196
DOC. 30 FOUNDATION OF GENERAL
RELATIVITY
in
which K denotes
the constant
6.7
x
10-8,
usually
called
the
constant
of
gravitation. By
comparison
we
obtain
K
~
8TTK
-
1.87
x
10-27
(69)
§
22.
Behaviour
of Rods
and Clocks in the Static Gravi-
tational
Field.
Bending
of
Light-rays. Motion of
the Perihelion
of
a
Planetary Orbit
To
arrive
at Newton's
theory
as a
first
approximation
we
had to calculate
only one
component,
g44,
of
the ten
guv
of the
gravitational
field,
since
this
component
alone enters
into the
first
approximation,
(67),
of the
equation
for
the
motion of
the
material
point
in the
gravitational
field.
From
this,
however,
it
is
already
apparent
that other
components of
the
guv
must
differ
from the
values
given
in
(4) by
small
quantities
of
the
first order.
This
is
required
by
the condition
g
=
-
1.
For
a
field-producing
point
mass
at
the
origin
of co-ordin-
ates,
we
obtain, to
the
first
approximation,
the
radially
symmetrical
solution
g,.=
-Spa-Ä0
(p,
o =
1,
2,
3)
9p4
=
94p
=
0
i
a
744
-
1
-
(p
=
1, 2, 3)
(70)
r
[33]
where
8po
is
1
or 0, respectively,
accordingly
as p
=
o
or
p
#
o,
and
r
is
the
quantity +
/x21
+
x22
+
x23
On account of
(68a)
a-
=
kM
47T
'
(70a)
if
M
denotes
the
field-producing mass.
It
is
easy
to
verify
that the
field
equations (outside
the
mass)
are
satisfied to
the
first
order
of
small
quantities.
We
now
examine the
influence
exerted
by
the
field
of
the
mass
M
upon
the
metrical
properties
of
space.
The relation
ds2
=
guvdxudxv.
always
holds
between the
"locally"
(§ 4)
measured
lengths
and times
ds
on
the
one
hand, and
the
differences of co-ordin-
ates
dxv on
the other hand.