THEINTRODUCTION,CONTAINING
A Brief Account of theSolar System, and of theFixed Stars.
Of the Order and Periods of the Primary Planets revolving about the Sun; and of the Secondary Planets round their respective Primaries.
Planets.
TheSun is placed in the midst of an immense space, wherein six opaque spherical bodies revolve about him as their center. These wandering globes are called thePlanets, who, at different distances, andin different periods, perform their revolutions from West to East, in the following order:
1. ☿Mercuryis nearest to the Sun of all the planets, and performs its course in about three months. 2. ♀Venusin about seven months and a half. 3. ♁ TheEarthin a year. 4. ♂Marsin about two years. 5. ♃Jupiterin twelve. And lastly, ♄Saturn, whose[1]Orbitincludes all the rest, spends almost 30 years in one revolution round the Sun. The distances of the Planets from the Sun are nearly in the same proportion as they are represented inPlate1.viz.Supposing the distance of the Earth from the Sun to be divided into 10 equal parts; that ofMercurywill be about 4 of these parts; ofVenus7; ofMars15; ofJupiter52; and that ofSaturn95.The Characters placed before the names of the Planets, are for brevity’s sake commonly made use of by Astronomers, instead of the words at length, as ♀, forVenus, &c.
1. ☿Mercuryis nearest to the Sun of all the planets, and performs its course in about three months. 2. ♀Venusin about seven months and a half. 3. ♁ TheEarthin a year. 4. ♂Marsin about two years. 5. ♃Jupiterin twelve. And lastly, ♄Saturn, whose[1]Orbitincludes all the rest, spends almost 30 years in one revolution round the Sun. The distances of the Planets from the Sun are nearly in the same proportion as they are represented inPlate1.viz.Supposing the distance of the Earth from the Sun to be divided into 10 equal parts; that ofMercurywill be about 4 of these parts; ofVenus7; ofMars15; ofJupiter52; and that ofSaturn95.
The Characters placed before the names of the Planets, are for brevity’s sake commonly made use of by Astronomers, instead of the words at length, as ♀, forVenus, &c.
Plate 1.
Plate 1.
Nodes.
The orbits of the Planets are not all in the same plane, but variously inclined to one another; so that supposing one of them to coincide with the above scheme, the others will have one half above, and the other half below it; intersecting one another in a line passing through the Sun. The plane of the Earth’s orbit is called theEcliptic; and this the astronomers make the standard to which the planes of the other orbits are judged to incline. The right line passing thro’ the Sun, and the common intersection of the plane of the orbit of any planet and the Ecliptic, is called theLine of the Nodesof that planet; and the points themselves, wherein the orbit cuts the Ecliptic are called theNodes.
Excentricity.
The inclinations of the orbits of the Planets to the plane of the ecliptic, are as follows,viz.the orbit ofMercurymakes an angle with it of almost 7 degrees; that ofVenussomething above 3⅓ degrees; ofMarsa little less than 2 degrees; ofJupiter, 1⅓ degree; and ofSaturn, about 2½ degrees. The orbits of the Planets are not circles, but ellipses or ovals. What an ellipsis is, may beeasily understood from the following description. Imagine two small pegs fixed upright on any plane, and suppose them tied with the ends of a thread somewhat longer than their distance from one another: Now if a pin be placed in the double of the thread and turned quite round (always stretching the thread with the same force) the curved described by this motion is anEllipsis. The two points where the pegs stood, (about which the thread was turned) are called thefociof that ellipsis; and if, without changing the length of the thread, we alter the position of the pegs, we shall then have an ellipsis of a different kind from the former; and the nearer thefocus’sare together, the nearer will the curve described be to a circle; until at last, the twofocus’scoincide, and then the pin in the doubling of the thread will describe a perfect circle. The orbits of all the Planets have the Sun in one of theirfocus’s, and half the distance between the twofocus’sis called theExcentricityof the orbits. This excentricity is different in all the planets, but in most of them so small, that in little schemes or instruments, made to represent the planetary orbits, it need not be considered.
Primary Planets.
Secondary Planets.
The six Planets above-mentioned, are calledPrimaries, orPrimary Planets; but besides these, there are ten other lesser Planets, which are calledSecondaries,Moons, orSatellites. These moons always accompany their respective primaries, and perform their Revolutions round them, whilst both together are also carried round the Sun. Of the six Primary Planets, there are but three, as far as observation can assure us, that have these attendants,viz.theEarth,Jupiter, andSaturn.
The Earth is attended by theMoon, who performs her revolution in about 27⅓ Days, at the distance of about 30 Diameters of the Earth from it; and once a Year is carried round the Sun along with the Earth.
Jupiter’sfour Moons.
Jupiterhas fourMoons, orSatellites; thefirst, or innermost, performs its revolution in about one Day, and 18½ Hours, at the distance of 5⅔ Semidiameters ofJupiter, from his Center; thesecondrevolves aboutJupiterin 3 Days, 13 Hours, at the distance of 9 of his Semidiameters; thethirdin 7 Days, and 4 Hours, at thedistance of 14⅓ Semidiameters; thefourth, andoutermost, performs its course in the space of 16 Days, 17 Hours; and is distant fromJupiter’scenter, 25⅓ of his Semidiameters.
Saturnhas five Moons.
Saturnhas no less than fiveSatellites; thefirst, or innermost, revolves about him in 1 Day, and 21 Hours, at the distance of 4⅜ Semidiameters of ♄, from his center; thesecondcompleats his period in 2¾ Days, at the distance of 5³/₅ of his Semidiameters; thethird, in about 4½ Days, at the distance of 8 Semidiameters; thefourthperforms its course in about 16 Days, at the distance of 18 Semidiameters; thefifth, and outermost, takes 79⅓ Days, to finish his course, and is 54 Semidiameters ofSaturndistant from his center. The Satellites, as well as their primaries, perform their revolutions fromWesttoEast: The planes of the Orbits of the Satellites of the same Planet are variously inclined to one another, and consequently are inclined to the plane of the Orbit of their primary.
Saturn’sRing.
Besides these attendants,Saturnis encompassed with a thin plain Ring, that does no where touch his body; The diameter of this Ring isto the diameter ofSaturn, as 9 to 4; and the void space between the Ring and the body ofSaturnis equal to the breadth of the Ring itself; so that in some situations the Heavens may be seen between the Ring and his body. This surprizing phænomenon ofSaturn’s Ring, is a modern discovery; neither were the Satellites ofJupiterandSaturnknown to the ancients. TheJovialPlanets were first discovered by the famousItalianphilosopherGalilæus, by a telescope which he first invented; and the celebratedCassini, theFrenchking’s astronomer, was the first that saw all the Satellites ofSaturn; which by reason of their great distances from the Sun, and the smallness of their own bodies, cannot be seen by us, but by the help of very good glasses.
Annual Motion.
Diurnal Motion.
The motion of the primary Planets round the Sun (as also of the Satellites round their respective primaries) is called theirAnnual Motion; because they have one Year, or alteration of Seasons compleat, in one of these revolutions. Besides this annual motion, four of the Planets,viz. Venus, theEarth,Mars, andJupiterrevolve about their ownAxis, fromWesttoEast; and this is called theirDiurnal Motion. For by this rotation, each point of their surfaces is carried successively towards or from the Sun, who always illuminates the hemisphere which is next to him, the other remaining obscure; and while any place is in the hemisphere, illuminated by the Sun, it isDay, but when it is carried to the obscure hemisphere, it becomesNight; and so continues, until by this rotation the said place is again enlightened by the Sun.
Diurnal Motion of the ♁, ♀, ♂ and ♃.
☉ and ☽ likewise turn round their Axis.
TheEarthperforms its revolution round its axis in 23 Hours, 56 Minutes;[2]Venus, in 24 Days, 8 Hours;Mars, in 24 Hours, and 40 Minutes; andJupitermoves round his own axis in 9 Hours, and 56 Minutes. The Sun also is found to turn round his axis from West to East, in 27 Days: And the Moon, which is nearest to us of all the Planets, revolves about her axis in a Month, or in the same space of time that she turns round the Earth; so that theLunarianshave but 1 Day throughout the Year.
The Planets are Opaque and Globular.
I. The Planets are allOpaquebodies, having no light but what they borrow from the Sun; for that side of them which is next towards the Sun, has always been observed to be illuminated, in what position soever they be; but the opposite side, which the Solar rays do not reach, remains dark and obscure; whence it is evident that they have no light but what proceeds from the Sun; for if they had, all parts of them would be lucid, without any darkness or shadow. The Planets are likewise proved to beGlobular; because let what part soever of them be turned towards the Sun, its boundary, or the line separating that part from the opposite, always appears to be circular; which could not happen, if they were not globular.
The Planets turn round the Sun.
II. That the Earth is placed betwixt the Orbs ofMarsandVenus, and that ☿, ♀, ♂, ♃ and ♄, do all turn round the Sun, is proved from observations as follow:
Plate 2. Fig. 1. 2.
1. WheneverVenusis in conjunction with the Sun, that is, when she is in the same direction from the Earth, or towards the same part of the Heavens the Sun is in; she either appears with a bright and round face, like a Full Moon, or else disappears: Or, if she is visible, she appears horned, like a new Moon; which phænomena could never happen if ♀ did not turn round the Sun, and was not betwixt him and the Earth: For since all the Planets borrow their light from the Sun, it is necessary that ♀’s lucid face should be towards the Sun; and when she appears fully illuminated, she shews the same face to the Sun and Earth; and at that time she must be above or beyond the Sun; for in no other position could her illuminated face be seen from the Earth. Farther, when she disappears, or if visible, appears horned; that face of her’s which is towards the Sun is either wholly turned from the Earth, or only a small part of it can be seen by the Earth; and in this case she must of necessity be betwixt us and the Sun. Let S be theSun, T theEarth, and VVenus, having the same face presented both towards theSunandEarth; here it is plain that the Sun is betwixt us andVenusand therefore we must either placeVenusin anOrbit round the Sun, and likewise betwixt him and us, as inFig. 1.or else we must make the Sun to move round the Earth in an Orbit within that ofVenus, as inFig. 2.Again, afterVenusdisappears, or becomes horned, at her[3]☌ with the ☉, she then must be betwixt us and the Sun, and must move either in an Orbit round the Sun and betwixt us and him, as inFig. 1.or else round the Earth, and betwixt us and the Sun, as inFig. 2.ButVenuscannot move sometimes within the Sun’s Orbit, and sometimes without it, as we must suppose if she moves round the Earth; therefore it is plain that her motion is round the Sun.
WhyVenusis always either our Morning or Evening Star.
Besides the forgoing, there is another argument to prove thatVenusturns round the Sun in an Orbit that is within the Earth’s, because she is always observed to keep near the Sun, and in the same quarter of the Heavens that he is in, never receding from him more than about ⅛ of a whole circle; and therefore she can never come in opposition to him; which would necessarily happen, did she perform her course round the Earth either in a longer or shorter time than a Year. And this is thereason whyVenusis never to be seen near midnight, but always either in the Morning or Evening, and at most not above three or four Hours before Sun-rising or after Sun-setting. From the time of ♀’s superior conjunction (or when she is above the Sun) she is more Easterly than the Sun, and therefore sets later, and is seen after Sun-setting; and then she is commonly called theEvening Star. But from the time of her inferior conjunction, ’till she comes again to the superior, she then appears more Westerly than the Sun, and is only to be seen in the morning before Sun-rising, and is then called theMorning Star.
After the same manner we prove thatMercuryturns round the Sun, for he always keeps in the Sun’s neighbourhood, and never recedes from him so far asVenusdoes; and therefore the Orbit of ☿ must lie within that of ♀; and on the account of his nearness to the Sun, he can seldom be seen without a Telescope.
The Orbit ofMarsincludes the Earth’s.
Fig. 3.
Marsis observed to come in opposition, and likewise to have allother aspects with the Sun; he always preserves a round, full, and bright face, except when he is near his quadrate aspect, when he appears somewhat gibbous, like the Moon three or four Days before or after the full: Therefore the Orbit of ♂ must include the Earth within it, and also the Sun; for if he was betwixt the Sun and us at the time of his inferior conjunction, he would either quite disappear, or appear horned, asVenusand the Moon do in that position. Let S be theSun, T theEarth, and A PMars, both in his conjunction and opposition to the Sun, and in both positions full; and B CMarsat his quadratures, when he appears somewhat gibbous from the Earth at T. ’Tis plain hence, that the Orbit ofMarsdoes include the Earth, otherwise he could not come in opposition to the Sun; and that it likewise includes the Sun, else he could appear full at his conjunction.
Marswhen he is in opposition to the Sun, looks almost seven times larger in diameter than when he is in conjunction with him, and therefore must needs be almost seven times nearer to us in one positionthan in the other; for the apparent magnitudes of far distant objects increase or decrease in proportion to their distances from us: ButMarskeeps always nearly at the same distance from the Sun; therefore it is plain that it is not the Earth, but the Sun, that is the center of his motion.
It is proved in the same way, thatJupiterandSaturnhave both the Sun and the Earth within their Orbits, and that the Sun, and not the Earth, is the center of their motions; altho’ the disproportion of the distances from the Earth is not so great inJupiter, as it is inMars, nor so great inSaturn, as it is inJupiter, by reason that they are at a much greater distance from the Sun.
InferiorandSuperior Planets.
We have now shewn that all the Planets turn round the Sun, and thatMercuryandVenusare included between him and the Earth, whence they are called theInferior Planets, and that the Earth is placed between the Orbits ofMarsandVenus, and therefore included within the Orbits ofMars,Jupiter, andSaturn, whence they are called theSuperior Planets: And since the Earth is in the middle of thesemoveable bodies, and is of the same nature with them, we may conclude that she has the same sort of motions; but that she turns round the Sun is proved thus:
The Earth does not stand still, but turns round the Sun.
Fig. 4.
All the Planets seen from the Earth appear to move very unequally, as sometimes to go faster, at other times slower; sometimes to go backwards, and sometimes to be stationary, or not to move at all; which could not happen if the Earth stood still. Let S be the Sun, T the Earth, the great circle A B C D the Orbit ofMars, and the numbers 1, 2, 3,&c.its equable motion round the Sun; the correspondent numbers 1, 2, 3,&c.in the circlea,b,c,d, the motion ofMars, as it would be seen from the Earth. It is plain from this Figure, that if the Earth stood still, the motion ofMars, will be always progressive, (tho’ sometimes very unequal;) but since observations prove the contrary, it necessarily follows, that the Earth turns round the Sun.
The Annual and Diurnal Motions of the Planets, how computed.
The annual periods of the Planets round the Sun are determined by carefully observing the length of time since their departure from a certain point in the Heavens, (or from a fix’d Star) until they arriveto the same again. By these sort of observations the ancients determined the periodical revolutions of the Planets round the Sun, and were so exact in their computations, as to be capable of predicting Eclipses of the Sun and Moon. But since the invention of telescopes, astronomical observations are made with greater accuracy; and of consequence, our tables are far more perfect than those of the ancients. And in order to be as exact as possible, astronomers compare observations made at a great distance of time from one another, including several periods; by which means, the error that might be in the whole, is in each period subdivided into such little parts as to be inconsiderable. Thus the mean length of a Solar Year is known, even to Seconds.
The Diurnal rotation of the Planets round their axis, was discovered by certain spots which appear on the surfaces. These spots appear first in the margin of the Planet’s disk, (or the edge of their surfaces) and seem by degrees to creep toward their middle, and so on, going still forward, ’till they come to the opposite side or edge of the disk,where they set or disappear; and after they have been hid for the same space of time, that they were visible, they again appear to rise in or near the same place, as they did at first, then to creep on progressively, taking the same course as they did before. These spots have been observed on the surfaces of theSun,Venus,Mars, andJupiter; by which means it has been found that these bodies turn round their own axis, in the times before-mentioned. It is very probable thatMercuryandSaturnhave likewise a motion round their axis, that all the parts of their surface may alternately enjoy the light and heat of the Sun, and receive such changes as are proper and convenient for their nature. But by reason of the nearness of ☿ to the Sun, and ♄’s immense distance from him, no observations have hitherto been made whereby their spots (if they have any) could be discovered, and therefore their Diurnal motions could not be determined. The Diurnal motion of the Earth is computed from the apparent revolution of the Heavens, and of all the Stars round it, in the space of a natural Day. The Solar spots do not always remain the same, but sometimes oldones vanish, and afterwards others succeed in their room; sometimes several small ones gather together and make one large spot, and sometimes a large spot is seen to be divided into many small ones. But, notwithstanding these changes, they all turn round with the Sun in the same time.
How the relative distances of the Planets from the Sun are determined.
The relative distances of the Planets from the Sun, and likewise from each other, are determined by the following methods: First, the distance of the two inferior Planets ☿ and ♀ from the Sun, in respect of the Earth’s distance from him, is had by observing their greatest Elongation from the Sun as they are seen from the Earth.
Fig. 5. Elongation.
The greatestElongationofVenusis found by observation to be about 48 degrees, which is the angle S T ♀; whence, by the known rules of Trigonometry, the proportion of S ♀, the mean distance ofVenusfrom the Sun to ST, the mean distance of the Earth from him may be easily found. After the same manner, in the right-angled triangle S T ☿, may be found the distance S ☿ ofMercuryfrom the Sun. And if the mean distance of the Earth from the Sun S T be made 1000, the meandistance ofVenusS ♀ from the Sun will be 723; and ofMercuryS ☿ 387: And if the Planets moved round the Sun in circles, having him for their center, the distances here found would be always their true distances: But as they move in Ellipses, their distances from the Sun will be sometimes greater, and sometimes less. TheirExcentricitiesare computed to be as follows,viz.
HeliocentricandGeocentric Place, what.
The distances of the superior Planets,viz.♂, ♃, and ♄, are found by comparing their true places, as they are seen from the Sun, with their apparent places, as they are seen from the Earth. Let S be the Sun, the circle ABC the Earth’s orbit, AG a line touching the Earth’s orbit, in which we’ll suppose the superior Planets are seen from the Earth in the points of their orbits ♂, ♃, ♄; and let DEFGH be a portion of a great circle in the Heavens, at an infinite distance: Then the place ofMarsseen from the Sun is D, which is called his true, orHeliocentric Place; but from the Earth, he will be seen in G, whichis called his apparent, orGeocentric Place. So likewiseJupiterandSaturnwill be seen from the Sun in the points E and F, their Heliocentric places; but a spectator from the Earth will see them in the point of the Heavens G, which is their Geocentric place. The arches DG, EG, FG, the differences between the true and apparent places of the Superior Planets, are called theParallaxesof the Earth’s annual Orb, as seen from these Planets. If thro’ the Sun we draw SH parallel to AG, the angles A ♂ S, A ♃ S, A ♄ S, will be respectively equal to the angles D S H, E S H, and F S H; and the angle A G S is equal to the angle GSH, whose measure is the arch GH; which therefore will be the measure of the angle AGS, the angle under which the semidiameter A S of the Earth’s orbit, is seen from the Starry Heavens. But this semidiameter is nothing in respect of the immense distance of the Heavens or Fixed Stars; for from thence it would appear under no sensible angle, but look like a point. And therefore in the Heavens, the angle G S H, or the arch G H vanishes; and the Points G and H coincide; and the arches D H, E H, F H, may be considered as being ofthe same bigness with the arches D G, E G, and F G, which are the measures of the angles A ♂ S, A ♃ S, A ♄ S; which angles are nearly the greatest elongation of the Earth from the Sun, if the Earth be observed from the respective Planets, when the line G ♄ ♃ ♂ A, touches the Earth’s orbit in A. The nearer any of the superior Planets is to the Sun, the greater is the Parallax of the annual Orb, or the angle under which the semidiameter of the Earth’s orbit is seen from that Planet. InMarsthe angle ♂ S, (which is the visible elongation of the Earth seen fromMars, or the Parallax of the annual Orb seen from that Planet) is about 42 degrees, and therefore the Earth is always to the inhabitants ofMarseither their Morning or Evening Star, and is never seen by them so far distant from the Sun as we seeVenus. The greatest elongation of the Earth seen fromJupiter, being nearly equal to the angle A ♃ S, is about 11 degrees. InSaturnthe angle A ♄ S is but 6 degrees, which is not much above ¼ part of the greatest elongation we observe inMercury. And sinceMercuryis so rarely seen by us, probably the astronomers ofSaturn(except they havebetter Optics than we have) have not yet discovered that there is such a body as our Earth in the Universe.
The Parallax of the annual Orb, or the greatest elongation of the Earth’s orbit seen from any of the superior Planets, being given; the distance of that Planet from the Sun, in respect of the Earth’s distance from him, may be found by the same methods as the distances of the inferior Planets were. Thus, to find the distance ofMarsfrom the Sun, it will be as the Sine of the angle S ♂ A is to theRadius, so is the distance AS (the distance of the Earth from the Sun) to S ♂, the distance from the Sun toMars. After the same manner the distances ofJupiterandSaturnare also found. The mean distance of the Earth from the Sun being made 1000, the mean distances of the superior Planets from the Sun are,viz.the mean distance from the Sun of
To which, if you add or subtract their mean distances, we shall have the greatest or least distances of those Planets from the Sun.
There are other methods by which the relative distances of the Planets might be found; but that which hath been here illustrated, is sufficient to evince the certainty of that Problem.
How the absolute distances of the Planets from the Sun are computed.
Parallaxof theEarth’s Semidiameter.
Fig. 7.
Hitherto we have only considered the distances of the Planets in relation to one another, without determining them by any known measure; but in order to find their absolute distances in some determinate measure, there must be something given, whose measure is known. Now the circumference of the Earth is divided into 360 degrees, and each of these degrees into 60 Geographical miles, so that the whole circumference contains 21600; and by the known proportion for finding the diameter of a circle from its circumference, the Earth’s diameter will be found to be 6872 miles, and its semidiameter 3436 miles. The Parallax of the Earth’s semidiameter, or the angle under which it is seen from a certain Planet, may be found by comparing the true place of the Planet, as it would be seen from the center of the Earth (which is known by computation) with its apparent place, as it is seen from somepoint on the Earth’s surface. Let CZA be the Earth, ZC its semidiameter, ♁ some Planet, and BHT arch of a great circle in the Heavens, at an infinite distance. Now the Planet ♁ will appear from the Earth’s center C, in the point of the Heavens H; but a spectator from the point Z upon the Earth’s surface, will see the same object ♁ in the point of the Heavens B; and the arch BH the difference, is equal to the angle B ♁ H = Z ♁ C, theParallax; which being known, the side C ♁ the distance of the Planet from the center of the Earth, at that time, may be easily found. Now if this distance of the Planet from the Earth be determined, when the centers of the Sun, the said Planet, and of the Earth, are in the same right line, we have the absolute distance of the Planet’s orbit from the Earth’s in known measure; then it will be, as the relative distance betwixt the Earth’s orbit and that of the Planet is to the relative distance of the said Planet from the Sun; so is the distance of the Planet’s orbit from the Earth’s in known measure to the distance of the said Planet from the Sun in the same measure: Which being known, the distance of all the other Planets from the Sun may be found. For it will be, as the relative distance of any Planet from theSun, is to its distance from him in a known measure; so is the relative distance of any other Planet from him to its distance in the same measure. This may be done by finding the distance of the PlanetMars, when he is in opposition to the Sun, after the same manner as we find the distance of a tree, or the like, by two stations.
Let ♂ beMars, D the point on the Earth’s superficies, whereMarsis vertical when he is in opposition to the Sun, which may be found exactly enough by calculation, at which time let an observer, at the point Z (whose situation from D must be known) take the altitude ofMars, whose complement will be the angle ♂ ZR; then in the triangle ♂ ZC will be given the angle Z ♂ C, the angle C (whose measure is the arch DZ) and consequently the angle Z ♂ C the Parallax, and also the side Z C the semidiameter of the Earth; by which we may find C ♂ the distance ofMarsfrom the Earth. The extreme nicety required in this observation, makes it very difficult to determine the exact distances of the Planets from the Sun; but the celebrated Dr.Halleyhas, inthe Philosophical Transactions, shewed us a more certain method for finding the distances of the Planets; which is by observing the Transit ofVenusover the Sun.
How the Magnitudes of the Planets are determined.
Fig. 8.
The eye judgeth of the magnitudes of far distant objects, according to the quantities of the angles under which they are seen (which are called their apparent magnitudes;) and these angles appear greater or less in a certain proportion to their distances. Wherefore the distances of the Planets from the Earth, and their apparent diameters being given, their true diameters (and from thence their magnitudes) may be found. How the distances of the Planets may be found has been already shewn; their apparent diameters are found by a telescope, having a machine fix’d to it for measuring of angles, called a Micrometer. Let BD, or the angle BAD be the apparent diameter of any Planet, and AB, or AD, (which by reason of the great distance of the Planets in respect of their magnitudes) may be considered as being the distance of the said Planet from the observer. Now in the triangle ABD, having the sides AB, AD, given, and the angle, A, we have also the other angles B and D, (because the Side AB, AD, are equal) whence theside BD the diameter of the Planet may be easily found by Trigonometry.
Why the Moon appears bigger than any of the Planets.
From hence it appears, that the same body at different distances, will seem to have very different magnitudes. Thus the diameter BD will appear from the point E, to be twice as large as from the point A. It also follows, that a small body, when at no great distance from us, may appear to be equal, or even to exceed another at a great distance, tho’ immensely bigger. Thusb dappears under the same angle, and consequently of the same bigness from the point A, that the line B D doth, tho’ one vastly exceeds the other. And this is the reason, why the Moon, which is much less than any of the Planets, appears to us vastly bigger than either of them, and even to equal the Sun himself, which is many thousand times greater in magnitude.
The distances of the Planets, and periods round the Sun, their diameters and velocities round their own axis, according to modern computations, are as follows:
The cause ofEclipsesandPhasesof the Moon, and some other phænomena not here explained, shall be shewed when we come to give a Description of theOrrery.
Plate 2.
Plate 2.
Besides the Planets already mentioned, there are other great bodies that sometimes visit our system, which are a sort of temporary Planets; for they come and abide with us for a while, and afterwards withdraw from us, for a certain space of time, after which they again return. These wandering bodies are calledComets.
OfComets.
The motion of Comets in the Heavens, according to the best observations hitherto made, seem to be regulated by the same immutable law that rules the Planets; for their orbits are elliptical, like those of the Planets, but vastly narrower, or more excentric. Yet they have not all the same direction with the Planets, who move from West to East, for some of the Comets move from East to West; and their orbits have different inclinations to the Earth’s orbit; some inclining Northwardly, others Southwardly, much more than any of the Planetary orbits do.
Altho’ both the Comets and the Planets move in elliptic orbits, yet their motions seem to be vastly different: For the excentricities of the Planet’s orbits are so small, that they differ but little fromcircles; but the excentricities of the Comets are so very great, that the motions of some of them seem to be almost in right lines, tending directly towards the Sun.
Now, since the orbits of the Comets are so extremely excentric, their motions, when they are in theirPerihelia, or nearest distance from the sun, must be much swifter than when they are in theirAphelia, or farthest distance from him; which is the reason why the Comets make so short a stay in our system; and when they disappear, are so long in returning.
The figures of the Comets are observed to be very different; some of them send forth small beams, like hair, every way round them; others are seen with a long fiery tail, which is always opposite to the Sun. Their magnitudes are also very different, but in what proportion they exceed each other, it is as yet uncertain. Nor is it probable, that their numbers are yet known, for they have not been observed with due care, nor their theories discovered, but of late years. The ancientswere divided in their opinions concerning them; some imagined that they were only a kind ofMeteorskindled in our atmosphere, and were there again dissipated; others took them to be some ominous prodigies: But modern discoveries prove, that they are Worlds subject to the same laws of motion as the Planets are; and they must be very hard and durable bodies, else they could not bear the vast heat that some of them, when they are in theirPerihelia, receive from the Sun, without being utterly consumed. The great Comet which appeared in the year 1680, was within ¹/₆ part of the Sun’s diameter from his surface; and therefore its heat must be prodigiously intense beyond imagination. And when it is at its greatest distance from the Sun, the cold must be as rigid.
Of theFixed Stars.
The fixed Stars are at immense distance from us.
Thefixed Stars are those bright and shining bodies, which in a clear night appear to us every where dispersed through the boundless regions of space. They are term’d fix’d, because they are found to keep the same immutable distance one from another in all ages, without having any of the motions observed in the Planets. The fixed Stars are all placed at such immense distances from us, that the best of telescopes represent them no bigger than points, without having any apparent diameters.
The fixed Stars are luminous bodies like the Sun.
It is evident from hence, that all the Stars are luminous bodies, and shine with their own proper and native light, else they could not be seen at such a great distance. For theSatellitesofJupiterandSaturn, tho’ they appear under considerable angles through goodtelescopes, yet are altogether invisible to the naked eye.
The distance from us to the Sun is nothing in comparison of the vast distance of the fixed Stars.
Although the distance betwixt us and the Sun is vastly large, when compared to the diameter of the Earth, yet it is nothing when compared with the prodigious distance of the fixed Stars; for the whole diameter of the Earth’s annual orbit, appears from the nearest fixed Star no bigger than a point, and the fixed Stars are at least 100,000 times farther from us than we are from the Sun; as may be demonstrated from the observation of those who have endeavoured to find the Parallax of the Earth’s annual Orb, or the angle under which the Earth’s orbit appears from the fixed Stars.