Philosophical Transactions of the Royal Society - Vol 1 - 1666 / Giving some Accompt of the present Undertakings, Studies, and Labours of the Ingenious in many considerable parts of the World

by Various

The Earth and Moon being known to be Bodies of so great connexion (whether by any Magnetick, or what other Tye, I will not determine; nor need I, as to this purpose;) as that

the motion of the one follows that of the other; (The Moon observing the Earth as the Center of its periodick motion:) may well enough be looked upon as one Body, or rather one Aggregate of Bodies, which have one common center of Gravity; which Center (according to the known Laws of Staticks) is in a streight Line connecting their respective Centers, so divided as that its parts be in reciprocal proportion to the Gravities of the two Bodies. As for Example; Suppose the Magnitude (and therefore probably, the Gravity) of the Moon to be about an One and fourtieth part of that of the Earth; (and thereabouts Hevelius in his Selenography page 203. doth out of Tycho, estimate the proportion; and an exact certainty is not necessary to our present businesse.) And the distance of the Moons Center from the Center of the Earth, to be about fifty six Semidiameters of the Earth, (as thereabouts he doth there estimate it, in its middle distance; and we need not be now very accurate in determining the numbers; wherein Astronomers are not yet very well agreed.) The distance of the Common Center of Gravity of the two Bodies, will be from that of the Earth, about a two and fourtieth part of fifty six Semidiameters; that is, about ⁵⁶/₄₂ or ⁴/₃ of a Semidiameter; that is about ⅓ of a Semidiameter of the Earth, above its surface, in the Air, directly between the Earth and Moon.

Now supposing the Earth and Moon, joyntly as one Body, carried about by the Sun in the great Orb of the Annual motion; this motion is to be estimated, (according to the Laws of Staticks, in other cases,) by the motion of the common Center of Gravity of both Bodies. For we use in Staticks, to estimate a Body, or Aggregate of Bodies, to be moved upwards, downwards, or otherwise, so much as its Common Center of Gravity is so moved, howsoever the parts may change places amongst themselves.

And accordingly, the Line of the Annual motion, (whether Circular or Elliptical; of which I am not here to dispute,) will be described, not by the Center of the Earth (as we commonly estimate it, making the Earth a Primary and the Moon a Secondary Planet,) nor by the Center of the Moon, (as they would do, who make the Moon the Primary and the Earth a

Secondary Planet, against which we were before disputing:) But by the Common Center of Gravity of the Bodies, Earth and Moon, as one Aggregate.

See Fig. 2. and 3.

Now supposing A B C D E to be a part of the great Orb of the Annual motion, described by the Common Center of Gravity, in so long time as from a Full-Moon at A to the next New-Moon at E; (which, though an Arch of a Circle or Ellipse, whose Center we suppose at a due distance below it; yet being put about ¹/₂₅ of the whole, may well enough be here represented by a streight Line:) the Center of the Earth at T, and that of the Moon at L, must each of them (supposing their common Center of Gravity to keep the Line A E) be supposed to describe a Periphery about that Common Center, as the Moon describes her Line of Menstrual motion (Of which I have (in the Scheme) onely drawn that of the Earth; as being sufficient to our present purpose; parallel to which, if need be, we may suppose one described by the Moon; whose distance is also to be supposed much greater from T than in the figure is expressed, or was necessary to expresse.) And in like manner E F G H I, from that New moon at E, to the next Full-moon at I.

From A to E (from Full moon to New moon,) T moves (in its own Epicycle) upwards from the Sun: And from E to I, (from New moon to Full moon) it moves downwards, toward the Sun. Again, from C to G, (from last quarter to the following first quarter,) it moves forwards according to the Annual motion; But from G forward to C, (from the first Quarter to the ensuing last Quarter,) it moves contrary to the Annual motion.

It is manifest therefore, according to this Hypothesis, that from Last quarter to First quarter (from C to G, while T is above the Line of the Annual motion) its Menstrual motion in its Epicycle adds somewhat of Acceleration to the Annual motion, and most of all at E, the New-moon: And from the first to the last quarter (from G forward to C, while T is below the Line of the Annual motion,) it abates of the Annual motion; and most of all at I, or A the Full-moon.