of our latest discoveries” he seems to have made no addresses. He sailed back on the Mauretania on August 1, just before England declared war, and four days later she was instructed to run to Halifax, which she did, reaching it the following day.

That was destined to be his last voyage, for although he seemed well again he was working above his strength. His time in these years was divided between Flagstaff, where his days and nights were spent in observing and calculating, and Boston, where the alternative was between calculations and business. He was always busy and when one summer he hired a house at Marblehead near to his cousins Mr. and Mrs. Guy Lowell he would frequently drop in to see them; and was charming when he did so; but could not spare the time to take a meal there, and never stayed more than five minutes.

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