It's not specified anywhere in the literature I read that Cassini did *not*
find any frequency dependent deflection. Nor is it clear if
the data from each frequency was collected simultaneously. An
important proviso.
I read the
slac.standard.edu paper on the actual test data and page 2
confirms coronal dispersion was highly variable over short periods.
And then says...that because of this variability both 32 and 8 million
MHZ data were combined as one for deflection analysis.
If this is true then so much for seperate frequencies.
And finally could refraction between 42 and
8 million MHz be even quantifiable using Cassini?
I would have thought that time delay due to refraction
Between the two low frequency radio frequencies would be
impossibly small to measure anyways.
[[Mod. note -- The Cassini experiment did indeed measure the time delay
in question. Quoting from the caption for supplemental figure 1 of the
Bertotti et al paper cited above:
| The complete fractional frequency shift is the sum of three parts:
| the non-dispersive part $y_{nd}(t)$ (which includes the gravitational
| signal) and the time dependent plasma contributions $y_\wedge(t)$ and
| $y_\vee(t)$, proportional to the columnar electron content along the
| beam in the up- and the downlink, respectively. With three independent
| observables, the three quantities $y_\wedge(t)$, $y_\vee(t)$ and
| $y_{nd}(t)$ are separately determined.
Note particularly that last clause: "the three quantities $y_\wedge(t)$,
$y_\vee(t)$ and $y_{nd}(t)$ are separately determined".
-- jt]]
> 2. Another way to avoid contamination by solar-corona effects is to measure
> the bending of *visible* light. This is hard to do with ground-based
> experiments, but the ESA's Hipparcos satellite measured light bending
> over *the entire sky*, including regions of the sky > 90 degrees away
> from the Sun (where the effects of the solar corona are negligible).
Why would refraction not give the same inverse square relationship to
distance that gravity has? The density gradient of the plasma from the
corona to the farthest part of the solar wind "bubble" has to also follow
the same inverse square relationship.
[[Mod. note --
1. Because there's an integration over the entire path length,
gravitational light bending (or time delay) doesn't vary as the
inverse square of the impact parameter (the closest distance between
the path and the center of the Sun). As you can see from equation (1)
of the Bertotti et al paper, the actual variation is *logarithmic* in
the impact parameter. (There's a more detailed calculation in, for
example, sections 7.1 and 7.2 of Clifford M Will, "Theory and Experiment
in Gravitational Physics", 2nd edition, Cambridge U.P.)
2. Unfortunately my wording in a previous moderator's note was sloppy:
I wrote that "the ESA's Hipparcos satellite measured light bending
over *the entire sky*, including regions of the sky > 90 degrees away
from the Sun (where the effects of the solar corona are negligible)."
That final statement is true, but I gave the wrong reason for it:
the effects of the solar corona *on visible light* are very small
*everywhere* in the sky, including even lines-of-sight which pass
quite close to the Sun. The importance of Hipparcos's being able
to measure light bending > 90 degrees away from the Sun is for a
completey different region: to maintain a stable thermal environment,
Hipparcos was designed to *never* point its instantaneous lines-of-sight
close to the Sun.
-- jt]]
Not to mention Parker probe. Notice, contrary to assumptions,
it provided many new unexpected properties of the Corona.
> 3. We actually know the Sun's density profile (and hence its quadrupole
> moment J_2, which is what you're referring to) very well, thanks to
> helioseismology measurements .
We don't "know". We assume. Don't forget the basic rule of physics.
Assumption is not an observation.
[[Mod. note -- Arxiv:1103.1707 outlines some of the observations and
analysis (as of 10 years ago). It's pretty impressive. -- jt]]
> You can't (correctly) model the observed
> precession of Mercury (not to mention those of Venus, Earth, and Mars,
> all of whose orbital precessions are also well-observed) using Newtonian
> gravity and the Solar mass distribution.
Yes you can. Le Verrier did in his 1859 paper. Correctly. Or as close
as correct could be in 1859 due to uncertain measurements available
at the time.
He even is on the record for saying it wasn't neccesarily Vulcan. He
only speculated the additional source had to be outside the suns
theoretical center. And for the standards of the time...his calculations
presumably 3 body, were correct. 60 years before Einstein.
> 4. Newton never asserted that all of a planet's (or the Sun's) mass was
> located at its center. Rather, he (correctly) calculated that the
> external gravitational field of an extended spherically symmetric mass
"Correctly calculated"?
No he didn't. This is a false claim. If he did....why do his calculations
not correctly model the preccession of planets like Mercury?
[[Mod. note -- Newton's calculation of the gravitational field of a
spherical body (the "shell theorem") is briefly outlined in
https://en.wikipedia.org/wiki/Shell_theorem
So far as we know, Newton never calculated or modelled planetary
precessions (I don't think there's any mention of the topic in his
surviving writings). Much later, Leverrier, Lagrange, and others used
Newton's shell theorem (among many other mathematical techniques) to
calculate planetary precession -- including that of Mercury -- within
the framework of Newtonian gravitatation and mechanics.
-- jt]]
> distribution is the same as it would be if all the mass were located
> at the center. (Calculating the external gravitational field of an
> extended mass distribution requires calculus, which Newton invented
> in part to address this question.)
> 5. Newton was well aware of the possibility of experiments such as the
> Schiehallion experiment (the measurement of the external gravitational
> field of a mountain), but mistakenly thought that the effects would
> be to small to be accurately measured. Fortunately, he was wrong.
Newton's *excuse* was that it would be too small to measure. What
he didn't want to admit was that if it was measureable...then his
assumption that one can assume that all the mass could be put
at the center was incorrect. As Mercury's preccession proved.