The Sleepwalkers (247 page)

Why
planets
should
move
in
ellipses
is
easy
to
show
in
mathematical
terms;
leaving
mathematics
aside,
one
may
visualize
the
mechanism
as
a
tug-of-war
between
gravity
and
centrifugal
force.
If
the
string
to
which
the
revolving
stone
is
attached
be
made
of
elastic
material,
one
can
imagine
it
alternately
expanding
and
contracting,
thus
making
the
stone's
orbit
an
oval.
^*
Or
one
can
visualize
the
process
as
follows:
as
the
planet
approaches
the
sun,
its
speed
increases.
It
shoots
past
the
sun,
but
as
it
does
so,
the
clutching
hand
of
gravity
swings
it
round
–
as
a
running
child
grabbing
at
a
maypole
is
swung
around
it
–
so
that
it
now
continues
in
the
opposite
direction.
If
its
velocity
on
the
approach-run
had
been
exactly
the
amount
required
to
prevent
it
from
falling
into
the
sun,
it
would
continue
in
a
circle.
But
as
it
was
slightly
greater,
the
receding
run
will
carry
it
into
an
elongated
path,
which
the
planet
pursues
at
slackening
speed
in
the
teeth
of
the
sun's
attraction,
as
it
were,
gradually
curving
inward;
until,
after
passing
the
aphelion,
the
curve
again
approaches
the
sun
and
the
whole
cycle
starts
again.

____________________

The
"eccentricity"
of
the
ellipse
is
the
amount
by
which
it
deviates
from
the
circle.
The
eccentricities
of
the
planets
are
small,
owing
to
the
common
origin
of
the
solar
system
which
makes
their
tangential
velocities
almost
precisely
balance
gravity.

But
all
this
was
as
yet
merely
conjecture;
and
the
days
of
purely
speculative
hypotheses
were
past.
It
was
wild
conjecture
to
postulate
that
the
moon
was
constantly
"falling"
towards
the
earth,
like
a
projectile,
or
like
the
famous
apple
in
the
garden
at
Woolsthorpe
–
in
other
words,
that
the
earth's
attraction
reached
as
far
as
the
moon,
the
sun's
attraction
as
far
as
the
planets,
and
that
interstellar
space
was
indeed
"filled"
or
"charged"
with
gravity.
To
transform
a
wild
guess
into
scientific
theory,
Newton
had
to
provide
rigorous
mathematical
proof.

This
means,
he
had
to
calculate:
(
a
)
the
centrifugal
force
of
the
moon;
⁴
(
b
)
the
gravitational
force
which
the
earth
was
supposed
to
exert
on
the
moon;
and
(
c
)
he
had
to
show
that
the
interaction
of
these
two
forces
produced
a
theoretical
orbit
which
agreed
with
the
moon's
observed
orbit.

In
order
to
carry
out
this
operation,
he
must
first
of
all
know
at
what
rate
the
earth's
gravity
diminished
with
distance.
The
apple
fell
from
the
tree
at
a
known
acceleration
of
approximately
ten
yards
added
speed
per
second;
but
what
would
be
the
acceleration
of
the
distant
moon
towards
the
earth?
In
other
words,
he
had
to
discover
the
Law
of
Gravity
–
that
the
force
diminishes
with
the
square
of
distance.
In
the
second
place,
he
had
to
know
the
exact
value
of
the
moon's
distance.
Thirdly,
he
had
to
decide
whether
it
was
legitimate
to
treat
two
huge
globes
like
the
earth
and
the
moon
in
an
abstract
manner,
as
if
their
whole
mass
were
concentrated
in
a
single
central
point.
Lastly,
to
reduce
the
mathematical
difficulties,
the
moon's
orbit
had
to
be
treated
as
if
it
were
a
circle
instead
of
an
ellipse.

As
a
result
of
all
these
difficulties,
Newton's
first
calculations
only
agreed
"pretty
nearly"
with
the
facts;
and
that
was
not
good
enough.
For
nearly
twenty
years
he
dropped
the
whole
issue.

During
these
twenty
years,
Jean
Picard's
expedition
to
Cayenne
produced
much
improved
data
on
the
earth's
diameter
and
its
distance
from
the
moon;
Newton
himself
developed
his
own
brand
of
infinitesimal
calculus,
the
indispensable
mathematical
tool
for
attacking
the
problem;
and
the
Halley-Hooke-Wren
trio
kept
fitting
together
further
bits
of
the
puzzle.
The
orchestra
had
now
reached
the
stage
where
whole
groups
of
instruments
could
be
discerned
running
through
certain
passages;
only
the
rap
of
the
conductor's
baton
was
needed
to
make
everything
fall
into
place.