Re: Subject: The Big Bang

Amara Graps (
Tue, 4 Nov 1997 12:15:51 -0800

I wrote some text last Spring about the "solar-oblateness" concepts
relating Einstein's GR and Dicke's modification, and where Mercury's
perihelion advance fits in the story. Seems to be appropriate to post
some of that text here..

(I really don't have the time to jump in the middle of this heavy
discussion. But I have some comments.)

From: (Tony Hollick)

>Empirically falsified? In his first paper Einstein predicted that the
>precession of Mercury's perihelion should shift by 43 seconds of arc a
>century more than Newton says it should. It does.
> From my Relational Mechanics paper on:
> {X1} Mercury's Perihelion Advance
> ============================
> While it was for a long time the strongest argument for it, this is not
>now considered a corroboration of Einstein's theory. There was an observed,
>long-standing and acknowledged anomaly between the classically predicted
>movement of the planet Mercury (circling the Sun in a nearly "closed" or
>stationary ellipse, with a small perihelion advance caused by the gravitation
>of the other planets) and the observed advance of the perihelion (Mercury's
>closest approach to the sun), a difference of 43 seconds of arc
>(approximately 0.012 of a degree) per century. (Ritz's, Weber's and
>Neumann's theories of gravity as a propagated far-action also give
>approximately this result).
> The existence of another - intraMercurial - planet, "Vulcan", was
>suggested as a cause, but no planet "Vulcan" was found (sorry, fellow "Star
>Trek" fans). However, in 1970, the American astronomer Robert Henry Dicke
>suggested a (partial, 10%) classical cause for the anomaly as due to the
>oblateness of the Sun (a flattening at the poles caused by rotation). And
>the force of gravitational attraction is only a uniform central force for
>orbits lying in the equatorial plane of the sun; Mercury's orbit lies 7
>degrees off the plane of the ecliptic. The sun's equatorial rotation on its
>axis is 25.38 days; Mercury circles the Sun in 88 days. The sun's magnetic
>force and atmosphere extends far past Mercury; so does the "solar wind."
>There is a rotating accretion disc of particles, gas and dust extending on
>the plane of the ecliptic from the sun. The other planets affect Mercury's
>rotation. Light-pressure from sunlight acts on the planets.

Some quick notes on this last paragraph..

"Light-pressure", if what you mean is actually the
Poynting-Robertson effect, has effect only on small particles,
ie micron-sized particles.

Einstein didn't "predict" Mercury's perihelion advance, it was
known. He used his GR to explain it.

And the dust in our solar system is not really a "rotating accretion
disk of particles." I worte a long essay on dust evolution in the
universe here:

with some new text on interplanetary dust from results that were given
at Exo-zodiacal dust workshop at NASA-Ames last week. The solar system
dust cloud is very complex with lots of structures (bands, trails,
resonant rings, wakes, etc.)

Here's my solar oblateness text. (Copyright Amara Graps 1997).

Einstein's General Theory of Relativity and Solar Oblateness


One of the big tests for Einstein's General Theory of Relativity was
whether a planetary orbit would drift, or precess, when that object was
very close to a large mass. At that point, according to Einstein's
theory, the Newtonian theory of gravitation should fail to obey the
inverse-square law of mutual attraction. The reason the Newtonian theory
of gravitation fails is because the properties of space-time in the
vicinity of the large mass is modified (its magnitude is changed) by the
presence of the gravitational field of the large mass.


Mercury is the closest planet to the Sun. When it's at perihelion (the
spot in it's orbit closest to Sun), it will be most affected by the
Sun's gravitational attraction according to General Relativity, and
Mercury will never repeat it's orbit exactly -- the position of its
perihelion is no longer constant.

If one accounts for the gravitational effect of the nearby planets on
Mercury using Newton's gravitational equation, then Mercury's major axis
of its orbit still has 43.03 seconds-of-arc perihelion precession rate
per century that cannot be explained. Einstein, in 1915, showed that his
General Theory of Relativity altered the gravitation equation by just
enough to explain the unexplained portion of the motion of Mercury's
perihelion. The motion of the planet Mercury, was one of the first
successes of Einstein's theory.

But what if the Sun's shape had an effect on Mercury's perihelion
precession rate? If the Sun were not a perfect sphere, but had an
equatorial bulge (i.e., was "oblate"), that would cause Mercury's orbit
to precess slightly. Then Einstein's Theory would not "neatly"
explain the observations, and modifications to his theory would be

How could our Sun be oblate? Rotating gaseous balls should be slightly
oblate, so that the poles of the ball "flatten" and the equator of the
ball "bulges". Astronomers have thought that this simple process should
cause our Sun to be shaped as a (slightly) oblate sphere.

In 1967, Robert Dicke proposed the concept of the shape of the Sun as
an oblate sphere affecting Mercury's perihelion precession rate. In fact
at that time, it was already thought that the Sun wasn't a perfect sphere.
But is the Sun oblate "enough" to result in the General Theory of
Relativity not fitting the observations? According to Dicke at that
time, the answer was 'yes'.

In the 1960s, Dicke and Goldenberg claimed to have detected a much larger
solar equatorial bulge than the solar models predicted. The solar bulge
was large enough to destroy the neat agreement between General
Relativity and Mercury's orbit, but the solar oblateness was not large
enough to permit a Newtonian explanation.

Dicke presented a scalar-tensor theory of General Relativity, in which
only about 93% of the observed excess rate of perihelion advance could be
explained by relativistic effects (as opposed to Einstein's General
Theory of Relativity, which neatly explains the entire excess perihelion
advance). The remainder could be supplied by the quadrupole moment of
gravitational field which arises due to an oblate shape of the Sun.

The direct way of measuring oblateness in the Sun is to take the ratio
of the radius of the poles and of the equator. But the measurement is
very difficult because the Sun is a large gaseous ball, so where exactly
is the Sun's limb at these locations? In addition, due to observational
wavelength selection effects, astronomers see higher photospheric layers
towards the limb, an effect called "limb darkening." And the Sun's shape
changes over time, by very tiny (but measurable) amounts.

Techniques to Investigate the Solar Oblateness

Solar physicists have created a collection of ingenious methods to measure
the shape of the Sun. For example, one can measure the rotation of the
interior by measuring modes of oscillating sound waves. This method uses
the frequency splittings of the normal (spherical) modes of oscillation
to give a measure of the internal solar rotation.

Today, using helioseismic instruments, one can also observe the Sun's
limb at the equator and the poles at a sensitivity of 10 feet (i.e. one
can measure gases move by that amount).

---------------------end of my solar oblateness text --------

If you search on keywords "Solar Oblateness" on the NASA ADS abstracts,

you will turn up hundreds of references from the last 10-20
years. This is something that scientists are interested in, and
working on.

The following is an abstract from results given at the American Geophysical
Union conference last December 1996 by Jeffrey Kuhn, and some members
of my Stanford Solar Oscillations Group which has a helioseismology
instrument (Michelson Doppler Imager) on the SOHO spacecraft.

The result from this work shows that the sun is almost a perfect sphere.
The SoHO/MDI helioseismology instrument found that the Sun's
shape is distorted by only about one mile of its nearly 1
million-mile diameter.

SoHO and the Solar Oscillations Imager Experiment Measure Tiny
Changes in the Shape of the Sun

Jeffrey R. Kuhn (National Solar Observatory/Michigan State
University), Rock Bush (Stanford), Rick Bogart (Stanford), Luiz Sa
(Stanford), Xania Scheick (Jackson Community College, MI), Phil
Scherrer (Stanford).

>From the constant environment of space, the SOHO/MDI experiment
provides researchers with the longest series of finely detailed
electronic images of the sun we have ever obtained. Because the
spacecraft is above the blurring effects of the atmosphere, and with
the help of sophisticated computer analysis, it is possible to
measure exceedingly small changes in the shape of the sun. These
changes are caused by "oscillations" analogous to terrestrial
earthquakes. Other ground measurements have observed such
oscillations before, but never have we been able to actually detect
the shape of the sun fluctuate because of these sound waves. The
SOHO/MDI experiment is able to detect the edge of the sun move by
about 10 feet. This sensitivity is equivalent to measuring the size
of a quarter placed at the edge of the moon as seen from the surface
of the earth.


I hope this provides some food for thought.


Amara Graps email:
Computational Physics vita: finger
Multiplex Answers URL:
"Drosam pieder pasaule." (The world belongs to the brave.)
--a Latvian proverb