394 ' ASTRO 
through Mars at P, and be continued to the ecliptic, they 
will point out the apparent place oi Mars at thefe different 
ftations. Time, fuppofing the Earth at A, the planet will 
he feen antong the ftars at L ; when the Earth is arrived at 
B, the planetWill appear at M ; and, in the fame manner, 
when at C, ID, and K, it will he feen among the ftars at 
NRT; therefore, while the Earth moves over the large 
part of the orbit ABODE, the planet will have an appa¬ 
rent motion from L to T, and this motion is from weft to 
eaft, or the fame way 'with the Earth ; and the planet is 
faid to move dire ft, or according to the order of theftgns. 
When the Earth is near to A and E, the point of contaft 
of the tangent to the Earth’s orbit, the planet will be fta- 
tionary for a fh@rt fpace of time. 
When the Earth moves from E to H, the planet feems 
to return from T to N ; but, while it moves from H to A, 
it will appear to move in a contrary direction, and thus be 
retrograde from N to L, where it will again be ftationary: 
and, fince the part of the orbit which the Earth deferibes 
in pafting from A to E, is much greater than the part 
EHP, though the fpace TL which the planet deferibes 
in direct and retrograde motion is the fame, the direft mo¬ 
tion from L to T mu ft be much flower than the retrograde 
motion from T to L. When the Earth is at C, a line 
drawn from C through S and P to the ecliptic, fhews that 
Mars is then in comjunftion with the Sun. But, when the 
Earth is at H, a line drawn from El through P, and con¬ 
tinued to the ecliptic, would terminate in a pdlnt oppofite 
to S ; therefore in this fituation Mars would be in oppofi- 
tion to the Sun. Thus it appears, that the motion of 
Mars is direft: when in conjunction, and retrograde when 
in oppolition. The retrograde motions of the fuperior 
planets happen oftener, the flower their motions are; as 
the retrograde motions of the inferior planets happen of¬ 
tener, the fwifter their angular motions are ; becaufe the 
retrograde motions of the fuperior planets depend upon 
the motions of the Earth, but thofe of the inferior on 
their own angular motion. A fuperior planet is retro¬ 
grade once in each revolution of the Earth ; an inferior 
one in every revolution of its own. 
The fuperior planets are fometimes nearer the Earth than 
at other times; they alfo appearlarger, or fmaller, accord¬ 
ing to their different diffances from us. Thus, fuppofe the 
Earth to be at C ; if Mars be at V, he is the whole dia¬ 
meter of the Earth’s orbit nearer to us than if he were at 
P, and confequently his difk nnift appear larger at V than 
it would be at P. In other places, the diffances of Mars 
from the Earth are intermediate. The diameter of the 
Earth’s orbit bears a greater ratio to the diameter of the 
orbit of Mars than it does to the diameter of the orbit of 
Jupiter, and a greater to that of Jupiter than of Saturn ; 
confequently, the difference between the greateft and leaft 
apparent diameters is greater in Mars than in Jupiter, and 
greater in Jupiter than in Saturn. 
The fuperior, like the inferior, planets, do not always 
appear in the ecliptic, their orbits being inclined alfo to 
that of the Earth ; one half is therefore above the eclip¬ 
tic, the other half below it, nor are they ever feen in it 
but when they are in their nodes. They all move in an 
eliipfe; and their motions are very fimple, being com¬ 
pounded of a projeftile motion, forward in a right line, 
which is a tangent to the orbit, and a gravitation towards 
the Sun at the centre. Belides, being at fuch vaft dittan¬ 
ies from each other, the effefts of their mutual gravita¬ 
tion towards one another are in a confiderable degree, tho’ 
not altogether, infenfible; for the aftion of Jupiter upon 
Saturn, for example, is found to be of the attion of 
the Sun upon Saturn, by comparing the matter of Jupiter 
with that of the Sun, and the fquare of the diftance of 
each from Saturn. So that the elliptic orbit of Saturn 
will be found more juft, if its focus be fuppofed not in the 
centre of the Sun, but in the common centre of gravity 
of the Sun and Jupiter, or rather in the common centre 
of gravity of the Sun and all the planets below Saturn. 
And, in like manner, the elliptic orbit of any other planet 
N O M Y. 
will be found more accurate, by fuppofing its fociis to be- 
in the common centre of gravity of the Sun and all the 
planets that are below it. But the matter is far otherwise 
in refpeft of the fecondary planets, or fatellites; for eve¬ 
ry one of thefe, though it chiefly gravitates towards itsre- 
fpeftive primary one, as its centre, yet, at equal diffances 
from the Sun, it is alfo attratted towards him with an 
equally-accelerated gravity, as the primary one is towards 
him ; but at a greater diftance with lefs, and at a nearer 
diftance with greater: from which double tendency to¬ 
wards the Sun, and towards their own primary planets, it 
happens, that the motion of the fatellites, or fecondary 
planets, comes to be very much compounded, and affect¬ 
ed with various inequalities. 
The motions even of the primary planets, in their ellip¬ 
tic orbits, are not equable, becaufe the Sun is not in their 
centre, but their focus. Hence they move fometimes faft- 
er, and fometimes flower, as they are nearer to, or farther 
from, the Sun; but yet thefe irregularities are all certain, 
and follow according to an immutable law. Thus, the ei- 
lipfis PEA, &c. reprefenting the orbit of aplanet, and the 
focus S the Sun’s place : the axis of 
the eliipfe AP, is the line of theapfes; 
the point A, the higher aplis, or aphe¬ 
lion ; P, the lower aplis, or perihe¬ 
lion ; GS, the eccentricity; and ES, 
the planet’s mean diffance from the 
Sun. Now, the motion of the planet E 
in its perihelion P is fwifteft, but in its 
aphelion A it is (lowed ; and at E the 
motion as well as the diftance is a 
mean, being there Inch as, if continu¬ 
ed uniform, would deferibe the whole 
orbit in the fame time it is really de¬ 
scribed in. And the law by which the motion in every 
point is regulated, is this, that a line or radius drawn from 
the centre of the Sun to the centre of the planet, and thus 
carried along with an angular motion, does always deferibe 
an elliptic area proportional to the time; that is, the trili¬ 
neal area ASB, is to the area ASG, as the time the planet is 
in moving over AB, to the time it is in moving over AG. 
A planet’s motion, or diftance from its apogee, is called 
the mean anomaly of the planet, and is meafured by the area 
it deferibes in the given time ; when the planet arrives at 
the middle of its orbit, or the point E, the area or time is 
called the true anomaly. When the planet’s motion is reck¬ 
oned from the firft point of Aries, it is called its motion in 
longitude , which is either mean or true, viz. mean, which 
is fuch as it would have were it to move uniformly in a 
circle ; and true, which is that with which the planet ac¬ 
tually deferibes its orbit, and is meafured by the arc of 
the ecliptic it deferibes. And hence may be found the 
planet’s place in its orbit for any given time, after it has 
left the aphelion ; for, fuppofe the area of the ellipfls he 
fo divided by the line SG, that the whole elliptic area may 
have the fame proportion to the part ASG, as the whole 
periodical time in which the planet deferibes its whole or¬ 
bit, has to the given time; then will G be the planet’s 
place in its orbit fought. 
As to the periods and velocities of the planets, or the 
times in which they perform their courfes, they are found 
to have a wonderful harmony with their diftances from the 
Sun, and with one another: the nearer each pianet is to 
the Sun, the quicker ftill is its motion, and its period the 
fhorter, according to this general and regular law, viz. 
that the fquares of their periodical times are as the cubes 
of their mean diftances from the Sun or focus of their or¬ 
bits. Kepler deduced this law merely from obfervation, 
by a comparifon of the feveral diftances of the planets with 
their periods or times : the glory of inveftigating it from 
phylical principles is due to Sir Ifaac Newton, who has 
demonftrated that, in the prefent ftate of nature, fuch a 
law was inevitable. 
With refpeft to the proportional magnitudes of the pri¬ 
mary planets, we have, at Jig. 3, in the Aftronomical- 
Plate 
