Advance of perihelions
Corrado Massa
Hi boys,
in the book
Roman & Hannelore Sexl
" Weisse Zwerge - schwarze Loecher "
Rowohlt Taschenbuch Verlag - Reinbek
(Hamburg, 1975)
English translation:
" White Dwarfs, Black Holes "
(Academic Press, INC. New York 1979),
Italian translation:
" Nane Bianche, Buchi Neri "
Boringhieri (Torino 1981)
one reads in Chapter 2
( p. 35 of the Italian translation)
T = Theory, O = Observations
(Units: seconds of arc per century)
T O
Mercury 43.03 43.11 + / - 0.45
Venus 8.6 8.4 + / - 4.8
Earth 3.8 5.0 + / - 1.2
Icarus 10.3 9.8 +/ - 0.8
(Unfortunately, Roman & Hannelore Sexl give no reference).
In the book
P.A.M. Dirac,
" General Theory of Relativity "
Wiley (New York 1975);
Princeton University Press (Princeton 1996)
one reads in Chapter 18 (p. 32 in the Princeton version)
"the solution (18.6) [that is, the Schwarzschild solution]
leads to small corrections in the Newtonian theory for the
motions of the planets around the Sun. These corrections
are appreciable only in the case of Mercury, the nearest
planet".
in the book
Robert M. Wald
Space, Time, and Gravity
2nd Edition, the University of Chicago Press
(Chicago and London, 1992)
one reads in Chapter 3, Sec. 5, p. 37:
"This precession is much too small to observe for
all planets except Mercury, where general relativity
predicts an orbital precession of 43 seconds of arc
per century"
Can you solve this puzzle?
Thanks, and be happy
Corrado
Peter J
"Corrado Massa" <_cm...@tin.it> wrote in message
news:TqZsa.38689$3M4.1...@news1.tin.it...
[huge wads of quoted text deleted]
The figures for perihelic shift quoted by Roman & Hannelore... are
from R L Duncombe 1956. A web search should give the exact reference.
The other authors you quote say that the relativistic perturbation is
only appreciable for Mercury so how do we reconcile their statements
with R & H S?
Although perturbations can be measured for other planets, asteroids,
comets etc. there are many 'classical perturbations' to be filtered
out before one can be sure that what's left is due to relativistic
effects. Those other effects, due to interactions between planets,
the oblateness of the sun, slight variations in the angle of orbit
etc. swamp the relativistic effect which declines rapidly with
distance from the sun. The case of Mercury is the only one in which
the precession of the perihelion clearly agrees with the predictions
of GR.
That said, one can derive best fit lines for the perihelion advances
based (a) on Newtonian principles and (b) on GR. If you do this the
GR line fits closest. See Introduction to General Relativity Adler,
Bazin & Schiffer McGraw-Hill 1965.
Jonathan Thornburg
In article <TqZsa.38689$3M4.1...@news1.tin.it>,
Corrado Massa <_cm...@tin.it> wrote:
[[different books report different things about which planets have
had their general relativistic perihelion precessions observed]]
You're just seeing different authors (none of whom are specialists
in experimental tests of general relativity) reporting different
subsets of the known data. There are actually quite a few other
systems for which perihelion precession has been measured (other
planets, also some pulsars). Some of the best measurements to date
are those of Mars's orbit (which none of the quotations you gave
mentioned): The GR effects for Mars's orbit are a lot smaller than
those for Mercury, but the observations of Mars's orbit are -- or were
-- *very* precise
[For example, thanks to the Viking (Mars) landers there,
during 1976-1982 we knew the Earth-Mars range to a typical
experimental accuracy of a bit better than 10 meters.
Because of this spectacular accuracy, Mars' orbit is a
far more stringent and reliable test of GR than (say)
Mercury's perihelion advance. We don't have any spacecraft
landed on Mercury, so our uncertainties in Mercury's orbit
are orders of magnitude larger than those for Mars.]
If you want an account of this sort of observation/analysis written
by someone who is really an expert in this, see
Ronald W Hellings
"Testing Relativity with Solar System Dynamics"
p.365-385 in...
B Bertotti, F. de Felice, and A. Pascolini
"General Relativity and Gravitation"
[Invited Papers and Discussion Reports of the
10th International Conference on General Relativity
and Gravitation, Padua (Italy), 3-8 July 1983]
Reidel, Dordrecht (Holland), 1984
ISBN 90-277-1819-9
Another excellent reference (more technical) is
@article
{
Nordtvedt-1999-lunar-laser-ranging-vs-GR,
author = "Kenneth Nordtvedt",
title = "30 years of Lunar Laser Ranging
and the Gravitational Interaction",
journal = "Classical and Quantum Gravity",
volume = 16, X-number = "???",
pages = "A101--A112",
year = 1999, month = "December",
note = "maybe available online at
abstract
http://www.iop.org/EJ/S/3/31/D3W0eKTDEk.rPjcuFN2vhg/abstract/
0264-9381/16/12A/305
full paper
http://www.iop.org/EJ/S/3/31/D3W0eKTDEk.rPjcuFN2vhg/article/0
264-9381/16/12A/305/q91b05.ps.gz
",
}
A good general review article on this whole topic is
gr-qc/0103036, avilable at
http://xxx.arxiv.org/abs/gr-qc/0103036
(and mirrors all around the world):
Title: The Confrontation between General Relativity and Experiment
Authors: Clifford M. Will
Comments: 103 pages, 10 figures, accepted for publication in
Living Reviews in Relativity
Journal-ref: Living Rev.Rel. 4 (2001) 4
The status of experimental tests of general relativity and of theoretical
frameworks for analysing them are reviewed. Einstein's equivalence
principle (EEP) is well supported by experiments such as the E\"otv\"os
experiment, tests of special relativity, and the gravitational redshift
experiment. Future tests of EEP and of the inverse square law will search
for new interactions arising from unification or quantum gravity. Tests
of general relativity at the post-Newtonian level have reached high
precision, including the light deflection, the Shapiro time delay,
the perihelion advance of Mercury, and the Nordtvedt effect in lunar
motion. Gravitational wave damping has been detected to half a percent
using the binary pulsar, and new binary pulsar systems may yield further
improvements. When direct observation of gravitational radiation from
astrophysical sources begins, new tests of general relativity will
be possible.
ciao,
--
-- "Jonathan Thornburg (remove -animal to reply)" <jth...@aei.mpg-zebra.de>
Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
Golm, Germany, "Old Europe" http://www.aei.mpg.de/~jthorn/home.html
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam