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proximity to the sun--to perihelion) would differ from 360^0. The line of the orbit would not then be a closed
one but in the course of time it would fill up an annular part of the orbital plane, viz. between the circle of
least and the circle of greatest distance of the planet from the sun.
According also to the general theory of relativity, which differs of course from the theory of Newton, a small
variation from the Newton-Kepler motion of a planet in its orbit should take place, and in such away, that the
angle described by the radius sun-planet between one perhelion and the next should exceed that
corresponding to one complete revolution by an amount given by
eq. 41: file eq41.gif
(N.B. -- One complete revolution corresponds to the angle 2p in the absolute angular measure customary in
physics, and the above expression giver 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 seconds 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. *
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 delicacy 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
seconds of arc per century. The uncertainty of the empirical result amounts to a few seconds only.
(b) Deflection of Light by a Gravitational Field
PART III 47
In Section 22 it has been already mentioned that according to the general theory of relativity, a ray of light
will experience a curvature of its path when passing through a gravitational field, this curvature being similar
to that experienced by the path of a body which is projected through a gravitational field. As a result of this
theory, we should expect that a ray of light which is passing close to a heavenly body would be deviated
towards the latter. For a ray of light which passes the sun at a distance of D sun-radii from its centre, the
angle of deflection (a) should amount to
eq. 42: file eq42.gif
It may be added that, according to the theory, half of Figure 05 this deflection is produced by the Newtonian
field of attraction of the sun, and the other half by the geometrical modification (" curvature ") of space caused
by the sun.
This result admits of an experimental test by means of the photographic registration of stars during a total
eclipse of the sun. The only reason why we must wait for a total eclipse is because at every other time the
atmosphere is so strongly illuminated by the light from the sun that the stars situated near the sun's disc are
invisible. The predicted effect can be seen clearly from the accompanying diagram. If the sun (S) were not
present, a star which is practically infinitely distant would be seen in the direction D[1], as observed front the
earth. But as a consequence of the deflection of light from the star by the sun, the star will be seen in the
direction D[2], i.e. at a somewhat greater distance from the centre of the sun than corresponds to its real
position.
In practice, the question is tested in the following way. The stars in the neighbourhood of the sun are
photographed during a solar eclipse. In addition, a second photograph of the same stars is taken when the sun
is situated at another position in the sky, i.e. a few months earlier or later. As compared whh the standard
photograph, the positions of the stars on the eclipse-photograph ought to appear displaced radially outwards
(away from the centre of the sun) by an amount corresponding to the angle a.
We are indebted to the [British] Royal Society and to the Royal Astronomical Society for the investigation of
this important deduction. Undaunted by the [first world] war and by difficulties of both a material and a
psychological nature aroused by the war, these societies equipped two expeditions -- to Sobral (Brazil), and
to the island of Principe (West Africa) -- and sent several of Britain's most celebrated astronomers [ Pobierz całość w formacie PDF ]