The Sleepwalkers (155 page)

Since
he
had
no
notion
of
the
momentum
which
makes
the
planet
persist
in
its
motion,
and
only
a
vague
intuition
of
gravity
which
bends
that
motion
into
a
closed
orbit,
he
had
to
find,
or
invent,
a
force
which,
like
a
broom,
sweeps
the
planet
around
its
path.
And
since
the
sun
causes
all
motion,
he
let
the
sun
handle
the
broom.
This
required
that
the
sun
rotate
round
its
own
axis
–
a
guess
which
was
only
confirmed
much
later;
the
force
which
it
emitted
rotated
with
it,
like
the
spokes
of
a
wheel,
and
swept
the
planets
along.
But
if
that
were
the
only
force
acting
on
them,
the
planets
would
all
have
the
same
angular
velocity,
they
would
all
complete
their
revolutions
in
the
same
period
–
which
they
do
not.
The
reason,
Kepler
thought,
was
the
laziness
or
"inertia"
of
the
planets,
who
desire
to
remain
in
the
same
place,
and
resist
the
sweeping
force.
The
"spokes"
of
that
force
are
not
rigid;
they
allow
the
planet
to
lag
behind;
it
works
rather
like
a
vortex
or
whirlpool.
¹⁹
The
power
of
the
whirlpool
diminishes
with
distance,
so
that
the
farther
away
the
planet,
the
less
power
the
sun
has
to
overcome
its
laziness,
and
the
slower
its
motion
will
be.

It
still
remained
to
be
explained,
however,
why
the
planets
moved
in
eccentric
orbits
instead
of
always
keeping
the
same
distance
from
the
centre
of
the
vortex.
Kepler
first
assumed
that
apart
from
being
lazy,
they
performed
an
epicyclic
motion
in
the
opposite
direction
under
their
own
steam,
as
it
were,
apparently
out
of
sheer
cussedness.
But
he
was
dissatisfied
with
this,
and
at
a
later
stage
assumed
that
the
planets
were
"huge
round
magnets"
whose
magnetic
axis
pointed
always
in
the
same
direction,
like
the
axis
of
a
top;
hence
the
planet
will
periodically
be
drawn
closer
to,
and
be
repelled
by
the
sun,
according
to
which
of
its
magnetic
poles
faces
the
sun.

Thus,
in
Kepler's
physics
of
the
universe,
the
roles
played
by
gravity
and
inertia
are
reversed.
Moreover,
he
assumed
that
the
sun's
power
diminishes
in
direct
ratio
to
distance.
He
sensed
that
there
was
something
wrong
here,
since
he
knew
that
the
intensity
of
light
diminishes
with
the
square
of
distance;
but
he
had
to
stick
to
it,
to
satisfy
his
theorem
of
the
ratio
of
speed
to
distance,
which
was
equally
false.

6.
The Second Law

Refreshed
by
this
excursion
into
the
Himmelsphysik
,
our
hero
returned
to
the
more
immediate
task
in
hand.
Since
the
earth
no
longer
moved
at
uniform
speed,
how
could
one
predict
its
position
at
a
given
time?
(The
method
based
on
the
punctum
equans
had
proved,
after
all,
a
disappointment.)
Since
he
believed
to
have
proved
that
its
speed
depended
directly
on
its
distance
from
the
sun,
the
time
it
needed
to
cover
a
small
fraction
of
the
orbit
was
always
proportionate
to
that
distance.
Hence
he
divided
the
orbit
(which,
forgetting
his
previous
resolve,
he
still
regarded
as
a
circle)
into
360
parts,
and
computed
the
distance
of
each
bit
of
arc
from
the
sun.
The
sum
of
all
distances
between,
say
0°
and
85°,
was
a
measure
of
the
time
the
planet
needed
to
get
there.
But
this
procedure
was,
as
he
remarked
with
unusual
modesty,
"mechanical
and
tiresome".
So
he
searched
for
something
simpler:

"Since
I
was
aware
that
there
exists
an
infinite
number
of
points
on
the
orbit
and
accordingly
an
infinite
number
of
distances
[from
the
sun]
the
idea
occurred
to
me
that
the
sum
of
these
distances
is
contained
in
the
area
of
the
orbit.
For
I
remembered
that
in
the
same
manner
Archimedes
too
divided
the
area
of
a
circle
into
an
infinite
number
of
triangles."
²⁰

Accordingly,
he
concluded,
the
area
swept
over
by
the
line
connecting
planet
and
sun
AS-BS
is
a
measure
of
the
time
required
by
the
planet
to
get
from
A
to
B;
hence
the
line
will
sweep
out
equal
areas
in
equal
times
.
This
is
Kepler's
immortal
Second
Law
(which
he
discovered
before
the
First)
–
a
law
of
amazing
simplicity
at
the
end
of
a
dreadfully
confusing
labyrinth.