Richmond times-dispatch. [volume] (Richmond, Va.) 1914-current, 1918-03-25
SERV|sS EXPLAINS HOW
SUN MASTERS PLANETS
Nearer They Arc to Great Lumi-
nary tho Faster They Move
In Orbit
SPEED INCREASES DISTANCE
Should Earth Travel Faster 1t
Would Have Tendency to Sway
Away-SimpIc Rule for Deter
mining Velocity.
ny GAHItE.r.r T.. sERvIss.

( travels. But If the orbital speed o IA
| planet were increased it would fly
farther from the sun. and yet ut the
same time lose velocity until ii travelled
slower than 1t did to begin with
reader. puzzled by this paradox
| asks how it can be explained. He says,
taking the earth's velocity in its orbit
ut eighteen miles per second and It's
distance from the sun at ninety; two
million miles. an increase to twenty
miles per second would send the earth
farther away and thus enlarge its
orbit. hut In that new orbit IL would
travel slower than in the old one
So when and how" he asks would
its accelerated velocity be reduced.
and what would be its final speed and
size of Orbit?"
simple rule for determining the
velocity Of planet In its orbit is
contained in little equation which.
IN mathematical symbols, can be
packed into space a quarter of an
inch square, but which takes above
q dozen words for its expression In
everyday language: 9TH velocity is
lhVerseiy proportional TO the square
root OF the distance from the sun"
This enables us to ascertain. with n
few strokes of a pencil. the orbital
it's distance
For instance, suppose that new
planet should be discovered a hundred
times as far away as the earth: then
since the square root of 100 is 10, we
would Know that the stronger was
travelling at mean, or average, speed
cHuai TO onc-tenth that of the earth
ms should not be confused with the
more familiar third law Of Keplcr"
10 be found in most school books Of
astronomy, and which reads: The
squares of the periodic times of the
planets are proportional to the cubes
OF their mean distances from the sun"
The TWO rules both originate from the
same general law of gravitation, but
they are not the same thing.
Now, tho reason why the various
planets travel with velocitfcs invcrsol,-
proportional to their distances is this.
The force of the sun. which constrains
them to move in orbits. most of which
are not Tar from circles. increases with
'he'E approach TO him, the increase
ocine as the inverse square of the
Instance, which simply means that If
one planet is twice as far. or twice rs
near las another, the pull of the sun
uron it viii he four simcs less in the
The second, 4 being the square Of .
hut in order that planet shall have
ITS path through space bent from a
straight line into a circle or an ellinse
around the sun. there must be n certain
proportion between what we NAV call
lis independent motion, or proiccti!e
motion. and the motion impressed upou
II by the suns pull.
:At each instant the planet seeks
tosiy straight ahead. but the solar
Gravitation reins it in and forces il
10 circle like stone swung around in
a sling. If the planets energy OF mo-
'!on Is too great it VIII get away from
lie sun tbreak the graVitational strinE)
put IN moving away il uses up a Dor.
'!oh or It's energy, because the suns
pull although growing less with in
crease oil distance never ceases. and
at length the planet reaches the point
where It's velocity has been in this man
ncr reduced so far that :, balance is
re-cstabliShed between the TWO forces.
~ that point. then, IL is caught, as il
were IN the sling and once more travels
round the sun.
Take the case supposed of an in
crease of the earth's velocity from
eighteen up TO twenty miles per sec
ond. The earth would immediately
swa% away from the sum- but in doing
80 II would. in forcing itself away
against the solar attraction. use up the
extra energy that had been given to
Il. 1t would be like a stone thrown
UPWARD, the pull OF gravity continually
reducing motion. When it had ar
rived at Il distance from the sun OF
about 1880, 600 miles Calculated by
the inverse square foot rulc) bal
ancc would be struck again between its
energy and that OF the sun, and II would
turn INTO new, more elongated orbit.
In which 1t would continue to travel
with velocity Of about 1915 miles
per second The lost velocity would
have disappeared In the expenditure Of
energy required 10 enlarge the orbit.
But this could not go en- indefinitely.
ihcrc is very clear limit TO the suns
power 10 curb a planet and swing Il
into closed orbit. and this limit is also
hNcd w the law of Gravitatlon. When
| Inc planets tangcntial velocity COR
cross mot!cn) is just sufficient TO coun-
tcrbalancc the effect of tho suns pull
in unit OF time, the planet will travel
, In n circle.
If the tangcntial velocity is IL little
greater or little less than that pre-
else amount the planets orbit will be
an clipse. And if it becomes so much
as about AZ per cent greater or Is null
/ tp!ied by the square root of tho sun
will lose It's control. and the planet
viii move away on parabolic path
into space never 10 return Thus the
carth's actual velocity being about
eighteen and onc-half miles per second
/ and It's orbit being practically a circle.
! II the velocity were Increased in about
twcnty-siN and sixteenth eighteen
and onc-half multiplied by l,ild. the
! square root OF p, we should he carried
/ of through space on the most wonder
! ful journey ever imagined running
! away from our sun TO be frozen solid
! in the intcrminablc domain OF a5so-
lutte zero.