HYPOTHESIS OF PLANETS DERIVED FROM A SMALL

SECONDARY NEBULA

Distinctive features of the planetesimal hypothesis. The planetesimal or spiral nebula hypothesis of Chamberlin and Moulton postulates the sun already in existence from the ingathering of a primal nebula. It was at some later stage disrupted through the tidal forces produced by the close approach and passage of another star. The result was a secondary nebula, but one essentially unlike the primary. The secondary nebula was developed in a plane and initially possessed a spiral form with the sun at its center. All of its parts moved with freedom and independence in elliptic orbits, a point of difference from the Laplacian hypothesis. The nebula contained only a minute fraction of the solar matter, but was endowed by the passing star with a great rotational energy, so that, although so insignificant in mass, the planetary matter dominates enormously over the sun in the moment of momentum of the whole system. Thus the planetesimal hypothesis is a bold and frank abandonment of the terms of the original or nebular theory. It is too early as yet to predict what will be the ultimate fate of this hypothesis of a secondary, and, in a measure, an accidental origin of the planets, but, as expounded by its originators, it must be regarded as dynamically more satisfactory than the present form of the hypothesis of primary origin. The essential features will, therefore, be presented as the more probable preliminary steps in the genesis of the earth.

Forces of tidal disruption. The power of stars to disrupt each other without coming into actual contact, merely through relatively close approach, must be understood, as it is the basis of the planetesimal hypothesis.

The sun and moon raise terrestrial tides by virtue of the pull of gravity and thus modify that spheroidal form of the earth which is given by its own gravity and the centrifugal

force of its revolution. Suppose, in other examples of heavenly bodies, the tidal pull to be many times stronger, the self-gravitative cohesion to be many times weaker. A limit will be reached at which the body may be pulled to pieces. This phenomenon, which has been actually observed in the case of comets passing close to the sun, has been called tidal disruption.

Let M and N in Figure 1 be two bodies passing each other in space, and consider the action of the larger on the smaller. According to Newton's law, the bodies attract each other directly as their masses and inversely as the square of their distances, causing them to swing toward each other while passing by, but soon losing influence as they separate in their journeys through space. Consider three particles, a, b, c, on the line of attraction, taking them as separate parts of the smaller body. But a is nearer to M than is b, and b is nearer than c. Therefore if we represent the relative attractions by lines, these lines will correspond to the distances which the particles would move in a given time if free to obey the attrac

tion of the other body. The line at a is longer than that at b and the latter is longer than that at c. If N was not bound together by its own gravity or rigidity, a, b, and c would therefore drift apart and fan out while passing M. Consider that rigidity is negligible, as in a fluid globe; then, if a minus b, or b minus c are quantities which become greater than the self-gravitative force of N holding together a and c, the unity of the body becomes destroyed. The problem, however, is not quite so simple, since the influence of all other points in N must also be considered.

As the nearer part of the body is pulled from the center, and as the center is pulled from the farther side, there will, further, be two simultaneous tides of approximately equal height, but on opposite sides of the distorted body. They tend to be always on the line joining the two bodies. Thus, on the earth there are two tides on opposite sides, but the revolution of the earth on its axis, like a car wheel under two opposite brake-shoes, gives an apparent effect, to one on the surface of the earth, of a revolution of the tidal wave. As a result of the equal tides at opposite ends of a diameter there are, on any part of the ocean, two high tides in twenty-four hours.

Mode of tidal disruption in stars. A star is characterized by its enormous size and mass and by the possession of a gaseous constitution. The diameter and density are dependent upon the balance at every point between the tremendous expansive forces of internal heat and the equally great compressive forces due to its own gravity. If it contracts, then its surface and each component shell below comes nearer to the center, the effect of gravity upon any shell accordingly increases inversely as the square of the new radius, and a higher internal temperature becomes necessary to balance the higher gravitative force. From this there results the paradox known as Lane's law, that so long as a body maintains a gaseous

constitution its temperature must rise as it contracts, even though at the same time it is radiating heat. The temperature of the interior must furthermore be higher than the temperature of the surface, because of the greater compression with depth, as is illustrated in the different strata of the terrestrial atmosphere. In those convective or slow boiling movements which are necessary in the sun and other stars in order that they should be able to maintain their surface radiation, there is then a constant liberation of energy from the depths and a system of balanced motion which if disturbed could lead in any star to an explosive blowing out of material from it on an enormous scale.

The tide-generating force varies directly with the mass of the disturbing body and also with the radius of the body disturbed. It varies approximately inversely with the cube of the distance between the centers. The deforming force is, furthermore, greatest in the interior because the tidal forces acting on the zone at right angles to the line of attraction have a component which tends to squeeze in the points d, d' of Figure I toward the center. The gravitative control is accordingly weakened along the line a, b, c, and is strengthened in the directions at right angles. Now apply this principle to the gaseous balanced nature of a star, and it is seen that the expansion in the line a, b, c is no longer exactly balanced by the gravitative compression, and the unbalancing is greatest in the center, where also is the region of highest compression and highest temperature. The effect is as if one squeezed a syringe bulb with orifices for exit at both ends, a bulb, however, like an air rifle, filled with gas compressed to an explosive degree.

The sun is occa

Tidal disruption of the ancestral sun. sionally observed to shoot out streams of gas, known as solar prominences, to heights of nearly 300,000 miles, and at velocities ranging up to 300 miles per second. Such phe

nomena indicate the enormous elastic and explosive energy resident in the sun's interior, an expansive potency held in restraint by the equally prodigious power of the sun's gravity. Supposing then that the ancestral sun was subjected to tidal disruption by the approach of another and possibly much more massive star, it remains to be seen how the nebula resulting from tidal disruption can become the embryo of an orderly planetary system. If the matter were shot out from great depths in the sun by its normal expansive forces plus the tidal forces, the velocity of departure might rise high above the observed velocities of 300 miles per second. If 400 miles or more, it would be above the "critical velocity" of the sun. The gravitative attraction of the latter could then never reclaim that matter, because the decrease in the outward velocity due to the solar attraction would never bring the velocity down to zero, and could therefore never reverse the motion of the escaping matter and bring it back to the sun.

It is doubtful if the sun could have drawn back to itself material expelled with a velocity of even 300 miles per second, for the passing star, by lowering the gravitative power of the sun on the line passing through the two, would temporarily decrease on that line the critical velocity. In other words, it would help to drag matter away from the sun, even though that matter could not catch up to the passing star, but would be left wandering in interstellar space, forming possibly cometary and meteoric material for other systems. But some,

or possibly all, of the matter of the exploded sun may have had lesser velocities of escape and would consequently remain within its gravitative control. In so far as it was not deflected sideways by some extraneous force, it would fall back on the surface of the sun as the water of a geyser falls back into its pool. But the gravitative pull of the passing star would serve as such an extraneous force, analogous to the wind which blows part of the geyser water, as it rises and falls, to one