The Sleepwalkers (154 page)

But
before
he
can
do
that,
he
must
make
an
immense
detour.
For
if
the
orbit
of
Mars
is
not
a
circle,
its
true
shape
can
only
be
discovered
by
defining
a
sufficient
number
of
points
on
the
unknown
curve.
A
circle
is
defined
by
three
points
on
its
circumference;
every
other
curve
needs
more.
The
task
before
Kepler
was
to
construct
Mars's
orbit
without
any
preconceived
ideas
regarding
its
shape;
to
start
from
scratch,
as
it
were.

To
do
that,
it
was
first
of
all
necessary
to
re-examine
the
motion
of
the
earth
itself.
For,
after
all,
the
earth
is
our
observatory;
and
if
there
is
some
misconception
regarding
its
motion,
all
conclusions
about
the
motions
of
other
bodies
will
be
distorted.
Copernicus
had
assumed
that
the
earth
moves
at
uniform
speed
–
not,
as
the
other
planets,
only
"quasi-uniformly"
relative
to
some
equant
or
epicycle,
but
really
so.
And
since
observation
contradicted
the
dogma,
the
inequality
of
the
earth's
motion
was
explained
away
by
the
suggestion
that
the
orbit
periodically
expanded
and
contracted,
like
a
kind
of
pulsating
jellyfish.
¹³
It
was
typical
of
those
improvizations
which
astronomers
could
afford
so
long
as
they
felt
free
to
manipulate
the
universe
as
they
pleased
on
their
drawing
boards.
It
was
equally
typical
that
Kepler
rejected
it
as
"fantastic",
¹⁴
again
on
the
grounds
that
no
physical
cause
existed
for
such
a
pulsation.

Hence
his
next
task
was
to
determine,
more
precisely
than
Copernicus
had
done,
the
earth's
motion
round
the
sun.
For
that
purpose
he
designed
a
highly
original
method
of
his
own.
It
was
relatively
simple,
but
it
so
happened
that
nobody
had
thought
of
it
before.
It
consisted,
essentially,
in
the
trick
of
transferring
the
observer's
position
from
earth
to
Mars,
and
to
compute
the
motions
of
the
earth
exactly
as
an
astronomer
on
Mars
would
do
it.
¹⁵

The
result
was
just
as
he
had
expected:
the
earth,
like
the
other
planets,
did
not
revolve
with
uniform
speed,
but
faster
or
slower
according
to
its
distance
from
the
sun.
Moreover,
at
the
two
extreme
points
of
the
orbit,
the
aphelion
and
perihelion
(see
Figure
on
p.
320)
the
earth's
velocity
proved
to
be,
simply
and
beautifully,
inversely
proportional
to
distance.

At
this
decisive
point,
¹⁶
Kepler
flies
off
the
tangent
and
becomes
air-borne,
as
it
were.
Up
to
here
he
was
preparing,
with
painstaking
patience,
his
second
assault
on
the
orbit
of
Mars.
Now
he
turns
to
a
quite
different
subject.
"Ye
physicists,
prick
your
ears,"
he
warns,
"for
now
we
are
going
to
invade
your
territory."
¹⁷
The
next
six
chapters
are
a
report
on
that
invasion
into
celestial
physics,
which
had
been
out
of
bounds
for
astronomy
since
Plato.

A
phrase
seems
to
have
been
humming
in
his
ear
like
a
tune
one
cannot
get
rid
of;
it
crops
up
in
his
writings
over
and
again:
there
is
a
force
in
the
sun
which
moves
the
planet,
there
is
a
force
in
the
sun,
there
is
a
force
in
the
sun.
And
since
there
is
a
force
in
the
sun,
there
must
exist
some
beautifully
simple
relation
between
the
planet's
distance
from
the
sun
and
its
speed.
A
light
shines
the
brighter
the
nearer
we
are
to
its
source,
and
the
same
must
apply
to
the
force
of
the
sun:
the
closer
the
planet
to
it,
the
quicker
it
will
move.
This
is
his
instinctive
conviction,
already
expressed
in
the
Mysterium
Cosmographicum
;
but
now,
at
last,
he
has
succeeded
in
proving
it.

In
fact
he
has
not.
He
has
proved
the
inverse
ratio
of
speed
to
distance
only
for
the
two
extreme
points
of
the
orbit;
and
his
extension
of
this
"Law"
to
the
entire
orbit
was
a
patently
incorrect
generalization.
Moreover,
Kepler
knew
this,
and
admitted
it
at
the
end
of
the
thirty-second
chapter,
¹⁸
before
he
became
airborne;
but
immediately
afterwards,
he
conveniently
forgot
it.
This
is
the
first
of
the
critical
mistakes
which
"as
if
by
a
miracle"
cancelled
out,
and
led
Kepler
to
the
discovery
of
his
Second
Law.
It
looks
as
if
his
conscious,
critical
faculties
were
anaesthetized
by
the
creative
impulse,
by
his
impatience
to
get
to
grips
with
the
physical
forces
in
the
solar
system.