126
DOC.
7
GRAVITATIONAL INDUCTION
Doc.
7
Is
There
a
Gravitational Effect Which Is
Analogous
to
Electrodynamic
Induction?
by
A.
Einstein
fur
gerichtliche
Medizin
und
öffentliches
Sanitätswesen 44
(1912):
37-40]
Taking
a
plain special
case as a
model,
one can
formulate the
question
raised in the
title
as
follows.
Consider
a system
of
ponderable
masses
consisting
of
a spherical
shell K with
mass M,
which
is
homoge-neously
distrib-
uted
over
the surface
of
the
sphere,
and the material
point
P
with
mass m,
which is
set
in the
center
of
this
sphere.
Does
a
force
act
on
the fixed material
point
P
if
I
impart an
acceleration
Y
to
the shell
K?
The
[1] following
arguments
will induce
us
to
view such
a
force effect
as
really being present
and will
give
us
its
magnitude
in first
approximation.
1. According
to
the
theory
of
relativity,
the inertial
mass
of
a
closed
physical
system depends
on
its
energy
content
in such
a
way
that
an
increase of the
energy
[2]
of the
system by
E will increase the inertial
mass by
E/c2,
where
c
denotes the
[3]
velocity
of
light
in
a vacuum.
Thus,
if M denotes the inertial
mass
of
K in the
absence
of
P,
and
m
denotes the inertial
mass
of P in the absence of
K,
or,
in other
words,
if M
+
m
denotes the inertial
mass
of
the
system consisting
of P and K
together
in the
case
where
m
is
infinitely
far from
K,
then it follows that the inertial
mass
of the
system
consisting
of
K
and
m possesses
the value
w
kMm....(1)-m
M
+,
Rc2
if
m
is
in the
center
of
K,
where k denotes the
gravitational
constant
and
R
of
K.
For
kMm/R
(at
least in first
approximation)
is the
energy
that
one
must
apply
in order
to
transport
P from the
center
of
K
to
infinity.
2.
In
a
paper
that will
shortly appear
in the Annalen
der
Physik,
I
have
shown,
[4]
based
on a hypothesis
the
nature
of
the
static
gravitational
field,
that
a
material
point
moves
in
a
static
gravitational
field
according
to
the
following
equations:
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