But if the earth is supposed to move, the earth and moon together will be revolved about their common centre of gravity. And the moon (by Prop, lx.) will in the same periodic time, 27 days 7 hr. 43 min., with the same circum-terrestrial force diminished in the duplicate proportion of the distance, describe an orbit whose semi-diameter is to the semi-diameter of the former orbit, that is, to the sixty semi-diameters of the earth, as the sum of both the bodies of the earth and moon to the first of two mean proportionals between this sum and the body of the earth; that is, if we suppose the moon (on account of its mean apparent diameter 311⁄2 min.) to be about 1⁄42 of the earth, as 43 to 3√42 + 422 or as about 128 to 127. And, therefore, the semi-diameter of the orbit—that is, the distance of the centres of the moon and earth—will in this case be 601⁄2 semi-diameters of the earth, almost the same with that assigned by Copernicus; and, therefore, the duplicate proportion of the decrement of the force holds good in this distance. (The action of the sun is here disregarded as inconsiderable.)
This proportion of the decrement of the forces is confirmed from the eccentricity of the planets, and the very slow motion of their apsides; for in no other proportion, it has been established, could the circum-solar planets once in every revolution descend to their least, and once ascend to their greatest distance from the sun, and the places of those distances remain immovable. A small error from the duplicate proportion would produce a motion of the apsides considerable in every revolution, but in many enormous.
The Tides
While the planets are thus revolved in orbits about remote centres, in the meantime they make their several rotations about their proper axes: the sun in 26 days, Jupiter in 9 hr. 56 min., Mars in 242⁄3 hr., Venus in 23 hr., and in like manner is the moon revolved about its axis in 27 days 7 hr. 43 min.; so that this diurnal motion is equal to the mean motion of the moon in its orbit; upon which account the same face of the moon always respects the centre about which this mean motion is performed—that is, the exterior focus of the moon's orbit nearly.
By reason of the diurnal revolutions of the planets the matter which they contain endeavours to recede from the axis of this motion; and hence the fluid parts, rising higher towards the equator than about the poles, would lay the solid parts about the equator under water if those parts did not rise also; upon which account the planets are something thicker about the equator than about the poles.
And from the diurnal motion and the attractions of the sun and moon our sea ought twice to rise and twice to fall every day, as well lunar as solar. But the two motions which the two luminaries raise will not appear distinguished but will make a certain mixed motion. In the conjunction or opposition of the luminaries their forces will be conjoined and bring on the greatest flood and ebb. In the quadratures the sun will raise the waters which the moon depresseth and depress the waters which the moon raiseth; and from the difference of their forces the smallest of all tides will follow.
But the effects of the lumniaries depend upon their distances from the earth, for when they are less distant their effects are greater and when more distant their effects are less, and that in the triplicate proportion of their apparent diameters. Therefore it is that the sun in winter time, being then in its perigee, has a greater effect, whether added to or subtracted from that of the moon, than in the summer season, and every month the moon, while in the perigee raiseth higher tides than at the distance of fifteen days before or after when it is in its apogee.
The fixed stars being at such vast distances from one another, can neither attract each other sensibly nor be attracted by our sun.
Comets
There are three hypotheses about comets. For some will have it that they are generated and perish as often as they appear and vanish; others that they come from the regions of the fixed stars, and are near by us in their passage through the sytem of our planets; and, lastly, others that they are bodies perpetually revolving about the sun in very eccentric orbits.