Outlines of Astronomy By John Frederick William Herschel

Outlines of Astronomy By John Frederick William Herschel: "720 Now although it is true that the mean motions of no two planets are exactly commensurate yet cases are not wanting in which there exists an approach to this adjustment For instance in the case of Jupiter and Saturn a cycle composed of five periods of Jupiter and two of Saturn although it does not exactly bring about the same configuration docs so pretty nearly Five periods of Jupiter are 21663 days and two periods of Saturn 21519 days The difference is only 146 days in which Jupiter describes on an average 12 and Saturn about 5 so that after the lapse of the former interval they will only be 7 from a conjunction in the same parts of their orbits as before If we calculate the time which will exactly bring about on the average three conjunctions of the two planets we shall find it to be 21760 days their synodi cal period being 7253 4 days In this interval Saturn will have "



Outlines of Astronomy By John Frederick William Herschel: "described 8 6 in excess of two sidereal revolutions and Jupiter the same angle in excess of five Every third conjunction then will take place 8 6 in advance of the preceding which is near enough to establish not it is true an identity with but still a great approach to the case in question The excess of action for several such triple conjunctions 7 or 8 in succession will lie the same way and at each of them the elements of P's orbit and its angular motion will be similarly influenced so as to accumulate the effect upon its longitude thus giving rise to an irregularity of considerable magnitude and very long period which is well known to astronomers by the name of the great inequality of Jupiter and Saturn 721 The arc 8 6 is contained 44 times in the whole circumference of 360 and if we trace round this "



Outlines of Astronomy By John Frederick William Herschel: "particular conjunction we shall find it will return to the same point of the orbit in so many times 21760 days or in 2648 years But the conjunction we are now considering is only one out of three The other two will happen at points of the orbit about 123 and 246 distant and these points also will advance by the same arc of 8 6 in 21760 days Consequently the period of 2648 years will bring them all round and in that interval each of them will pass through that point of the two orbits from which we com "


Outlines of Astronomy By John Frederick William Herschel: "menced hence a conjunction one or other of the three will happen at that point once in one third of this period or in 883 years and this is therefore the cycle in which the great inequality would undergo its full compensation did the elements of the orbits continue all that time invariable Their variation however is considerable in so long an interval and owing to this cause the period itself is prolonged to about 918 years 722 We have selected this inequality as the most remarkable instance of this kind of action on account of its magnitude the length of its period and its high historical interest It had long been remarked by astronomers that on comparing together modern with ancient observations of Jupiter and Saturn the mean motions of these planets did not appear to be uniform The period of Saturn for instance appeared to have been lengthening throughout the whole of the seventeenth and that of "

Outlines of Astronomy By John Frederick William Herschel: "shortening that is to say the one planet was constantly lagging behind and the other getting in advance of its calculated place On the other hand in the eighteenth century a process precisely the reverse seemed to be going on It is true the whole retardations and accelerations observed were not very great but as their influence went on accumulating they produced at length material differences between the observed and calculated places of both these planets which as they could not then be accounted for by any theory excited a high degree of attention and were even at one time too hastily regarded as almost subversive of the Newtonian doctrine of gravity For a long while his difference baffled every endeavour to account for it till at length Laplace pointed out its cause in the near commensurality of the mean motions as above shown and succeeded in calculating its period and amount "


Outlines of Astronomy By John Frederick William Herschel: "723 The inequality in question amounts at its maximum to an alternate gain and loss of about 0 49 in the longitude of Saturn and a corresponding loss and gain of about 0 21 in that of Jupiter That an acceleration in the one planet must necessarily be accompanied by a retardation in the other might appear at first sight self evident if we consider that action and reaction being equal and in contrary directions whatever momentum Jupiter communicates to Saturn in the direction PM the same momentum must Saturn communicate to Jupiter in the direction "


Outlines of Astronomy By John Frederick William Herschel: "M P The one therefore it might seem to be plausibly argued will be dragged forward whenever the other is pulled back in its orbit The inference is correct so far as the general and final result goes but the reasoning by which it would on the first glance appear to be thus summarily established is fallacious or at least incomplete It is perfectly true that whatever momentum Jupiter communicates directly to Saturn Saturn communicates an equal momentum to Jupiter in an opposite linear direction But it is not with the absolute motions of the two planets in space that we are now concerned but with the relative motion of each separately with respect to the sun regarded as at rest The perturbative forces the forces which disturb these relative motions do not act along the line of junction of the planets art 614 In the reasoning thus objected to the attraction of each On the sun has been left out of the account and it remains to be shown that these attractions neutralize and destroy each other's effects in considerable periods of time as bearing upon the result in question Suppose then that we for a moment abandon the point of view in "


Outlines of Astronomy By John Frederick William Herschel: "which we have hitherto all along considered the subject and regard the sun as free to move and liable to be displaced by the attractions of the two planets Then will the movements of all be performed about the common centre of gravity just as they would have been about the sun's centre regarded as immovable the sun all the while circulating in a small orbit with a motion compounded of the two elliptic motions it would have in virtue of their separate attractions about the same centre Now in this case M still disturbs P and P M but the whole disturbing force now acts along their line of junction and since it remains true that whatever momentum M generates in P P will generate the same in M in a contrary direction it will also be strictly true that so far as a disturbance of their elliptic motions about the cotwnon centre of gravity of the system is alone regarded whatever disturbance of velocity is generated in the one a contrary disturbance of velocity only in the inverse ratio of the masses and modified though never contradicted by the directions in which they are We arc here reading a sort of recantation In the edition of 1S33 the remarkable result in question is"