The Moon’s motion thro’ open space described.
265. If the Earth had no annual motion, the Moon’s motion round the Earth, and her track in absolute space, would be always the same[[58]]. But as the Earth and Moon move round the Sun, the Moon’s real path in the Heavens is very different from her path round the Earth: the latter being in a progressive Circle, and the former in a curve of different degrees of concavity, which would always be the same in the same parts of the Heavens, if the Moon performed a compleat number of Lunations in a year.
An idea of the Earth’s path and the Moon’s.
266. Let a nail in the end of the axle of a chariot-wheel represent the Earth, and a pin in the nave the Moon; if the body of the chariot be propped up so as to keep that wheel from touching the ground, and the wheel be then turned round by hand, the pin will describe a Circle both round the nail and in the space it moves through. But if the props be taken away, the horses put to, and the chariot driven over a piece of ground which is circularly convex; the nail in the axle will describe a circular curve, and the pin in the nave will still describe a circle round the progressive nail in the axle, but not in the space through which it moves. In this case, the curve described by the nail will resemble in miniature as much of the Earth’s annual path round the Sun, as it describes whilst the Moon goes as often round the Earth as the pin does round the nail: and the curve described by the nail will have some resemblance of the Moon’s path during so many Lunations.
Fig. II.
[PL. VII.]
Let us now suppose that the Radius of the circular curve described by the nail in the axle is to the Radius of the Circle which the pin in the nave describes round the axle as 3371⁄2 to 1; which is the proportion of the Radius or Semidiameter of the Earth’s Orbit to that of the Moon’s; or of the circular curve A 1 2 3 4 5 6 7 B &c. to the little Circle a; and then, whilst the progressive nail describes the said curve from A to E, the pin will go once round the nail with regard to the center of it’s path, and in doing so, will describe the curve abcde. The former will be a true representation of the Earth’s path for one Lunation, and the latter of the Moon’s for that time. Here we may set aside the inequalities of the Moon’s Moon, and also the Earth’s moving round it’s common center of gravity and the Moon’s: all which, if they were truly copied in this experiment, would not sensibly alter the figure of the paths described by the nail and pin, even though they should rub against a plain upright surface all the way, and leave their tracks visible. And if the chariot should be driven forward on such a convex piece of ground, so as to turn the wheel several times round, the track of the pin in the nave would still be concave toward the center of the circular curve described by the pin in the Axle; as the Moon’s path is always concave to the Sun in the center of the Earth’s annual Orbit.
Proportion of the Moon’s Orbit to the Earth’s.
In this Diagram, the thickest curve line ABCD, with the numeral figures set to it, represents as much of the Earth’s annual Orbit as it describes in 32 days from west to east; the little Circles at a, b, c, d, e shew the Moon’s Orbit in due proportion to the Earth’s; and the smallest curve abcdef represents the line of the Moon’s path in the Heavens for 32 days, accounted from any particular New Moon at a. The machine, Fig. 5th is for delineating the Moon’s path, and will be described, with the rest of my Astronomical machinery, in the [last Chapter]. The Sun is supposed to be in the center of the curve A 1 2 3 4 5 6 7 B &c. and the small dotted Circles upon it represent the Moon’s Orbit, of which the Radius is in the same proportion to the Earth’s path in this scheme, that the Radius of the Moon’s Orbit in the Heavens bears to the Radius of the Earth’s annual path round the Sun; that is, as 240,000 to 81,000,000, or as 1 to 3371⁄2.
Fig. II.
When the Earth is at A the New Moon is at a; and in the seven days that the Earth describes the curve 1 2 3 4 5 6 7, the Moon in accompanying the Earth describes the curve ab; and is in her first Quarter at b when the Earth is at B. As the Earth describes the curve B 8 9 10 11 12 13 14 the Moon describes the curve bc; and is opposite to the Sun at c, when the Earth is at C. Whilst the Earth describes the curve C 15 16 17 18 19 20 21 22 the Moon describes the curve cd; and is in her third Quarter at d when the Earth is at D. Once more, whilst the Earth describes the curve D 23 24 25 26 27 28 29 the Moon describes the curve de; and is again in conjunction at e with the Sun when the Earth is at E, between the 29th and 30th day of the Moon’s age, accounted by the numeral Figures from the New Moon at A. In describing the curve abcde, the Moon goes round the progressive Earth as really as if she had kept in the dotted Circle A, and the Earth continued immoveable in the center of that Circle.