_Of the Order and Periods of the Primary Planets
revolving about the Sun; and of the Secondary
Planets round their respective Primaries._
[Sidenote: _Planets._]
The Sun 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 the _Planets_, who, at different distances, and
in different periods, perform their revolutions from West to East, in
the following order:
1. ☿ _Mercury_ is nearest to the Sun of all the planets,
and performs its course in about three months. 2. ♀ _Venus_
in about seven months and a half. 3. ♁ The _Earth_ in a year.
4. ♂ _Mars_ in about two years. 5. ♃ _Jupiter_ in twelve.
And lastly, ♄ _Saturn_, whose[1]_Orbit_ includes 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 in _Plate_ 1. _viz._
Supposing the distance of the Earth from the Sun to be divided
into 10 equal parts; that of _Mercury_ will be about 4 of these
parts; of _Venus_ 7; of _Mars_ 15; of _Jupiter_ 52; and
that of _Saturn_ 95.
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 ♀, for _Venus_, &c.
[Illustration: Plate 1.
THE SOLAR SYSTEM Or the Orbits of the Planets _according to their mean
distances from the Sun_.]
[Sidenote: _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 the _Ecliptic_; 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 the _Line of the Nodes_ of that planet; and the
points themselves, wherein the orbit cuts the Ecliptic are called the
_Nodes_.
[Sidenote: _Excentricity._]
The inclinations of the orbits of the Planets to the plane of the
ecliptic, are as follows, _viz._ the orbit of _Mercury_ makes an
angle with it of almost 7 degrees; that of _Venus_ something above
3⅓ degrees; of _Mars_ a little less than 2 degrees; of _Jupiter_, 1⅓
degree; and of _Saturn_, about 2½ degrees. The orbits of the Planets
are not circles, but ellipses or ovals. What an ellipsis is, may be
easily 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 an _Ellipsis_. The two points where the pegs stood,
(about which the thread was turned) are called the _foci_ of 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 the _focus’s_ are together, the
nearer will the curve described be to a circle; until at last, the two
_focus’s_ coincide, 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 their _focus’s_, and half the distance between the two
_focus’s_ is called the _Excentricity_ of 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.
[Sidenote: _Primary Planets._]
[Sidenote: _Secondary Planets._]
The six Planets above-mentioned, are called _Primaries_, or _Primary
Planets_; but besides these, there are ten other lesser Planets, which
are called _Secondaries_, _Moons_, or _Satellites_. 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._ the _Earth_, _Jupiter_,
and _Saturn_.
The Earth is attended by the _Moon_, 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.
[Sidenote: _Jupiter’s_ four Moons.]
_Jupiter_ has four _Moons_, or _Satellites_; the _first_, or innermost,
performs its revolution in about one Day, and 18½ Hours, at the
distance of 5⅔ Semidiameters of _Jupiter_, from his Center; the
_second_ revolves about _Jupiter_ in 3 Days, 13 Hours, at the distance
of 9 of his Semidiameters; the _third_ in 7 Days, and 4 Hours, at the
distance of 14⅓ Semidiameters; the _fourth_, and _outermost_, performs
its course in the space of 16 Days, 17 Hours; and is distant from
_Jupiter’s_ center, 25⅓ of his Semidiameters.
[Sidenote: _Saturn_ has five Moons.]
_Saturn_ has no less than five _Satellites_; the _first_, or innermost,
revolves about him in 1 Day, and 21 Hours, at the distance of 4⅜
Semidiameters of ♄, from his center; the _second_ compleats his
period in 2¾ Days, at the distance of 5³/₅ of his Semidiameters;
the _third_, in about 4½ Days, at the distance of 8 Semidiameters;
the _fourth_ performs its course in about 16 Days, at the distance
of 18 Semidiameters; the _fifth_, and outermost, takes 79⅓ Days, to
finish his course, and is 54 Semidiameters of _Saturn_ distant from
his center. The Satellites, as well as their primaries, perform their
revolutions from _West_ to _East_: 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.
[Sidenote: _Saturn’s_ Ring.]
Besides these attendants, _Saturn_ is encompassed with a thin plain
Ring, that does no where touch his body; The diameter of this Ring is
to the diameter of _Saturn_, as 9 to 4; and the void space between
the Ring and the body of _Saturn_ is 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 of _Saturn_’s Ring, is a
modern discovery; neither were the Satellites of _Jupiter_ and _Saturn_
known to the ancients. The _Jovial_ Planets were first discovered by
the famous _Italian_ philosopher _Galilæus_, by a telescope which he
first invented; and the celebrated _Cassini_, the _French_ king’s
astronomer, was the first that saw all the Satellites of _Saturn_;
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.
[Sidenote: _Annual Motion._]
[Sidenote: _Diurnal Motion._]
The motion of the primary Planets round the Sun (as also of the
Satellites round their respective primaries) is called their _Annual
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_, the _Earth_, _Mars_, and _Jupiter_ revolve about
their own _Axis_, from _West_ to _East_; and this is called their
_Diurnal 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 is
_Day_, but when it is carried to the obscure hemisphere, it becomes
_Night_; and so continues, until by this rotation the said place is
again enlightened by the Sun.
[Sidenote: Diurnal Motion of the ♁, ♀, ♂ and ♃.]
[Sidenote: ☉ and ☽ likewise turn round their Axis.]
The _Earth_ performs its revolution round its axis in 23 Hours, 56
Minutes;[2]_Venus_, in 24 Days, 8 Hours; _Mars_, in 24 Hours, and 40
Minutes; and _Jupiter_ moves 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 the _Lunarians_ have but 1
Day throughout the Year.
[Sidenote: The Planets are Opaque and Globular.]
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_.
[Illustration: 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 called _Comets_.
[Sidenote: Of _Comets_.]
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 from
circles; 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 their _Perihelia_, or nearest distance from
the sun, must be much swifter than when they are in their _Aphelia_,
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 ancients
were divided in their opinions concerning them; some imagined that they
were only a kind of _Meteors_ kindled 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 their _Perihelia_, 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.
[Illustration]