DOC.
14 EINSTEIN AND
BESSO MANUSCRIPT 429
[p. 34]
(Einstein)
[150]On
[p.
34],
the calculation
on [p. 32]
is
continued.
Inserting
the corrected version of
[eq.
196] (see note 144)
into
[eq.
192]
and
writing
the
factor
k
that
got
absorbed into
S
on
[p.
20]
(see
note
99)
separately again,
one
arrives
at
[eq. 202]
for
the
angle
between
perihelion
and
aphelion
of
an
orbit
in
the
field
of
a
rotating
sun.
From
[eq. 202]
it follows that
the
rotation of
the
sun
produces
a
retrogression
of
the perihelion. Inserting
[eq. 201]
(=
[eq. 3]
on
[p.
1])
for
k
and
[eq.
203]
for
C into
[eq.
202],
one
arrives
at
[eq. 204] (see
the editorial
note,
"The Einstein-Besso
Manuscript
on
the Motion of the
Perihelion
of
Mercury,"
sec.
II.2b,
eq.
(18)).
With
regard
to
[eq.
203],
note
that
C to
a
good approximation
is
equal to
twice
the
area velocity (see
[eq.
143]
on [p. 21]).
Hence, C is
approximately equal
to
twice
the
area
of
the
orbit divided
by
the
period
of revolution.
[151]In
the
top right
corner
of
[p. 34],
it
is
checked
whether
the right-hand side
of
[eq. 202]
is
dimensionless.
Possibly
as a
result of
these
considerations, the
factor
k was
added
to
[eq.
202].
The
comment
"factor
k
missing"
on [p.
19]
(see
note
89) was perhaps
made in connection with
this dimensional
analysis.
[152]In
[eqs.
205-207],
S0
is
temporarily
written
as
So
again.
When
it is
assumed that the
sun
has
a
uniform
mass
distribution,
the
integral
in the definition of
S
(see [eq. 128]
on [p.
19])
is
readily
evaluated
(see
[eq.
205]).
In
[eq.
206],
the
angular velocity is
written
as o
=
2t/Ts,
where
Ts
is
the
period
of revolution of
the
sun.
[153]The logarithm
of
So is
computed
with
the
help
of
[eq. 207].
The result
is
then used
to
compute
the
logarithm
of
the
factor SoMT3
in
[eq.
204].
The various numbers that
are
inserted
are
all
copied
from
the
auxiliary
calculations
to
the
right (see
notes 154-157).
[154]The
logarithm
of
the
mass
Ms
of
the
sun
is
computed
via
the
relation
Ms
=
(Ms/Me)pe
Ve
(see
note 120).
[155]The
logarithm
of
the
radius
Rs
of
the
sun
is
computed
via
the
relation
Rs
=
(Rs/Re)Re,
with
Rs/Re
=
108.56 and
Re
=
6.37
•
108
cm
(see note
120).
[156]The logarithm
of the
period
of revolution of the
sun,
Ts
=
25.16
days,
is
converted
to
seconds.
[157]The
numbers 6.8808
and 12.7595
given
at
the bottom of
[p.
34] are
the
logarithms
of
the
period
T
in
seconds and the
semi-major
axis
a
in
centimeters of
Mercury's
orbit around
the
sun,
respectively
(see
notes
121-122). Note
that .49715
+ .30103
-
0.7982
- log2r.