The Sleepwalkers (281 page)

Authors: Arthur Koestler

BOOK: The Sleepwalkers

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Copernicus assumed the mean distance
of the earth from the sun = 1142 earth radii ( De revolutionibus,
Lib. IV, Cap. 21). In round figures, the radius of the earth's orbit
thus amounts to 1200 × 4000 = 4.8 million miles; and the minimum
radius of the universe to 4.8 × 500 = 2400 million miles. Later on,
however, in the Epitome, he enlarged the radius of the universe to
sixty million earth radii, i.e. 24. 10
¹⁰miles. He arrived
at this figure by assuming that the orbital radius of Saturn was the
geometrical mean between the radius of the sun and the radius of the
sphere of the fixed stars; and the radius of the sun to be fifteen
times the radius of the earth. ( Epitome, IV, 1, O.O., VI, p. 332.)

Letter
to
Herwart
,
16.12.
1598,
loc
cit.
Kepler
himself
never
accepted
infinity.
He
believed
that
the
fixed
stars
were
all
placed
at
almost
exactly
the
same
distance
from
the
sun,
so
that
their
"sphere"
(which,
of
course,
he
did
not
regard
as
real)
was
only
"two
German
miles"
in
thickness.
(
Epitome,
IV
,
1,
O.O.,
VI,
p.
334.)

Letter
to
Maestlin
,
16/26.2.
1599,
G.
W.
,
Vol.
XIII,
p.
289
seq
.

Ibid.

For
a profound analysis of the subjective elements in Newton's cosmology,
see Burtt, op. cit.

Kepler's
discoveries
were
not
of
the
kind
that
"lie
in
the
air";
the
three
laws
were
the
result
of
a
devious
tour
de
force
,
and
represent
a
rather
exceptional
"one-man
show",
as
it
were.
Even
Galileo
failed
to
see
their
point.

Letter
to
Maestlin
,
8.12.
1598,
G.
W.
,
Vol.
XIII,
p.
249
seq
.

12.9.
1597,
G.
W.
,
Vol.
XIII,
p.
131
seq
.

"Letter
to
Herwart,
16.12.1598",
G.
W.
,
Vol.
XIII,
p.
264
seq
.

"Letter
to
Maestlin,
29.8.1599",
G.
W.
,
Vol.
XIV,
p.
43
seq
.

"Letter
to
Maestlin,
22.11.1599",
G.
W.
,
Vol.
XIV,
p.
86
seq
.

"Maestlin
to
Kepler,
25.1.1600",
G.
W.
,
Vol.
XIV,
p.
105
seq
.

Part
IV
Chapter
IV.
TYCHO
DE
BRAHE

J.
L.
E.
Dreyer,
Tycho
Brahe
,
Edinburgh,
1890,
p.
27.
Dreyer's
is
the
modern
standard
biography
of
Tycho.
He
also
edited
Tycho
Opera
Omnia
.

Loc.
cit.

OP.
cit., p. 14.

To
be
precise,
he
used
two
threads,
passing
through
two
pairs
of
stars,
and
intersecting
in
the
Nova.

Op.
cit., p. 86 f.

An
Itinerary
written
by
Fynes
Morison
,
etc.,
London,
1617,
fol.,
p.
60,
quoted
by
Dreyer,
p.
89.

Dreyer,
op. cit., p . 105.

Ibid,
p. 262 n.

His
other, principal achievements were: improved approximations of the
sun's and moon's orbits; discovery of the "moon's equation"
(independently from Kepler); demolition of the Copernican belief in a
periodic inequality in the precession of the equinoxes.

Ibid.,
p. 261.

Ibid.,
p. 249 f.

Ibid.,
p. 279.

Nicolai
Raimari Ursi Dithmar si Fundamentum astronomicum, Strasburg, 1588.

The
only differences between the system of Ursus and the Tychonic system
were that in the former the daily rotation was attributed to the
earth, in the latter to the fixed stars; and that different orbits
were attributed to Mars.

"To
Ursus,
15.11.1595",
G.
W.
,
Vol.
XIII,
p.
48
f.

Nicolai
Raimari Ursi Dithwar si de astronomicis Hypothesibus, etc., Prague,
1597.

"To
Tycho,
13.12.1597",
G.
W.
,
Vol.
XIII,
p.
154.

"Tycho
to
Kepler,
1.4.1598",
G.
W.
,
Vol.
XIII,
p.
197
seq
.

21.4.
1598,
G.
W.
,
Vol.
XIII,
p.
204
f.

19.2.
1599,
G.
W.
,
Vol.
XIII,
p.
286
f.

The
passage
runs:
"Some
doctor
stopped
on
his
return
journey
from
Italy
in
Gratz
and
showed
me
a
book
of
his
[Ursus']
which
I
hurriedly
read
in
the
three
days
for
which
I
was
permitted
to
keep
it.
I
found
in
it
...
certain
golden
rules
which,
as
I
remembered,
Maestlin
had
frequently
used
in
Tuebingen,
and
also
the
science
of
the
sine
and
of
the
computation
of
triangles
–
subjects
which,
though
generally
known,
were
new
to
me
...
for
afterwards
I
found
in
Euclid
and
Regiomontanus
most
of
what
I
had
ascribed
to
Ursus."