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The total, however, of the rotational moment of momentum of the system barely reaches two per cent. of the whole amount; this is of course almost entirely contributed by the sun, for all the planets together have not a thousandth part of the sun's rotational moment.
Speaking in round numbers, the revolutional moment of momentum of Jupiter is about thirty times as great as the rotational moment of momentum at present possessed by the sun. I do not know that there is anything impossible in the supposition that the sun might, by an augmented volume and an augmented velocity of rotation, contain many times the moment of momentum that it has at this moment.
Hence it follows that whatever transfer of moment of momentum has taken place in the sun-Jupiter system has been almost entirely obtained at the expense of Jupiter. Now in the solar system at present, the orbital moment of momentum of Jupiter is nearly fifty thousand times as great as his present store of rotational moment of momentum.
For stability the molecular rotation must be such as to give the same velocity at the boundary of the rotational fluid core as that of the irrotationally circulating liquid in contact with it, because, as I have proved, frictional slip between two portions of liquid in contact is inconsistent with stability.
The pull of gravity becomes more and more intense, and as the one circles the other, the tide is pulled up, and the mighty ball of fire, which, for all its existence has been practically motionless as far as rotation goes, begins to acquire a greater and greater rotational speed as the tidal drag urges it on.
The further story of the moon, as it is known to astronomers, may be given in a few words. The rotational movement of the earth is becoming gradually slower on account of tidal influence; our day, in fact, becomes an hour longer every few million years. It can be shown that this had the effect of increasing the speed, and therefore enlarging the orbit, of the moon, as it revolved round the earth.
The remainder of the investment is in rotational moment of momentum, the collective amount of which is to be estimated by multiplying the angular velocity of each planet into its density, and the fifth power of its radius if the planet be regarded as homogeneous, or into such other power as may be necessary when the planet is not homogeneous.
Strong tried to mask his surprise, but a lifted eyebrow gave him away. "And how did you arrive at this conclusion, Manning?" "I was unable to get a sight on Alpha Centauri due to the present position of Jupiter, sir," replied Roger easily. "So I took a fix on Earth, allowed for its rotational speed around the sun and took the cross-fix with Regulus as ordered in the problem.
But now let there be a different rotational velocity imparted to the jointed square round the axis of the two projecting hooked rods, such as to give a resultant moment of momentum round any given line through the center of inertia of the system; and let pairs of the hooked rods in the model thus altered, which is no longer a model of a mere spring balance, be applied as connections between millions of pairs of particles as before, with the lines of resultant moment of momentum all similarly directed.
"If," he said pontifically, "they are oriented in the same direction, we refer to the substance as orthohydrogen. If they are oriented in opposite directions, it is parahydrogen. The ortho molecules rotate with odd rotational quantum numbers, while the para molecules rotate with even quantum numbers.
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