Orbital moment of momentum of Jupiter60Orbital moment of momentum of Saturn24Orbital moment of momentum of Uranus6Orbital moment of momentum of Neptune8Rotational moment of momentum of Sun2—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 Jupiter600,000Rotational moment of momentum of Sun20,000Rotational moment of momentum of Jupiter12
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 satelliteshas 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 of elongating it. The accelerating force is vastly greater at periastron (when the two bodies are nearest each other) than at apastron (when their distance is greatest). At periastron the disturbing force will, therefore, increase the apastron distance by an enormous amount, while at apastron it increases the periastron distance by a very small amount.Thus, while the ellipse is being gradually expanded, the orbit grows more and more eccentric, until the axial rotations have been sufficiently reduced by the transfer of axial to orbital moment of momentum.
And now we must draw this chapter to a close, though there are many other subjects that might be included. The theory of tidal evolution is, indeed, one of quite exceptional interest. The earlier mathematicians expended their labour on the determination of the dynamics of a system which consisted of rigid bodies. We are indebted to contemporary mathematicians for opening up celestial mechanics upon the more real supposition that the bodies are not rigid; in other words, that they are subject to tides. The mathematical difficulties are enormously enhanced, but the problem is more true to nature, and has already led to some of the most remarkable astronomical discoveries made in modern times.
Our Story of the Heavens has now been told. We commenced this work with some account of the mechanical and optical aids to astronomy; we have ended it with a brief description of an intellectual method of research which reveals some of the celestial phenomena that occurred ages before the human race existed. We have spoken of those objects which are comparatively near to us, and then, step by step, we have advanced to the distant nebulæ and clusters which seem to lie on the confines of the visible universe. Yet how little can we see with even our greatest telescopes, when compared with the whole extent of infinite space! No matter how vast may be the depth which our instruments have sounded, there is yet a beyond of infinite extent. Imagine a mighty globe described in space, a globe of such stupendous dimensions that it shall include the sun and his system, all the stars and nebulæ, and even all the objects which our finite capacities can imagine. Yet, what ratio must the volume of this great globe bear to the whole extent of infinite space? The ratio is infinitely less than that which the water in a single drop of dew bears to the water in the whole Atlantic Ocean.
The Sun.
The sun's mean distance from the earth is 92,900,000 miles; his diameter is 866,000 miles; his mean density, as compared with water, is 1·4; his ellipticity is insensible; he rotates on his axis in a period between 25 and 26 days.
The Moon.
The moon's mean distance from the earth is 239,000 miles. The diameter of the moon is 2,160 miles; and her mean density, as compared with water, is 3·5. The time of a revolution around the earth is 27·322 days.
The Planets.
Distance from the Sun inMillions of Miles.Periodic Timein Days.MeanDiameterin Miles.Axial Rotation.DensitycomparedwithWater.Mean.Least.Greatest.Mercury36·028·643·387·9693,030(?)6·85(?)Venus67·266·667·5224·707,700(?)4·85Earth92·991·194·6365·267,91823 56 4·095·58Mars141128155686·984,23024 37 22·74·01Jupiter4834595054,332·686,5009 55 —1·38Saturn88683493610,75971,00010 14 —0·72Uranus1,7821,7001,86030,68731,900Unknown1·22Neptune2,7922,7602,81060,12734,800Unknown1·11
The Satellites of Mars.
Mean Distance from Centreof Mars.Periodic Time.hrs.mins.secs.Phobos5,800 miles73914Deimos14,500 miles301754
The Satellites of Jupiter.
Mean Distance from Centreof Jupiter.Periodic Time.days.hrs.mins.secs.New Inner Sattellite Barnard112,500 miles0115722I.261,000 miles1182734II.415,000 miles3131342III.664,000 miles734233IV.1,167,000 miles16163211
The Satellites of Saturn.
Mean Distance from Centreof Saturn.Periodic Time.days.hrs.mins.secs.Mimas115,000 miles022376Enceladus148,000 miles18537Tethys183,000 miles1211826Dione235,000 miles217419Rhea329,000 miles4122512Titan760,000 miles15224127Hyperion921,000 miles2163831Iapetus2,215,000 miles7975640
The Satellites of Uranus.
Mean Distance from Centreof Uranus.Periodic Time.days.hrs.mins.secs.Ariel119,000 miles2122921Umbriel166,000 miles432737Titania272,000 miles8165630Oberon364,000 miles131176
The Satellite of Neptune.
Mean Distance from Centreof Neptune.Periodic Time.days.hrs.mins.secs.Satellite220,000 miles521244