ASTRONOMY. 
orbit described are not in that ratio. The 
planets being at different distances from the 
sun, perform their periodical revolutions in 
different times : but it has been found that 
the cubes of their mean distances are con- 
stantly as the squares of their periodical 
times; viz. of, the times of their performing 
their periodical revolutions. These two last 
propositions were discovered by Kepler, by 
observations on the planets ; but Sir Isaac 
Newton demonstrated, that it must have 
been so on the principle of gravitation, which 
formed the basis of his theory. This law of 
universal attraction, or gravitation, disco- 
vered by Newton, completely confirms the 
system of Copernicus, and accounts for all 
the phenomena which were inexplicable 
on any other theory. The sun, as the 
largest body in our system, forms the centre 
of attraction, round which all the planets 
move ; but it must not be considered as the 
only body endued with attractive power, 
for all the planets also have the property of 
attraction, and act upon each other as well 
as upon the sun. The actual point therefore 
about which they move will be the common 
centre of gravity of all the bodies which are 
included in our system ; that is, the sun, 
with the primary and secondary planets. 
But because the bulk of the sun greatly ex- 
ceeds that of all the planets put together, 
this point is in the body of the sun. The at- 
traction of the planets on each other also 
somewhat disturbs their motions, and causes 
some irregularities. It is this mutual attrac- 
tion between them and the sun that pre- 
vents them from flying off from their orbits 
by the centrifugal force which is generated 
by their revolving in a curve, while the cen- 
trifugal force keeps them from falling into 
the sun by the force of gravity, as they 
would do if it were not for this motion im- 
pressed upon them. Tlius these two powers 
balance each other, and preserve order and 
regularity in the system. It is well known, 
that if, when a body is projected ina straight 
line it be acted upon by another force, 
drawing it towards a centre, it will be made 
to describe a curve, which will be either a 
circle or an ellipsis, according to the pro- 
portion between the projectile and centri- 
petal force. If a planet at B (fig. 3, Plate II.) 
gravitates or is attracted towards the sun, 
S, so as to fall from B to y, in the time that 
the projectile force would have carried it 
from B to X, it will describe the curve BY 
by the combined action of these two forces 
in the same time that the projectile force 
singly would have carried it from B to X, or 
the gravitating power singly have caused it 
to descend from B to y ; and these two 
forces being duly proportioned, the planet 
obeying them both will move in the circle 
B Y T V. But if, whilst the projectile force 
would carry the planet from B to b, the 
sun’s attraction should bring it down from B 
to 1, the gravitating power woidd then be 
too strong for the projectile force, and would 
cause the planet to describe the curve B C. 
When the planet comes to C, the gravitating 
power (which always increases as the square 
of the distance from the sun, S, diminishes) 
will be yet stronger for the projectile force, 
and by conspiring in some degree therewith, 
will accelerate the planet’s motion all the 
way from C to K, causing it to describe the 
arcs BC, CD, D E, EF, &c. all in equal 
times. Having its motion thus accelerated, 
it thereby acquires so much centrifugal force, 
or tendency to fly off at K, in the line K k, 
as overcomes the sun’s attraction ; and the 
centrifugal force being too great to allow the 
planet to be brought nearer to the sun, or 
even to move round him in the circle k l m 
n, &c. it goes off, and ascends in the curve 
KLMN, &c. its motion decreasing as gra- 
dually from K to B as it increased from B 
to K, because the sun’s attraction now acts 
against the planet’s projectile motion just as 
much as it acted with it before. When the 
planet has got round to B, its projectile 
force is as much diminished from its mean 
state as it was augmented at K ; and so the 
sun’s attraction being more than sufficient to 
keep the planet from going off at B, it de- 
scribes the same orbit over again by virtue 
of the same forces or powers. A double 
projectile force will always balance a qua- 
druple power of gravity. Let the planet at 
B have twice as great an impulse from 
thence towards X as it had before ; that is, 
in the same length of time that it was pro- 
jected from B to b, as in the last example ; 
let it now be projected from B to c, and it 
will require four times as much gravity to 
retain it in its orbit ; that is, it must fall as 
far as from B to 4 in the time that the pro- 
jectile force would carry it from B to C, 
otherwise it would not describe the curve 
B D, as is evident from the figure. But in 
as much time as the planet moves from B to 
C, in the higher part of its orbit, it moves 
from I to K or from K to L in the lower 
part thereof; because from the joint action 
of these two forces, it must always describe 
equal areas in equal times throughout its an- 
nual course. These areas are represented 
by the triangles B S C, C S D, D S E, E S F, 
