384
DOC.
42
SPECIAL AND GENERAL RELATIVITY
144
Relativity
24jcV
+
TV(
\-ez)
(N.B.-One
complete
revolution
corresponds
to
the
angle
2n
in
the
absolute
angular
measure
customary
in
physics,
and
the
above
expression gives
the
amount
by
which
the
radius
sun-planet
exceeds this
angle during
the interval
between
one
perihelion
and
the
next.)
In
this
expression
a
represents
the
major
semi-axis
of
the
ellipse,
e
its
eccentricity,
c
the
velocity
of
light,
and
T
the
period
of
revolution of the
planet.
Our
result
may
also
be stated
as
follows:
According to
the
general
theory
of
relativity,
the
major
axis
of the
ellipse rotates
round
the
sun
in
the
same sense as
the
orbital motion of the
planet.
Theory
requires
that
this rotation should
amount to
43
sec-
onds
of
arc per century
for
the
planet Mercury,
but
for
the
other
planets
of
our
solar
system its
magnitude
should be
so
small
that it
would
necessarily escape
detection.1
In
point
of
fact,
astronomers
have found
that the
theory
of
Newton does
not
suffice
to
calculate
the
observed motion of
Mercury
with
an
exactness corresponding
to
that
of
the
deli-
cacy
of observation attainable
at
the
present
time. After
taking
account
of
all
the
disturbing
influences exerted
on
Mercury by
the
remaining planets,
it
was
found
(Leverrier-1859-and
Newcomb-1895)
that
an
unexplained perihelial movement
of the
orbit
of
Mercury
remained
over,
the
amount
of which
does
not
differ
sensibly
from the above-mentioned
+43
sec-
[89]
1 Especially
since the
next planet
Venus has
an
orbit that
is
almost
an exact
circle,
which makes
it
more
difficult
to
locate the
perihelion
with
precision.