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Popular Science Monthly

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the Sun only 1/7 of 1 per cent. of its mass could scarcely succeed in shifting the axis of rotation of the remaining 99 6/7 per cent. very much, I think. If the angle were 30 degrees or 50 degrees or 80 degrees, instead of 7 degrees, the case for the planetesimal hypothesis would be somewhat stronger. A remarkable fact concerning the Sun is that the equatorial region rotates once around in a shorter time than the regions in higher latitudes require. The rotation period of the Sun's equator is about 24 days; the period at latitude 45 degrees is 28 days; and at 75 degrees, 33 days. The planetesimal hypothesis attributes this equatorial acceleration to the falling back into the Sun of the materials which had been lifted out to a short distance by the disturbing body, and to the forward-rushing tide raised in the equatorial regions by the disturbing body. This may well have occurred. However, we must remember that the same phenomenon exists certainly in Jupiter and Saturn, and quite probably in Uranus and Neptune; that is, in all the bodies in the system that are gaseous and free to show the effect. It seems to be the result of a principle which has operated throughout the solar system, not requiring, at least not directly requiring, the passage of a disturbing star. I think the most plausible explanation of this curious phenomenon is that great quantities of materials originally revolving around the Sun and around each of the planets have gradually been drawn into these bodies, by preference into their equatorial areas. Such masses of matter moving in orbits very close to these bodies must have traveled with speeds vastly higher than the surface speeds of the bodies. To illustrate, the rotational velocity of a particle now in the Sun's surface at the equator is approximately 2 km. per second. A small body revolving around the Sun close to his surface, rapidly enough to prevent its falling quickly upon the Sun, must have a velocity of more than 400 km. per second. If, now, this small body encounters some resistance it will fall into the Sun, and as it is traveling more than 200 times as rapidly as the solar materials into which it drops, it will both generate heat and accelerate the rotational velocity of the surrounding materials. In the same way the equatorial accelerations in Jupiter and Saturn can receive simple explanation. The point is not necessarily in opposition to the planetesimal hypothesis; but whatever the explanation, it ought to apply to the planet as well as to the Sun. If the spiral nebulae have been formed in accordance with Chamberlin and Moulton's hypothesis, the secondary nuclei in them must revolve in a great variety of elliptic orbits. The orbits would intersect, and in the course of long ages the separate masses would collide and combine and the number of separate masses would constantly grow smaller. Moulton has shown that IN GENERAL the combining of two masses whose orbits intersect causes the combined mass to move in an orbit more nearly circular than the average orbit of the separate masses, and in general in orbit planes more nearly coincident with the general plane of the system. Accordingly, the major planets should move in orbits more nearly circular and more nearly in the plane of the system than do the asteroids; and so they do. If the asteroids should combine to form one planet the orbit of this planet should be much less eccentric than the average of all the present asteroid eccentricities, and the deviation of its orbit plane should be less than the average deviation of the present planes. We can not doubt that this would be the case. Mercury and Mars, the smallest planets, should have, according to this principle, the largest eccentricities and orbital inclinations of any of the major planets. This is true of the eccentricities, but Mars's orbit plane, contrarily, has a small inclination. Venus and the Earth, next in size, should have the next largest inclinations and eccentricities, but they do not; Venus's eccentricity is the smallest of all. The Earth's orbital inclination and eccentricity are both small. Jupiter and Saturn, Uranus and Neptune, should have the smallest orbital inclinations; their average inclination is about the same as for Venus and the Earth. They should likewise have the smallest eccentricities. Neptune, the smallest of the four, has an orbit nearly circular; Jupiter, Saturn and Uranus have eccentricities more than 4 times those of Venus and the Earth. Considering the four large planets as one group and the four small planets as another group, we find that the inclinations of the orbits of the two groups, per unit mass, are about equal; but the average eccentricity of the orbits of the large planets, per unit mass, is 21 times that of the orbits of the small planets.[1] The evidence, except as to the asteroids and Mercury, is not favorable to the planetesimal hypothesis, unless we make special assumptions as to the distribution of materials in the spiral nebulae. [2] The average eccentricity of the orbits of the four inner planets (per unit mass) is 0.0221, and of the four outer planets is 0.0489. The fact that the disturbing body drew 225 times as much matter a great distance to form the four large planets as it drew out a short distance to form the four small planets and the asteroids seems difficult of explanation on the planetesimal hypothesis. However, this distribution of matter is at present a difficulty in any of the hypotheses. The planetesimal hypothesis explains well all west to east rotations of the planets on their axes, but to make Uranus rotate nearly at right angles to the plane of the system, and Neptune in a plane inclined 135 degrees to the plane of the system, is a difficulty in any of the hypotheses, unless special assumptions are made to fit each case. The authors succeed well, I think, in showing that the satellites should prefer to revolve around their planets in the direction of the planetary revolution and rotation, especially for close satellites, and, on the basis of special assumptions, in the reverse direction for satellites at a greater distance. They show that the chances favor small eccentricities for satellites revolving about their planets in the west to east, or direct sense, and large eccentricities for satellites moving

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