Grubaugh Polar Alignment Model
From: grubaugh@aol.com (GRUBAUGH)
Newsgroups: talk.origins
Subject: Numbers for Dehner's N-body Model
Date: 28 Dec 1994 23:17:31 -0500
Organization: America Online, Inc. (1-800-827-6364)
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Reply-To: grubaugh@aol.com (GRUBAUGH)
Received your listing, many thanks.
Suggest you try these numbers when you have the opportunity.
G=6.667E-8
SUN Mass=1.9891E+33
X=-1.8665E+10
Y=0
VX=0
VY=-3.70188E+3
JUPITER Mass=1.899E+30
X=1.498134E+13
Y=.360152E+12
VX=7.686E+4
VY=2.971512E+6
SATURN Mass=5.684E+29
X=1.498134E+13
Y=-1.1662E+12
VX=-.248877E+6
VY=2.971512E+6
VENUS Mass=4.8689E+27
X=1.498134E+13
Y=-1.862745E+12
VX=-.39753E+6
VY=2.971512E+6
EARTH Mass=5.9742E+27
X=1.498134E+13
Y=-2.007959E+12
VX=-.428519E+6
VY=2.971512E+6
Bob G.
From: btd@iastate.edu (Benjamin T. Dehner)
Newsgroups: talk.origins
Subject: Re: Numbers for Dehner's N-body Model [Results]
Date: 29 Dec 94 18:36:16 GMT
Organization: Iowa State University, Ames, Iowa
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In <3dtd8r$cn2@newsbf02.news.aol.com> grubaugh@aol.com (GRUBAUGH) writes:
>Received your listing, many thanks.
>Suggest you try these numbers when you have the opportunity.
Okay, I know I just posted something saying I'm busy. But I just
couldn't wait to try thses new numbers.
Here is what I saw:
The initial condition performed much better than the previous
attempts. The in-line configuration remained recognizable, although the
distances between the bodies had become altered, for almost an entire
year. Venus and Earth were close enough to be undifferentiable on the
display.
However, after about 1.2 years, there was a close interaction with
the Earth-Venus pair and Jupiter. The result was that Earth and Venus were
thrown *well* clear of the system, going on a wide orbit, which went off
of the display on my screen. Jupiter and Saturn continued to orbit more or
less undisturbed, although they gradually seperated. For a while after the
interaction, a linear configuration was sort of recognizable, but with
Jupiter and Saturn reversed in the stack. After a short time, any
semblance of the stack was destroyed.
After 1.58 years, the relative change in total z angular momentum of
the system (caused by numerical inaccuarcy) was -6.54e-11, and the change in
total energy was 3.12e-10.
After about 5.3 years, the Earth finally wandered back into the
display region. Venus had been thrown on a wider orbit, and didn't get
back in at the time. Earth appeared to be an an orbit about the Sun with
an aphelion of about 4.3 AU.
My guess as to the cause of this behavior is that there is a
neglected term (tangential acceleration?) in the static analysis, which
allows perturbations from the given configuration. These perturbations
then cause the system to deviate from the static configuration. I would
also speculate that part of the problem is an incorrect definition of
stability in setting the initial conditions -- the system is stable in
the sense that "all forces ballance", and NOT in the sense of "experiences
restoring forces in the event of small perturabations".
Ben
--
-----------------------------------------------------------------------------
Benjamin T. Dehner Dept. of Physics and Astronomy PGP public key
btd@iastate.edu Iowa State University available on request
Ames, IA 50011
From: throopw%sheol.uucp@dg-rtp.dg.com (Wayne Throop)
Newsgroups: talk.origins
Subject: Re: Numbers for Dehner's N-body Model [Results]
Date: 1 Jan 1995 03:17:03 GMT
Organization: Alcatel Network Systems (Raleigh, NC)
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References: <3dtd8r$cn2@newsbf02.news.aol.com> <btd.788726176@pv7440.vincent.iastate.edu>
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:: grubaugh@aol.com (GRUBAUGH)
:: Suggest you try these numbers when you have the opportunity.
: From: btd@iastate.edu (Benjamin T. Dehner)
: Here is what I saw:
: The in-line configuration remained recognizable, although the
: distances between the bodies had become altered, for almost an entire
: year. Venus and Earth were close enough to be undifferentiable on the
: display.
: [...] after about 1.2 years, there was a close interaction with the
: Earth-Venus pair and Jupiter. The result was that Earth and Venus
: were thrown *well* clear of the system, going on a wide orbit, which
: went off of the display on my screen.
: [...] After 1.58 years, the relative change in total z angular momentum of
: the system (caused by numerical inaccuarcy) was -6.54e-11
My own n-body simulation matches these results (though the longer-term
eccentric orbits of venus and earth weren't pursued). However, there are
some points I'd like to expand on Benjamin's description, and I'll also
append a pair of GIF images showing the results.
First, in my simulation, angular momentum was conserved to within only
10^-8 or so, and Ben's simulation is tens of times more accurate than
my own home-brew. But note: despite this difference, the same
gross behavior is observed. Therefore, it is very unlikely that the
departure from an inline situation is due to numerical error. Remotely
possible I suppose, but it seems *very* unlikely at this point.
"The in-line configuration remained recognizable [] for almost an entire
year" is putting it somewhat kindly. More bluntly, within 5 megaseconds
there was more than a degree of angle between the earth-venus line and
the saturn-jupiter line. Things got progressively worse, and by about 17
or 18 megaseconds into it (a bit more than a half year) there had several
times been more than 10 degrees between the venus-saturn line and the
saturn-jupiter line, and venus and earth had started an eliptical orbit
about each other with a period of perhaps 7 megaseconds or so. The
linear alignment was completely destroyed by 20 meseconds.
Now, *to* *the* *eye*, the configuration was still somewhat linear.
As Ben says "Venus and Earth were close enough to be undifferentiable
on the display". It was only when I probed the earth-venus line
numerically, and blew up the display, that I saw they were actually well
out of allignment by 20 megaseconds. Treating venus and earth as a
single point, the remaining parts of the lineup remained within 10
degrees, which I take to be what Ben describes happening until
1.2 years in.
After the close passage at 1.2 years (or 38 megaseconds for the start of
the interaction), earth and venus are put into very eccentric orbits,
unrelated to saturn or jupiter. Ben reports that saturn and venus
"gradually separated", while I'd say they separated fairly quickly, and
were well apart by a third of a year later.
But the major elements of interaction match quite well.
The linear alignment started to degrade immediately, and it continued
to get worse. At 20 megaseconds earth and venus were no longer any
recognizable part of it. At 38 megaseconds a close passage destroyed
any vestige of a linear alignment.
I'm appending two GIF images, uuencoded. (I suppose I should give up
and rewrite my news and email scripts to generate MIME enclosures with
base64 encoding, sigh, but for now, I uuencode.) They show the planet
positions every half-megasecond, the first giving positions the first
year, the second giving positions the second year. The positions were
drawn in as lines connecting the planet positions (omitting the sun).
The earth-venus line is blue, the venus-saturn line green, and the
saturn-jupiter line red. This makes visible how the angle between the
various alignments changes as time goes on. On each gif, the time index
it stopped at is written, as well as the positions of the planets and
the sun at stopping time indicated by initial letters.
Comments welcome, and comments from Ben on how well these GIFs agree
with what his simulation showed would be greately appreciated.
I'm a bit surprised that the linearity held up even as well as it did.
Any comments as to the dynamics of why (akin to Richard Harter's intuitive
explanation of the angular separation in the earlier scenarios) would
also be especially welcome, from any of you more into orbital dynamics
than I am.
--
Wayne Throop throopw%sheol.uucp@dg-rtp.dg.com
throop@aur.alcatel.com
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end
Newsgroups: talk.origins
From: dtalbott@netcom.com (Dave Talbott)
Subject: Re: What happen to Grubaugh?
Message-ID: <dtalbottD5sx0v.HFI@netcom.com>
Organization: NETCOM On-line Communication Services (408 261-4700 guest)
References: <GDR11.95Mar19125909@stint.cl.cam.ac.uk>
Date: Tue, 21 Mar 1995 17:38:55 GMT
Lines: 112
Sender: dtalbott@netcom5.netcom.com
gdr11@cl.cam.ac.uk (Gareth Rees) writes:
>The conclusions of the discussion about Grubaugh's attempt to find a
>plausible astrophysical basis for the Saturn hypothesis was that
>Grubaugh wasn't able to demonstrate a good understanding of Newtonian
>dynamics, and that while his program could correctly simulate a circular
>orbit, it was unable to correctly simulate elliptical orbits.
>So what happened to Grubaugh? Has he admitted his mistakes and gone
>back to the textbooks?
You are quite right: No one reading the Grubaugh threads on t.o could
deny that your assumption was repeated hundreds of times by assorted
critics. Since I know nothing about dynamics, and found the t.o forum to
be a complete madhouse, I asked Dr. Robert Bass to spearhead an analysis
of Grubaugh's work over the next 60 days, in consultation with a modest
group of email consultants off the newsgroups. Dr. Bass, a
Rhodes Scholar and former professor of physics, had no prior familiarity with
Grubaugh's analytical model or computer simulations, but agreed to give the
task his best efforts.
In the meantime, I thought it would be fun, in connection with a
long-term project to summarize evolving discussion for the publication
AEON, to draw up a list of repeated t.o criticisms of Grubaugh, to see how
well they would stand up when put to various telephone and email
consultants. This process will probably take another thirty days or so,
and I'm in no hurry to complete it since, in the absence of the
background noise, every day seems to produce interesting revelations.
Though I have no plans to return to this forum, I will post a preliminary
draft of the AEON article, in three or four installments, when it is
complete. That may, however, be several months down the road. (Oh yes, and
I will make a final decision on the $100 winner within the next week, a matter
of old business that I have let drag on too long, not knowing how to
assess the relative merits of three or four claimants).
Here's the present list of t.o criticisms:
Grubaugh's collinear arrangement is an obvious violation of Kepler's
Third Law.
Grubaugh's equations for determining collinear equilibrium are useless,
having more unknowns than knowns.
It was foolish of Grubaugh to assert that in-line equilibrium of planets
could be maintained against the massive gravity of the Sun.
Every competent student of the subject knows that L-3 is unstable.
Hence, even apart from the effects of the Sun, an in-line system would
break down in mere days, weeks or months, and certainly would not hold
together for the minimum of several years that the "Saturnists" require.
Grubaugh claimed that polar coordinates were *self-evidently* preferable to
rectilinear in dealing with synchronous orbits and perturbations
thereof. In this, he only showed his ignorance of the subject, since
mathematical truth is not dependent on coordinate systems.
This one is difficult to summarize--
Grubaugh claimed that standard rectilinear integration routines involve
an inherent error in the treatment of curvilinear motion. In effect, Bob
said, they apply the Pythagorean equation appropriate for straight-line motion
along the x and y axes, rather than the differential equation for integrating
motion along a curved path. (Bob gave the two differential equations,
but mistyped the Pythagorean equation, though everyone except Paul Gans
recognized the equation.) Virtually every critic attacked Bob's claims,
though the responses are entirely contradictory. The conclusion was
surprisingly unanimous: Bob needs an education on numerical integration.
Since several n-body programs have shown the in-line planetary
arrangement to break down after an orbit or two (at best), only an
obstinate fool would continue arguing for Grubaugh's ideas.
Bob's own simulations have no validity because he is *assuming circular
orbits, periodicity and stability* rather than proving anything.
In Bob's 4-planet retrograde model, he places the planetary CG on a
automatic circular march around the Sun. That is preposterous, a perfect
example of assuming what you are supposed to be proving.
The difference in angular momentum between the suggested former
configuration and the present planetary system is so great as to make the
existence of the former virtually impossible, apart from magic.
In placing a Jupiter-Saturn binary in a retrograde orbit around its CG,
while the system moves in a prograde orbit around the Sun, Grubaugh has J
and S dangling in inertial space, with no angular momentum to keep the
two gas giants apart.
Most of these primary criticisms can, of course, be broken down into
additional components, based on actual t.o "discussion," but I believe
this is a reasonably accurate summary, hitting the most fundamental of
issues. But here is a conclusion calculated to leave the howlers
howling--howling louder than anything you've heard before. I am
now tentatively satisfied that--are you ready--THE CRITICS ARE WRONG ON
EVERY FRIGGIN' ISSUE. None of the above-cited criticisms has held up
under investigation. Not a single one.
How confident am I of this "tentative" conclusion, drawn from discussion
off the talk groups? I will make one exception to my decision not to
participate in t.o further. Let the loudest of the critics, Paul Gans,
select the most *persuasive* of the criticisms (and re-state it if he feels
that is necessary). Let Paul draw on any consultation he chooses, and I
will do the same, so that we can focus on the most obvious flaw in
Grubaugh's claims or approach and save everyone a lot of time.
Unless we can contain the discussion in this way, I will stick with my
plan to carry on the investigation exclusively off the newsgroups.
Dave
From: throopw%sheol.uucp@dg-rtp.dg.com (Wayne Throop)
Newsgroups: talk.origins
Subject: Re: What happen to Grubaugh?
Date: 25 Mar 1995 22:56:41 GMT
Organization: Alcatel Network Systems (Raleigh, NC)
Lines: 213
Message-ID: <3l2739$bjq@aurns1.aur.alcatel.com>
References: <GDR11.95Mar19125909@stint.cl.cam.ac.uk> <dtalbottD5sx0v.HFI@netcom.com>
NNTP-Posting-Host: aurxx1.aur.alcatel.com
: From: dtalbott@netcom.com (Dave Talbott)
: THE CRITICS ARE WRONG ON EVERY FRIGGIN' ISSUE
As before, the issues are phrased in unnecessarily absolutist terms,
and I don't doubt that they can be misinterpreted on that basis. But
*in context*, I doubt very much that Talbott's impression is correct.
I'll go over the issues Talbott enumerates, and show specifically
what I mean.
: Grubaugh's collinear arrangement is an obvious violation
: of Kepler's Third Law.
Several people raised the issue. Many t.o. participants (myself included)
sided with Grubaugh on this. Listing it as one of a "present list of
t.o. criticisms" is at the very least misleading. Insofar as it is
someting to point at in which "Grubaugh is right", is it padding,
graveyard votecounting, pure and simple.
: Grubaugh's equations for determining collinear equilibrium are
: useless, having more unknowns than knowns.
I don't recall this one. I made a tenative comment about that,
but I don't recall anybody else raising the issue on t.o., and I
was careful to note on several occasions that equilibria exist.
On the other hand, it *is* a fact that Grubaugh, when asked, produced
equilibrium conditions of insufficient accuracy to last a single orbit.
: It was foolish of Grubaugh to assert that in-line equilibrium of
: planets could be maintained against the massive gravity of the Sun.
Foolish, schmoolish. The substantive issue is, does Grubaugh's
simulation or his analysis adequately account for solar tides.
And near as I can tell, the answer is, no, it does not.
: Every competent student of the subject knows that L-3 is unstable.
: Hence, even apart from the effects of the Sun, an in-line system would
: break down in mere days, weeks or months, and certainly would not hold
: together for the minimum of several years that the "Saturnists" require.
The "hence" is incorrect. In this context, what we are saying is that
simulations with known error bounds show that it *does* break down
in less than an orbit when perterbed by 1 part in a thousand, and less
than two orbits when perterbed by 1 part in a million. Grubaugh's results
showing periodic behavior upon such large perterbations are inconsistent
with the theoretically-proved instability.
: Grubaugh claimed that polar coordinates were *self-evidently*
: preferable to rectilinear in dealing with synchronous orbits and
: perturbations thereof. In this, he only showed his ignorance of the
: subject, since mathematical truth is not dependent on coordinate systems.
We've gone over and over this one, and this characterization simply
doesn't adequately address the issue. In context, the point was that
any inaccuracies introduced by coordinate system issues are *many*
*times* smaller than the instabilities in Grubaugh's supplied initial
conditions. Several t.o. commentators agreed that there were reasons
to prefer polar coordinates in some circumstances. But for Grubaugh to
claim that analyses or simulations carried out in rectangular
coordinates contain errors of sufficient size to bring the results into
question on account of the coordinate system choice alone is wildly
wrong. The only way one gets Grubaugh being "RIGHT" one this "FRIGGIN'
ISSUE" is by totally ignoring the context, and focussing on
theoretically-true-but-quantitatively-unimportant issues.
: Grubaugh claimed that standard rectilinear integration routines
: involve an inherent error in the treatment of curvilinear motion. In
: effect, Bob said, they apply the Pythagorean equation appropriate for
: straight-line motion along the x and y axes, rather than the
: differential equation for integrating motion along a curved path. [...]
Let's look at the context; let's look at the actual code that
Grubaugh is attempting to criticize. The predictor-corrector integration
methods, and the Runge-Kutta integration methods, use the equations
of curves for the projected path. Not straight lines. The issue is
simple, and clear-cut. In the context of whether the simulations used
to evaluate his initial conditions used equations "appropriate [only]
for straight-line motion along the x and y axes", the answer is
simple and unambiguous: Grubaugh is wrong on this issue. This is
undergraduate physics, cookbook-numerical-analysis stuff. There is
no sane question here: Grubaugh is wrong on this "FRIGGIN' ISSUE",
in this friggin' context.
: Since several n-body programs have shown the in-line planetary
: arrangement to break down after an orbit or two (at best), only an
: obstinate fool would continue arguing for Grubaugh's ideas.
Again, *in* *context* this is true: it is foolish to continue to claim
that the specific in-line configuration Grubaugh proposed is stable, and
the simulations are all incorrect. Of course, this doesn't have any
strong indication that *no* general in-line scenario is possible; but
the particular one proposed by Grubaugh and evaluated, and the closely
related family of solutions he proposes, are essentially kaput.
The only way to rescue Grubaugh's position is to argue vague generalities:
*in* *context*, he is quite flatly wrong.
: Bob's own simulations have no validity because he is *assuming
: circular orbits, periodicity and stability* rather than proving anything.
: In Bob's 4-planet retrograde model, he places the planetary CG on a
: automatic circular march around the Sun. That is preposterous, a
: perfect example of assuming what you are supposed to be proving.
Specifically, in ret-ve.bas, he's assuming that the COG of the lineup
orbits in a regular circular orbit about the sun. He has not addressed
Richard Harter's objections to this point (at least, not on t.o.).
: The difference in angular momentum between the suggested former
: configuration and the present planetary system is so great as to make
: the existence of the former virtually impossible, apart from magic.
I didn't think Grubaugh's analysis addressed this point at all.
But be that as it may, it's clear that enough foreign bodies zipping
through the solar system can carry away (or supply) any necessary
angular momentum for just about any orbital transfer. But the
quantity *is* large enough for this to be a major problem for any
such scenario proposed for the recent past to address with specific
proposals and evidence. In fact, replacing "magic" with "wildly
unlikely processes", in just what way are "THE CRITICS" wrong on
this particular "FRIGGIN' ISSUE"?
: In placing a Jupiter-Saturn binary in a retrograde orbit around its
: CG, while the system moves in a prograde orbit around the Sun,
: Grubaugh has J and S dangling in inertial space, with no angular
: momentum to keep the two gas giants apart.
This seems like quite a distortion of Van Flandern's point (a point
made by others independently). It seems a very strange way of speaking
to say "angular momentum to keep the two gas giants apart". Certainly,
there are 2nd-order forces (eg: solar tides) that have a component
along the line connecting the two planets, so saying "there is nothing
to keep J and S apart" is at best oversimple. Nevertheless, *in* *context*,
the criticism is a telling one: there seems no way to keep their distance
and alignment stable when they are an order of magnitude or so closer
together than their solar orbital radius. They will tend to fall towards
each other, and will suffer the differential angular blowup such closely
aligned solar orbits do, indeed, produce. That is, even if the planets
have something "keeping them apart" (that is, they don't impact), it remains
true that the "balanced retrograde/prograde siguation" is not going to
yield a stable in-line situation.
: Most of these primary criticisms can, of course, be broken down into
: additional components, based on actual t.o "discussion," but I believe
: this is a reasonably accurate summary, hitting the most fundamental of
: issues.
It seems to at least touch on most issues. But it seems to me to distort
the criticism a bit, and it lacks any quantitative issues, eg: Grubaugh
claims there's an error: how large? What's the error expression? What,
specifically, is wrong with Runge-Kutta routines in "Numerical Recipies
in C"? How, specifically, does a simple predictor-corrector (essentially)
from "Elementary Numerical Analysis" succeed in correctly inverting
Grubaugh's posted initial conditions after 600 days, and many other
tests of accuracy and applicability, and yet (according to Grubaugh)
have wildly incorrect results? General handwaving about "curvilinear
integration" and posting differentials for path-length instead of
position simply don't address the issues at all. Just saying "your
criticisms are in error, because they use rectangular coordinates" just
doesn't cut it, especially since results employing circular coordinates
by Hahn show roughly the same results.
Let's me sum up.
On the t.o. side, analytical results show general problems with Grubaugh's
methods, such as the assumption that the plantary lineup COG has a regular
circular orbit, and multiple independent numerical simulations show that
the initial conditions Grubaugh proposes aren't even minimally stable.
These results all agree with textbook analyses of in-line equilibria,
and the simulations are using well-known and understood methods with
well-understood and very small error bounds.
On Grubaugh's side, he's made no effort to justify the assumptions of
his simulations, and his criticisms of the textbook numerical methods
(eg: they use equations for "straight line motion") are wildly incorrect.
His results disagree with textbook analyses of in-line equilibria,
and his simulations are known to have very bad behaviors when only
slightly perterbed from simple circularity.
And yet, Talbott is "now tentatively satisfied that--are you ready--
THE CRITICS ARE WRONG ON EVERY FRIGGIN' ISSUE".
I've wondered before, and I'm wondering again now. Just what does
it take to convince Talbott that 2+2=4? Talbott says "I bet you can't
do X", and we trivially accomplish it. Grubaugh says "GRAVITY needs
0.7 orbital speed to work", and this is wrong. Grubaugh's simulations
show inline equlibria remaining stable upon perterbations that theory
and well-proven simulations show are unstable. Just when does Talbott
start wondering if perhaps all these little tests going against
Grubaugh's position are, maybe, just a *slight* indication that,
--gasp-- Grubaugh is wrong, and the family of orbits he proposes
are not stable.
I am specifically interested: does Dr. Bass now think Grubaugh's
proposed family of orbits *are* potentially stable, and can he
comment on at least some of the issues, such as why the simulations
we've done show instability?
: I will make one exception to my decision not to participate in t.o
: further. Let the loudest of the critics, Paul Gans, select the most
: *persuasive* of the criticisms (and re-state it if he feels that is
: necessary). Let Paul draw on any consultation he chooses, and I will
: do the same, so that we can focus on the most obvious flaw in
: Grubaugh's claims or approach and save everyone a lot of time.
Ah, well. I'm not Gans, so Talbott will ignore me again. Sigh.
Life is hard on the net.
If anybody were listening to me, I'd say the single most persuasive
aspect of the facts of the matter are: multiple t.o. simulations agree
with theoretical predictions and have known, small error behaviors, while
Grubaugh's do not, and indeed his ret-ve.bas simulation seems to involve
an assumption known false on theoretical grounds.
--
Wayne Throop throopw%sheol.uucp@dg-rtp.dg.com
throop@aur.alcatel.com