The Mountaineer. [volume] (Great Salt Lake City [Utah]) 1859-1861, 1860-03-31
GREAT SALT LAKE CRY, SATURDAY, MARCH 81, 1860.

falling body near the eaTth's surface: but OBJ
seTvalion proves that the earth falls towards
the sun with velocity several hundred thou
sand times greater: Its deviation from tho tam
gentof its orbit being about the 1-Sth Of an
inch per second; or, more accurately. the earth.
falls towards the sun about 1,49O times slower
than q stone falls near tho surface 81 the earth
Now u 6s0, 2Ie ,92l be divided By l.400 the
quotisnt will be about 3S9, S51 that 81 the sln
contains 369 b6l times more matter than the
earth and thua the earth falls towards the sun
.3S9, 66l times fastsr than II would, II the mass
q the sun were only equal 70 that Of the
Neptune, being abeul so times The distance
Of the earth from the sun, falls towards the
latter with velocity about 800 times hess
than the falllng velocity of ths sasth tOwafds
that Iurninafy M .sl.5.
a planet, twice the distance 81 the earth
from the sun, will fall four times Iess distance
in One second; ct three times the distance is
falling velocity will be nine times lesr; at four
times the distance, sixteen times less; ~ ten
times che diatance, one hundred times less;
&c, SC. 3. #
CENTnIHu0AL FoEcIa - AZ We have learned
the law Of grayltation, and determined pro-
per measure Of its force for any given quantity
of matter. and for any given distance, next
letus examine the nature Of those opposing
forces By which the planets and satellites are
prevented from. falling 10 one common centre
Al In my fiFst lecture, pointed out the prlncI-
pie Of the composition Of forces and motions;
that o body aeted upon By two forces would
move In direction intermediates between
them, II one Of the two motions Is uniform,
while The other Is accelerated, the intefme-
diatspath will be q curve; lis concavity being
In the direction oi the constant force which
produces the arcelleTation @ i@
All the planets and satellites Of our System
are under the Influence Of pTojeetile force, Or
q force which originally gave them motion,
and then ceased to act; the same ne powder
ceases 10 act upon q ball, after the moment Of
explosion Without q resisting medium. or
sone other extraneoas cause, The planetary
bodies must have continued 10 move for ever
In the straight line ii which they were pro-
jeeted. But gravitation every moment defects
them from this straight line into curyilInear
orbits. The nature Of these orbits will depend
upon tho intensity and direction Of the two
forces. # 81 y: =z
4 LIST. II tho motion arising from the
projection 10 ut right angles to the motion
arising from grasitation. and Il the velocity Of
the former Is exactly proportioned to that Of
the latter, so as To keep the body at Ill times
at the same. distance from the centre, its orbit
will be a circle. s, s:1 .<< 4 s{5 Is$
2nd Though the projectile velocity Il ex-
actly such rs worlt produce q circular orbit,
when operating at right angles, to the con.
trail force, yet, II operating 1t nm acute or OBJ
fuse angle to the latter force, the body must
dssarihA Al ipsai and In AHA ease, Az mean
velocity will be equal to that Of Its projection,
Bird. ia body be projected al right angles Is
the central force with q velocity insufficient to
produce q circular orbit, IL will describe an
sllipsc Of which the point Of projection will be
the aphelion. Il ss$gs s'.., HI ii Il. 4.
4th. II a body be projected at right angles 10
the central force with = velocity somewhat too
great for the central force to defect il into a
circle It will reyolye In ellipBe of which the
point Of projection will be the perihelion. s
9th. II q body be projected IN q line making
an asute or obtnse angle with the direction Of
the central force, and with o velocity soIie..
what smaller or greater than that which tifa
the same distance, and acting Ut right angIesl,
would produce circle, il will describe an.
ellipse. $< 4 :3.z.=
9th. II the projectiis velocity il equal to
that which the. body would acquire In falling
from the point Of projection to the sun, Il will
describs a curve called q paraboia; the body, in
this case, would follow one Of the branches Of
this curve with retarded velocity far beyond
the limits ofour solar system, never to return
10 it again. s::. i @..s.; $sS III
It'll. II the projectile velocity IL greater
than that which u body would acquire In fol.
lowing from the point of projection to the sun,
Il would described curve called hyperboIa.
As the branch 81 this curve In which the body
is moving. extends like the parabola, to an
infinite distance, the body never could return
again to the solar system f.: Z. !: ,=s
= The circle, ellipse, parabola, and hyperbola, |
are the only possible orbits or curves In which |
bodies can move under the influence of pTo.
jectile aud Erayitating forces = =: -
At q given distance, there ID only one velo. |
city Of projection, which will produce circll. |
lar orbit; and there is only Que velocity which |
will describe q parabola: but there is an inf. |
mite number Of yelecities which will produce ON |
infinite number OF elliptic orbits between a /
straight line and u circle. And there Is also /
IN infinite number of veloeities which will /
cause bodies to describe an infinite number OF +
hypeTbotic curves of different forms. b: S'&
All the planets and satellites Of our system
describe ellipsea which do not vary much from
circles Some of the comets describe ellipses
very eccentric: and some Of them are supposed I
To describe parabolas and hyperbolas. =:
Let us next determine q measure for pfejee- Z
tile forces, that they may be properly adjusted
TO any given central forces. .-.-.-.. RI. /
For the salSeof simplifying our statements,
let US suppose bodies to move in circles around
central forces, II Is required to determine +
what effect different velocitses and distances
will have In relation 10 central forces z
Let string one foot long he attached TO a
ball OF lead Of the weight Of one pound; let It
be whiTled around in a horizontal plane. and II
will have tendency to recede from the cen
ire: the greater the velocity Of revolution, the
greater will be the force pulling upon the
string in direction ontwards from the centre. +
This Il called the centrifugal force When the
string peIforms Areyolution in l,09352 seconds
il will become stretched, by the circular We
iocity, equal to the force ofits weight, that's,
centrifugal force will be equal 10 one pound 4
Let,the velocity Of revolution, which generates I
one pound Of centrifugal force, be represented T
by one. 2-.c=--. = = 49, -.
+ Suppose the string connecting the ball with |
the centre, 10 he varied In its length while its
velocity remains the same. what will be the |
law Of foree eXerted upon the sHiRgl Both
experiment and calculation demonstrate that,
WIth he iape psloeity, btt Centrifugal fort ps'1ss
isve ssly a taE ltslytb Of Las string. =
Examples; A string one foot long with .
certain velocity, generates . centrifugal force
Of one pound: string two feet long gives .