South Bend news-times. (South Bend, Ind.) 1913-1938, 1918-06-05
How the Sun Masters the Planets
BY GARRETT P. sERvIss.

The nearer a planet is to the sun
the faster it travels in its orbit. and
the farther away it is the slower
it travels. But if the orbital speed
of a planet were increased it would
fly farther from the sun, and yet at
the same time lose velocity until it
travelled slower than il did TO begin
with
A reader. puzzled by this para
dox, asks how it can be explained.
He says, taking the earth's velocity
in its orbit at rs miles per second.
and its distance from the sun at
2.00O.O 600 miles, an increase of 20
miles per second would send the
earth farther away and thus en-
large its orbit. but in that new orbit
ii 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?"
A simple rule for determining the
velocity of d planet in its orbit
is contained in a little equation
which, in mathematical symbols,
can be packed into a space "a quar-
ter OF an inch square, but which
takes above dozen words for its
expression in every day language:
THE velocity is inversely proper
tional TO the square root of the dis
lance from the sun This enables
US to ascertain, with a few strokes
of a pencil. the orbital speed of any
planet when once we know its dis
lance.
For instance. suppose that a new
planet should be discovered a hun
dred times as far away as the
earth then. since the square root
of 100 is 10, we would know that
the stranger was travelling az a
mean. or average. speed equal to
one-tenth that OF the earth This
should not be confused with the
more familiar third law OF KEEP
4 Ter" 10 be found in most school
/ books of astronomy, and which
reads. The squares OF the peri
odic times of the planets are pro-
portiOnal to the cubes of their
mean distances from the sun. The
/ two rules both originate from the
same general rule of gravitat.. n,
/ but they are not the same thing.
Now. the reason why the various
planets travel with velocities in
versely proportional 10 their dis
/ tances is this. The force of the
! sun. which constrains them TO move
lin orbits. most OF which are
I not far from circles. increases with
their approach 10 him. the increase
being as the inverse square OF the
distance. which simply means that
liz one planet Is twice as far. or
twice as near, as another. the pull
OF the sun upon il will be four times
I Jess in the first case and four times
greater in the second. four being the
\ square Of two. But IN order that a
planet shall have its path through
I space bent from a straight line into
a circle or an eclipse around the
sun. there must be a certain pro-
portion between what we NAV call
i its independent motion or projec-
tile motion. and the motion i'm
; pressed upon II by the suns pull.
At each instant the planet seeks
10 ny straight ahead. but the solar
+ gravitation reins il in and forces
il 70 circle like a stone swung
around in a sling. II the planet s
[ energy OF motion Is toe great il
WA get away from the sun (break
the gravitatOnal string. but in
moving away II uses up d portion
OF its energy. because the suns
pull. although growing less with
increase OF distance, never ceases.
and at length the planet reaches
the point where its velocity has
been in this manner reduced so far
that a balance Is reesta bllshed be
! tween the two forces At that