Now, by an easy calculation of these two spaces, it appears that the former force is to the latter as the square of the semi-diameter of the earth is to the square of that of the moon's orbit. The moon's centripetal force, therefore, is equal to the force of gravity ; and consequently these forces are not different, but they are one and the same ; for if they were different bodies, acted on by the two pow ers conjointly, they would fall towards the earth with a velocity double to that aris ing from the sole power of gravity.
It is evident, therefore, that the moon's centripetal force, by which she is retained in her orbit, and prevented from running off in tangents, is the very power of gra vity of the earth extended thither. See " Newton's Principia," lib. i. prop. 45, cor. 2. and lib. iii. prop. 3 ; where the numeral calculation may be seen at full length.
The moon, therefore, gravitates to wards the earth, and reciprocally the earth towards the moon, and this is also farther confirmed by the phenomena of the tides.
The like reasoning may also be applied to the other planets. For as the revolu
tions of the primary planets round the sun, and those of the satellites of Jupiter and Saturn round their primaries, are phenomena of the same kind with the re volution of the moon about the earth ; and as the centripetal powers of the pri mary are directed towards the centre of the sun, and those of the satellites to wards the centres of their primaries ; and, lastly, as all these powers are reci procally as the squares of the distances from the centres, it may safely be con cluded that the power and causes are the same in all. Therefore, as the moon gra vitates towards the earth, and the earth towards the moon, so do all the seconda ries to their primaries, and these to the secondaries ; and so also do the primaries to the sun, and the sun to the primaries. Newton's Princip. lib. iii, prop. 4, 5, 6; Greg. Astron. lib. i. sect. 7, prop. 46 and 47.
The laws of universal gravity are the same as those of bodies gravitating to wards the earth, before laid down. See ASTRONOMY, ATTRACTION, GEOGRAPHY.