The Story of the Heavens by Sir Robert Stawell Ball (best detective novels of all time .txt) 📖

as the planet is rotating. There can hardly be a doubt that the solar tides on Mars have abated its velocity of rotation in the manner just suggested.

It has always seemed to me that the matter just referred to is one of the most interesting and instructive in the whole history of astronomy. We have, first, a very beautiful telescopic discovery of the minute satellites of Mars, and we have a determination of the anomalous movement of one of them. We have then found a satisfactory physical explanation of the cause of this phenomenon, and we have shown it to be a striking instance of tidal evolution. Finally, we have seen that the system of Mars and his satellite is really a forecast of the destiny which, after the lapse of ages, awaits the earth-moon system.

It seems natural to enquire how far the influence of tides can have contributed towards moulding the planetary orbits. The circumstances are here very different from those we have encountered in the earth-moon system. Let us first enunciate the problem in a definite shape. The solar system consists of the sun in the centre, and of the planets revolving around the sun. These planets rotate on their axes; and circulating round some of the planets we have their systems of satellites. For simplicity, we may suppose all the planets and their satellites to revolve in the same plane, and the planets to rotate about axes which are perpendicular to that plane. In the study of the theory of tidal evolution we must be mainly guided by a profound dynamical principle known as the conservation of the "moment of momentum." The proof of this great principle is not here attempted; suffice it to say that it can be strictly deduced from the laws of motion, and is thus only second in certainty to the fundamental truths of ordinary geometry or of algebra. Take, for instance, the giant planet, Jupiter. In one second he moves around the sun through a certain angle. If we multiply the mass of Jupiter by that angle, and if we then multiply the product by the square of the distance from Jupiter to the sun, we obtain a certain definite amount. A mathematician calls this quantity the "orbital" moment of momentum of Jupiter.[46] In the same way, if we multiply the mass of Saturn by the angle through which the planet moves in one second, and this product by the square of the distance between the planet and the sun, then we have the orbital moment of momentum of Saturn. In a similar manner we ascertain the moment of momentum for each of the other planets due to revolution around the sun. We have also to define the moment of momentum of the planets around their axes. In one second Jupiter rotates through a certain angle; we multiply that angle by the mass of Jupiter, and by the square of a certain line which depends on his internal constitution: the product forms the "rotational" moment of momentum. In a similar manner we find the rotational moment of momentum for each of the other planets. Each satellite revolves through a certain angle around its primary in one second; we obtain the moment of momentum of each satellite by multiplying its mass into the angle described in one second, and then multiplying the product into the square of the distance of the satellite from its primary. Finally, we compute the moment of momentum of the sun due to its rotation. This we obtain by multiplying the angle through which the sun turns in one second by the whole mass of the sun, and then multiplying the product by the square of a certain line of prodigious length, which depends upon the details of the sun's internal structure.

If we have succeeded in explaining what is meant by the moment of momentum, then the statement of the great law is comparatively simple. We are, in the first place, to observe that the moment of momentum of any planet may alter. It would alter if the distance of the planet from the sun changed, or if the velocity with which the planet rotates upon its axis changed; so, too, the moment of momentum of the sun may change, and so may those of the satellites. In the beginning a certain total quantity of moment of momentum was communicated to our system, and not one particle of that total can the solar system, as a whole, squander or alienate. No matter what be the mutual actions of the various bodies of the system, no matter what perturbations they may undergo--what tides may be produced, or even what mutual collisions may occur--the great law of the conservation of moment of momentum must be obeyed. If some bodies in the solar system be losing moment of momentum, then other bodies in the system must be gaining, so that the total quantity shall remain unaltered. This consideration is one of supreme importance in connection with the tides. The distribution of moment of momentum in the system is being continually altered by the tides; but, however the tides may ebb or flow, the total moment of momentum can never alter so long as influences external to the system are absent.

We must here point out the contrast between the endowment of our system with energy and with moment of momentum. The mutual actions of our system, in so far as they produce heat, tend to squander the energy, a considerable part of which can be thus dissipated and lost; but the mutual actions have no power of dissipating the moment of momentum.

The total moment of momentum of the solar system being taken to be 100, this is at present distributed as follows:--

Orbital moment of momentum of Jupiter 60
Orbital moment of momentum of Saturn 24
Orbital moment of momentum of Uranus 6
Orbital moment of momentum of Neptune 8
Rotational moment of momentum of Sun 2
--
100

The contributions of the other items are excessively minute. The orbital moments of momentum of the few interior planets contain but little more than one thousandth part of the total amount. The rotational contributions of all the planets and of their satellites is very much less, being not more than one sixty-thousandth part of the whole. When, therefore, we are studying the general effects of tides on the planetary orbits these trifling matters may be overlooked. We shall, however, find it desirable to narrow the question still more, and concentrate our attention on one splendid illustration. Let us take the sun and the planet Jupiter, and, supposing all other bodies of our system to be absent, let us discuss the influence of tides produced in Jupiter by the sun, and of tides in the sun by Jupiter.

It might be hastily thought that, just as the moon was born of the earth, so the planets were born of the sun, and have gradually receded by tides into their present condition. We have the means of enquiry into this question by the figures just given, and we shall show that it is impossible that Jupiter, or any of the other planets, can ever have been very much closer to the sun than they are at present. In the case of Jupiter and the sun we have the moment of momentum made up of three items. By far the largest of these items is due to the orbital revolution of Jupiter, the next is due to the sun, the third is due to the rotation of Jupiter on its axis. We may put them in round numbers as follows:--

Orbital moment of momentum of Jupiter 600,000
Rotational moment of momentum of Sun 20,000
Rotational moment of momentum of Jupiter 12

The sun produces tides in Jupiter, those tides retard the rotation of Jupiter. They make Jupiter rotate more and more slowly, therefore the moment of momentum of Jupiter is decreasing, therefore its present value of 12 must be decreasing. Even the mighty sun himself may be distracted by tides. Jupiter raises tides in the sun, those tides retard the motion of the sun, and therefore the moment of momentum of the sun is decreasing, and it follows from both causes that the item of 600,000 must be increasing; in other words, the orbital motion of Jupiter must be increasing, or Jupiter must be receding from the sun. To this extent, therefore, the sun-Jupiter system is analogous to the earth-moon system. As the tides on the earth are driving away the moon, so the tides in Jupiter and the sun are gradually driving the two bodies apart. But there is a profound difference between the two cases. It can be proved that the tides produced in Jupiter by the sun are more effective than those produced in the sun by Jupiter. The contribution of the sun may, therefore, be at present omitted; so that, practically, the augmentations of the orbital moment of momentum of Jupiter are now achieved at the expense of that stored up by Jupiter's rotation. But what is 12 compared with 600,000. Even when the whole of Jupiter's rotational moment of momentum and that of his satellites has become absorbed into the orbital motion, there will hardly be an appreciable difference in the latter. In ancient days we may indeed suppose that Jupiter being hotter was larger than at present, and that he had considerably more rotational moment of momentum. But it is hardly credible that Jupiter can ever have had one hundred times the moment of momentum that he has at present. Yet even if 1,200 units of rotational momentum had been transferred to the orbital motion it would only correspond with the most trivial difference in the distance of Jupiter from the sun. We are hence assured that the tides have not appreciably altered the dimensions of the orbit of Jupiter, or of the other great planets.

The time will, however, come when the rotation of Jupiter on his axis will be gradually abated by the influence of the tides. It will then be found that the moment of momentum of the sun's rotation will be gradually expended in increasing the orbits of the planets, but as this reserve only holds about two per cent. of the whole amount in our system it cannot produce any considerable effect.

The theory of tidal evolution, which in the hands of Professor Darwin has taught us so much with regard to the past history of the systems of satellites in the solar system, will doubtless also, as pointed out by Dr. See, be found to account for the highly eccentric orbits of double star systems. In the earth-moon system we have two bodies exceedingly different in bulk, the mass of the earth being about eighty times as great as that of the moon. But in the case of most double stars we have to do with two bodies not very different as regards mass. It can be demonstrated that the orbit must have been originally of slight eccentricity, but that tidal friction is capable not only of extending, but also