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| Velocities of the same body in two frames of reference
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Advance
of Mercury's perihelion
The
major axes of the elliptical trajectories of the planets about the
Sun turn slowly within their planes because of the interactions
of the planets with each other, but it was discovered in the 19th
century that interplanetary perturbations could not account fully
for the turning rate of Mercury's orbit, leaving unexplained about
43 seconds of arc per century. The general theory of relativity,
however, accounts exactly for this discrepancy. In 1967 Dicke--and
more recently Henry Allen Hill, also of the United States--suggested
that a small part of Mercury's perihelion advance may be caused
by the slight flattening of the Sun at its poles, thus opening the
way for possible modification of general relativity. On the other
hand, support for Einstein's original version of the theory has
come from a comprehensive evaluation of solar system data by the
American investigator Ronald W. Hellings and from investigations
of the binary pulsar system PSR 1913+16 by the American astronomer
Joseph H. Taylor.
General
relativity predicts that the wavelength of light emanating from
sources within a gravitational field will increase (shift toward
the red end of the spectrum) by an amount proportional to the gravitational
potential at the site of the source. This effect was found first
in astronomical objects, particularly in stars called white dwarfs,
on whose surfaces the gravitational potential is large. The best
quantitative confirmation of gravitational redshift was obtained
in laboratory experiments in Great Britain and the United States
in the 1960s; an accuracy of one part in 100 was achieved in measuring
the minute difference in gravitational potential
between two sites differing in altitude by a few metres.
General
relativity predicts that the curvature of space-time results in
the apparent bending of light rays passing through gravitational
fields and in an apparent reduction of their speeds of propagation.
The bending was first observed, within a couple of years of Einstein's
publication of the new theory, during a total eclipse, when stellar
images near the occulted disk of the Sun appeared displaced by fractions
of 1 of arc from their usual locations in the sky. The associated
delay in travel time was observed in the late 1960s, when ultraintense
radar pulses were reflected off Mercury and Venus just as these
planets were passing behind the Sun. These experiments are difficult
to perform and their accuracy is difficult to evaluate, but it seems
conservative to conclude that they confirm the relativistic effect
within a few parts in 100. Finally, extended massive objects such
as galaxies may act as "gravitational lenses," providing more than
one optical path for light emanating from a source far behind the
lens and thus producing multiple images. Such multiple images, typically
of quasars, had been discovered by the early 1980s.
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Contents:
Introduction
The
special theory of relativity
Historical
background
Relativity
of space and time
Consequences
The
limiting character of the speed of light
Variable
mass
Invariant
intervals
The
"twin paradox"
Four-dimensional
space-time
The
general theory of relativity
Physical
origins
The
principle of equivalence
Curved
space-time
The
principles
The
mathematical expression
Confirmation
of the theory
Advance
of Mercury's perihelion
Gravitational
redshift
Optical
effects of gravitation
Gravitational
waves
Future
astrophysical tests
Conceptual
implications of general relativity
Schwarzschild's
solution of the field equations
Applications
of relativistic principles
Particle
accelerators
Relativistic
particle physics
Relativistic
cosmology
Modifications
of general relativity
Bibliography
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