Part 2
I. The Planets are all _Opaque_ bodies, 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 be _Globular_; 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.
[Sidenote: The Planets turn round the Sun.]
II. That the Earth is placed betwixt the Orbs of _Mars_ and _Venus_, and that ☿, ♀, ♂, ♃ and ♄, do all turn round the Sun, is proved from observations as follow:
[Sidenote: _Plate 2. Fig. 1. 2._]
1. Whenever _Venus_ is 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 the _Sun_, T the _Earth_, and V _Venus_, having the same face presented both towards the _Sun_ and _Earth_; here it is plain that the Sun is betwixt us and _Venus_ and therefore we must either place _Venus_ in an Orbit round the Sun, and likewise betwixt him and us, as in _Fig. 1._ or else we must make the Sun to move round the Earth in an Orbit within that of _Venus_, as in _Fig. 2._ Again, after _Venus_ disappears, 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 in _Fig. 1._ or else round the Earth, and betwixt us and the Sun, as in _Fig. 2._ But _Venus_ cannot 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.
[Sidenote: Why _Venus_ is always either our Morning or Evening Star.]
Besides the forgoing, there is another argument to prove that _Venus_ turns 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 the reason why _Venus_ is 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 the _Evening 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 the _Morning Star_.
After the same manner we prove that _Mercury_ turns round the Sun, for he always keeps in the Sun’s neighbourhood, and never recedes from him so far as _Venus_ does; 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.
[Sidenote: The Orbit of _Mars_ includes the Earth’s.]
[Sidenote: _Fig. 3._]
_Mars_ is observed to come in opposition, and likewise to have all other 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, as _Venus_ and the Moon do in that position. Let S be the _Sun_, T the _Earth_, and A P _Mars_, both in his conjunction and opposition to the Sun, and in both positions full; and B C _Mars_ at his quadratures, when he appears somewhat gibbous from the Earth at T. ’Tis plain hence, that the Orbit of _Mars_ does 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.
_Mars_ when 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 position than in the other; for the apparent magnitudes of far distant objects increase or decrease in proportion to their distances from us: But _Mars_ keeps 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, that _Jupiter_ and _Saturn_ have 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 in _Jupiter_, as it is in _Mars_, nor so great in _Saturn_, as it is in _Jupiter_, by reason that they are at a much greater distance from the Sun.
[Sidenote: _Inferior_ and _Superior Planets_.]
We have now shewn that all the Planets turn round the Sun, and that _Mercury_ and _Venus_ are included between him and the Earth, whence they are called the _Inferior Planets_, and that the Earth is placed between the Orbits of _Mars_ and _Venus_, and therefore included within the Orbits of _Mars_, _Jupiter_, and _Saturn_, whence they are called the _Superior Planets_: And since the Earth is in the middle of these moveable 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:
[Sidenote: The Earth does not stand still, but turns round the Sun.]
[Sidenote: _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 of _Mars_, and the numbers 1, 2, 3, _&c._ its equable motion round the Sun; the correspondent numbers 1, 2, 3, _&c._ in the circle _a_, _b_, _c_, _d_, the motion of _Mars_, as it would be seen from the Earth. It is plain from this Figure, that if the Earth stood still, the motion of _Mars_, will be always progressive, (tho’ sometimes very unequal;) but since observations prove the contrary, it necessarily follows, that the Earth turns round the Sun.
[Sidenote: 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 arrive to 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 the _Sun_, _Venus_, _Mars_, and _Jupiter_; by which means it has been found that these bodies turn round their own axis, in the times before-mentioned. It is very probable that _Mercury_ and _Saturn_ have 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 old ones 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.
[Sidenote: 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.
[Sidenote: _Fig. 5. Elongation._]
The greatest _Elongation_ of _Venus_ is 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 of _Venus_ from 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 ☿ of _Mercury_ from the Sun. And if the mean distance of the Earth from the Sun S T be made 1000, the mean distance of _Venus_ S ♀ from the Sun will be 723; and of _Mercury_ S ☿ 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. Their _Excentricities_ are computed to be as follows, _viz._
{ _Mercury_ 80 } of the parts _Excent._ of { _Venus_ 5 } above-mentioned. { _Earth_ 169 }
[Sidenote: _Heliocentric_ and _Geocentric 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 of _Mars_ seen from the Sun is D, which is called his true, or _Heliocentric Place_; but from the Earth, he will be seen in G, which is called his apparent, or _Geocentric Place_. So likewise _Jupiter_ and _Saturn_ will 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 the _Parallaxes_ of 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 of the 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. In _Mars_ the angle ♂ S, (which is the visible elongation of the Earth seen from _Mars_, or the Parallax of the annual Orb seen from that Planet) is about 42 degrees, and therefore the Earth is always to the inhabitants of _Mars_ either their Morning or Evening Star, and is never seen by them so far distant from the Sun as we see _Venus_. The greatest elongation of the Earth seen from _Jupiter_, being nearly equal to the angle A ♃ S, is about 11 degrees. In _Saturn_ the angle A ♄ S is but 6 degrees, which is not much above ¼ part of the greatest elongation we observe in _Mercury_. And since _Mercury_ is so rarely seen by us, probably the astronomers of _Saturn_ (except they have better 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 of _Mars_ from the Sun, it will be as the Sine of the angle S ♂ A is to the _Radius_, so is the distance AS (the distance of the Earth from the Sun) to S ♂, the distance from the Sun to _Mars_. After the same manner the distances of _Jupiter_ and _Saturn_ are 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
{ ♂ 1524 } { 141 } { ♃ 5201 } and the Excentricity { 250 } { ♄ 9538 } { 547 }
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.
[Sidenote: How the absolute distances of the Planets from the Sun are computed.]
[Sidenote: _Parallax_ of the _Earth’s Semidiameter_.]
[Sidenote: _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 some point 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, the _Parallax_; 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 the Sun, 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 Planet _Mars_, 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 ♂ be _Mars_, D the point on the Earth’s superficies, where _Mars_ is 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 of _Mars_, 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 of _Mars_ from 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. _Halley_ has, in the Philosophical Transactions, shewed us a more certain method for finding the distances of the Planets; which is by observing the Transit of _Venus_ over the Sun.
[Sidenote: How the Magnitudes of the Planets are determined.]
[Sidenote: _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 the side BD the diameter of the Planet may be easily found by Trigonometry.
[Sidenote: 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. Thus _b d_ appears 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:
|Revolves about the | Distance in |Sun in the space of| Miles | Y. D. H | | | _Saturn_ | 29:167:22 | 777.000.000 _Jupiter_ | 11:314:12 | 424.000.000 _Mars_ | 1:321:23 | 123.000.000 _Earth_ | 0:365: 6 | 81.000.000 _Venus_ | 0:224:16 | 59.060.000 _Mercury_ | 0: 87:23 | 32.000.000
_Moon_} Round the { D. H. M. | } Earth. { 27: 7: 43 | 240.000
| Periods round | Diameters | their own axis.| in Miles. | D. H. M. | _Sun_ | 25: 6: 0 | 763.000 _Saturn_ | | 61.000 _Jupiter_ | 0: 9: 56 | 81.000 _Mars_ | 1: 0: 40 | 4.440 _Earth_ | 0: 23: 56 | 7.970 _Venus_ | 24: 8: 0 | 7.900 _Mercury_ | | 4.240 _Moon_ | 27: 7: 43 | 2.170
The cause of _Eclipses_ and _Phases_ of the Moon, and some other phænomena not here explained, shall be shewed when we come to give a Description of the _Orrery_.
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 called _Comets_.
[Sidenote: Of _Comets_.]