MOO
( ?77 )
MOO
6. Nor is the Apogee of the Moon without an Irregularity ; being round to move forwards, when it coincides with the Line of Syzygies, and backwards, when it cuts the Line at right Angles. See Apogee : Nor is this Progrefs and Hegrefs in any meafure equal : in the Conjunction, or Op- pohtion, it goes briskly forwards 5 and in the Quadratures, moves either ilowly forwards, mads ilill, or goes back- ward. See Syzygies.
7. The Motion of the Nodes is not uniform 5 but when the Line of the Nodes coincides with that of rhe Syzygies, ihey fland (till ; when the Nodes are in the Quadratures, i.e. when their Line cuts that of the Syzygies at right An- gles, they go backwards, from Eaft to Weft ; and this, Sir LNezvion (hews, with the Velocity of 1.6", 19"', 24."", in an Hour. See Node.
The only equable Motion the Moon has, is that where- with ihe turns round her Axis exactly in the fame fpace of Time, in which /lie revolves round us in her Orbit ; whence it happens, that fhe always turns the fame Face towards us.
For, as the Moon's Motion round its Axis is equal, and yet its Motion or Velocity in its Orbit is unequal ; it fol- lows, that when the Moon is in its Perigee, where it moves Jwifteit in its Orbit, that part of its Surface, which, on ac- count of its Motion in the Orbir, would be turn'd from the Earth, is not fo, entirely; by reafon of its Motion round its Axis : Thus, fome Parts in the Limb, or Margin of the Moo;;, fometimes recede from the Center of theDisk, and fometimes approach towards it, and fome Parts, that were before invifible, become confpicuous: which is call'd the Moon's Lib ration.
Yet this Equability of Rotation occafions an apparent Irregularity; (or the Axis of the M007/, not being perpen- dicular to the Plane of its Orbit, but a little inclined to it: and this Axis maintaining its Parallel ifm, in its Motion round the Earth ; it mult ncceflarily change its Situation, in refpecl of an Obfcrver on the Earth; to whom, fome- times the one, and fometimes the other Pole of the Moon, becomes vifible. Whence it appears to have a kind of Libration. SeeLiBRATioN and Axis.
Phyjical Laws of the Moon's Motion.
Thus much for the Lunar Phenomena : It remains that we aflign the Phyfical Catife thereof. The Meow, we have obferved, moves round the Earth, by the fame Laws, and in the fame Manner, as the Earth round the Sun and 0- ther Planets. The Solution therefore of the Lunar Mo- tion, in grr.^rai, comes under thofe of the Earth, and other Planets. See Planet and Earth.
As for the particular irregularities in the Moon's Motion, to which the Earth, and other Planers, are not fubjec> > they arife from the Sun, which ails on, and difturbs her in her ordinary Progrefs thro her Orbit ; and are all me- chanically deducible from the fame great Law, whereby her general Morion is directed, viz-, the Law of Gravitation or Attraffion. See Gravitation.
Other fecondary Planers, v. ». the Satellites of Jupiter and Saturn, are doubrlefs fubjecl to the like Irregularities with the Moon; as being expofed to the fame perrurbating or diirurbing Force of the Sun ; but their Diitance fecures them from our Obfervation. See Satellite and Di- sturbing Force.
The Laws of the feveral Irregularities In the Syzygies, Quadratures, &c. fee under Syzygies, Quadratures,
The Jftronomy of the Moon.
1. To determine the Period of the Moon's Revolution round the Earth, or the Periodical Month ; and the Time between one Oppcfition and another, or theSynodical Month : fince, in the middle of a Lunar Eclipfe, the Moon is oppofite to the Sun: (See Eclipse.) Compute the time between two Eclipfes, or Oppoiitions ; and divide this, by the number of Lunations, that have pafl'ed in the mean time: the Quotient will be the Quantity of the Sy- nodical Month. Compute the Sun's mean Motion du- ring the time of the Synodical Month, and add this to the entire Circle defcribed by the Moon : Then, as the Sum is to 5<5o c , fo is the Quantity of the Synodical Month to the Periodical.
Thus, Copernicus in the Year 15C0, November 6. at 1a at
Night, obferved an Eclipfe of the Moon at Rome; and Au-
ptfi 1, 1525, at 4b.. 2,5', another at Cracow: hence, the
Quantity of the Synodical Month is thus determined:
Obf.n A. 1523d. 2.37b.. 4.25'
Obf. 1 A. t5cod. 310 h. 2.20'
Interval of Time A 22 d. 292 b. 2.5.
And the Days 5
Exaft Interval A. 22 d. 297 h. 2.5'
or 11991005?
Which divided by 282 Months elapfed, In the mean time B gives the Quantity of the Synodical Month 4.2521', 9", 9'" J that is, 29 days, 12 hours, 41 minutes.
From two other Obfervaiions of Eclipfes, the one at Cracozv, the other at Baby/on, the fame Author determines more accurately the Quantity of the Synodical Month to be t 4-524-'. 3 10'". 9"".
I nat is 29 d. ir h.
The Sun's Motion in the time 29.6". 24-18 The Moo;; '5 Motion 389. 6. 24.18
Quantity of the Periodical Month 27 d. 7 b. 43'. 5 ".
Hence, 1. The Quantity of rhe Periodical Month being given; by the Rule of Three we may find the Moon's di- urnal and hourly Motion, &>c. And thus may Tables of the mean Motion of the Moon be conftrucled. See Ta- bles; fee alfo Diurnal and Horary.
2. If the Sun's mean diurnal Motion be fubftraclcd from the Moon's mean diurnal Motion ; the Remainder will give the Moons diurnal Motion from the Sun : and rhus may a Table of Latitudes be conflrucled, fuch as thofe of Bullial- dus. See Latitudes.
3. Since in the middle of a total Eclipfe, the Moon is in the Node ; if rhe Sun's Place be found for that time, and to this be added fix Signs, the Sum will give the Place of the Node. See Node.
4. From comparing the antient Obfervations wirh the modern, it appears that the Nodes have a Motion, and that they proceed in Antecedentia, i. e. from Taurus to Aries i from Aries to Pifces, f£c. If then to the Moon's mean di- urnal Motion, be added the diurnal Motion of the NbdeSj the fame will be the Motion of the Latitude ; and thence-, by the Rule of Three, may be found in what time the Moon goes 360 from the Dragon's Head, or in what time, fhe goes from, and returns to it : That is the Quantity of the Vracomic Month.
5. If me Motion of the diurnal Apogee be fubftracled from the mean Motion of the Moon, the Remainder will be ;he Moon's mean Motion from the Apogee; and thence, by the Rule of Three, is determin'd the Quantity of the Anomalifirc Month.
According to the Obfervations of Kepler, the mean Sy- nodical Month is29d. 12 h. 44'. 3'. i 1 '-'. Her Periodical Month 27 d.' 7 h. 43'. 8". The Place of the Apogee for theYeari7oo, Januaryi, Old Sile, wasnS.S^ 1 . 57'. 1". The Plane of the Nodes 4S. 279. 39', 17". Mean diurnal Motion of the Moon 13°. 10'. 35". Diurnal Motion of the Apogee 6'. 41. Diurnal Moiion of the Nodes 3'. it". LatUy, the Eccentricity 4362 Parts, fuch, whereof the Diameter of the Eccentrice is 1 000c : and therefore the diurnal Motion of the Latitude isi3°. 13'. $6"; and the diurnal Motion from the Apogee 13^. 3'. 54".
Theory of the Lunar Motions and Irregularities.
The Tables of Equation, which ferve to folve the Irre- gularities of the Sun, do likewife ferve for thofe of the Moon. See Equation.
But then thefe Equations mull: be corrected for the Moo;:; otherwife they will not exhibit the true Motions iri the Syzygies. The Method is thus: Suppofe the Moon's Place in the Zodiac, required in Longitude, for any given time; here, we firft find, in the Tables, the place where it would be, fuppofing its Motion uniform, which we call mean, and which is fometimes fafter, and fometimes flower than the true Motion : then, to find where the true Motion will place her, which is alfo the parent, we are to find in another Table at what Diflance it is from its Apogee i for, according to this Diflance, the Difference between her true and mean Motion, and the two Places which correfpond thereto, is the greater. The true Place thus found, is not yet the true Place ; but varies from it, as the Moon is more, or lefs remote both from the Sun, and the Sun's Apogee : which Variation refpecling, at the fame time, thofe two> different Diftances, they are to be both confidered and combined together, as in a Table apart. Which Table gives the Correction td be made of the true Places firft found : That Place thus corrected, is not yet the true Place, unlefs the Moon be either in Conjunction, or Oppo- fition : If me be out of thefe, there mull be another Correction, which depends on two things taken together, and compared, viz. the Diflance of the Moons corrected Place from the Sun ; and of that at which fhe is with re- gard to her own Apogee ; this laft Diflance having beea changed by the firfl Correction.
By all thefe Operations and Corrections, we at length, arrive at the Moon's true Place for that inflant. In this it mufl be owned, occur prodigious difficulties : The Lunar Inequalities are fo many, that it was in vain the Aflro- nomers laboured to bring *em under any Rule, before the Great Sir If. Newton ; to whom we are indebted both for the mechanical Caufes of thefe Inequalities, and for the Method of computing and afcertaining them : So that he 7 H ha»
