80 | The Solar System |
est perturbative action on the rings is Mimas, his effect being more than three times that of Enceladus and more than twice that of Tethys.
The equations of motion are for x—
of which the first is the direct force of the central body, whose mass is taken as i, upon m; and the other terms are the perturbing force of m on m'.
Assuming the three to be in conjunction, this last becomes where . Supposing to be 74,000 miles from the centre of Saturn, and Mimas, Enceladus, and Tethys at 117,000, 150,000, and 186,000 miles respectively, and taking the masses as proportionate to their volumes, their radii being taken as 400, 400, and 600 miles, we find for their relative perturbative effects :—
Mimas | . | . | . | . | . | . | . | 299 |
Enceladus | . | . | . | . | . | . | . | 82 |
Tethys | . | . | . | . | . | . | . | 110 |
The action of the others is smaller still. Now the major axis of a part of the ring which has a period commensurate with that of Mimas may be found from the formula —