On the Grubaugh Polar Configuration Model
Tim Thompson
Although I think you have already seen the bulk of my objections
to the Grubaugh Polar Configuration Model (GPCM), I did say that I
would gather my objections in a more orderly fashion, and I will
do that now. I will attempt to list my objections in order of
preference, meaning that those presented first are intended to be
most important. This ordering is subjective of course, and someone
else might chose to order objections differently, but I suspect
the differences would be minor over a representative collection
of physicists. Some of these objections have been seen here already,
but I believe I have also added points that have not yet been
included in earlier criticisms.
ONE (part A)
The most glaring deficit, immediately visible upon inspection
of the calculations in the appendices, is that the method chosen
by Grubaugh to physically analyze the GPCM is not applicable to
that kind of physics. This objection I consider sufficient, by
itself, to completely negate everything the paper had to say.
The Newtonian formula [ F = GMm/r^2 ] is a static formula, and
is not used in orbit calculations. The Grubaugh approach can be
recognized at once by any competent physicst as hopelessly
oversimplistic, even for a "proof of concept" idea.
Grubaugh himself only made matters worse in his response posted
for him by Ev Cochrane. I didn't keep a copy, but he made
some remark about not needing to bother with complications like
"energy", and he even put the word energy in quotation marks!
Neither the writing, nor the mathematics, carries any indication
that Grubaugh actually knows anything at all about orbits.
The proper handling of orbits can be found in condensed, thumbnail
fashion in "Fundamental Formulas of Physics", edited by Donald H.
Menzel, vol. II, chapter 29, "Celestial Mechanics", by Edgar W.
Woolard of the U.S. Naval Observatory. More proper, and full
treatments of the orbit game can be found in the old standard book
"Celestial Mechanics" by F.R. Moulton (1914, available in Dover
reprint), or the more recent "Orbital Motion" by A.E. Roy. Physics
Fans can find the basic physics explained in almost any book on
theoretical mechanics, but the treatment in Goldstein's "Classical
Mechanics" is noteworthy, and my own professor, the late Ted Clay
Bradbury wrote an excellent book, "Theoretical Mechanics", which
also covers orbits in readable (for a physicist) fashion.
ONE (part B)
I call this "part B" because it is closely tied, at least in
a philosophical sense, to part A. One of the reasons behind
Grubaugh's failure appears to be self delusion of the worst kind.
He defined the GPCM, as if by fiat, without the slightest
consideration as to whether or not the model is even physically
possible. By combining a simplistic analysis with a fantasy
model, he simply deluded himself into believing he was doing
something meaningful, when he was not.
The polar configuration is physically impossible under any
circumstances, which should be fairly obvious. In any case, even
if one did not know that, it certainly looks suspicious enough
to warrant an investigation into the basics, before one expends
effort on some kind of detailed model. Grubaugh did not do this,
which is a poor handling of the scientific method. A real scientist
should have known better.
We now know, from the models run by Dehner that the system is
unstable, as Ellenberger and Slabinski have noted in the past.
TWO
See Appendix E of Grubaugh's paper, page 48 of Aeon, III, 3.
Grubaugh never even solved his own, simplistic problem. Look at
step three, wherein we find "Since there are eight unknowns and
seven original equations, solution requires that the dimensions b,
c, and d be normalized by dividing each by a so that a/a=1, b/a=b,
c/a=c and d/a=d. This gives then three equations in three unknowns."
('a' stands for the distance from Jupiter to Saturn, 'b' from Saturn
to Venus, 'c' from Venus to Mars, 'd' from Mars to Earth.
Now it is evident that Mr. Grubaugh can't even get his high school
algebra right. One does not solve seven equations in eight unknowns.
One gets rid of an unknown, or one finds another equation. Grubaugh
chose the former, and although he never explicitly says so, he
arbitrarily sets a=1, and thinks he has solved something! At best,
this means that the derived values given for b,c, and d are not
absolute numbers, but are relative to a.
This "solution" implies that any arbitrary distance can be chosen
for Jupiter-Saturn, and that the rest of the planets, if spaced
proportionally, as his "solution" indicates, should maintain a polar
configuration. There are no boundary conditions, and no constraints,
which implies that this solution is valid for all values of 'a', even
when the planets become so widely seperated as to be essentially two
body systems, wherein Kepler's laws must apply rigorously. This is
clearly un-physical, and violates not only very basic physics, but
basic algebra as well.
THREE
It's time to consider Kepler's Laws. On page 43 (Aeon III, 3)
Grubaugh says "In regard to the apparent disagreement between the
model and Kepler's third law, it should be noted that Kepler's law
is not applicable to more than one planet if the planets are close
enough to influence each other significantly, as they clearly are
in the synchronous configuration."
This surely sounds erudite, but I have read it over and over, and
I still don't know what it means. What's this "one planet"? If there
is only one planet, then who orbits whom? Kepler's Laws express the
physics of orbital motion in a two body problem, which they will
describe exactly. Motion becomes perturbed from the Keplerian, when
the interactions require more than two bodies to be considered.
In cases where more than two bodies are to be considered, we do not
assume that some cosmic switch has suddenly turned off Kepler's Laws.
As the affect of the extra bodies increases, the motion departs smoothly
from what we would call Keplerian, and the basic laws of physics do
remain intact.
The GPCM (or any other PCM) requires that angular velocity of the
planets remain constant as radial distance from the barycenter
increases. This requires the angular momentum to go up considerably,
with very high angular momentum sequestered in the outermost planets.
This is akin, but not equal, to using the well known spinning skater
analogy to argue that the skater slows down as her arms are drawn in,
and speeds up when they extend! This is a highly unphysical system,
which certainly has the appearance of violating the law of conservation
of angular momentum, and therefore being impossible.
Grubaugh's cavalier dismissal of Kepler's Laws is just a clever
way out of being forced to explain away the physical impossibilities
involved in any PCM.
FOUR
See diagram 4, page 42 (Aeon III, 3), wherein Grubaugh proposes
a magnetic torque to provide the torque necessary to force the axis
of rotation of the Earth to precess 360 degrees/year. The diagram
shows the magnetic axies of Jupiter and Saturn as parallel, with
field lines connecting the north magnetic pole of Jupiter to the
north magnetic pole of Saturn. Last I heard, like magnetic poles
repelled one another, and unlike poles attracted. The diagram is
exceedingly impossible.
The suggested model shows the parallel field lines of the combined
fields of Jupiter and Saturn impinging on the magnetic equator of
the prone Earth, with its axis of rotation in the plane of rotation
of the other planets. The obvious presumption is that this imposed
field will grab the Earth by the waist and tug it around. Yet this
proposal violates even the simplest considerations of the physics of
electro-magnetic fields.
Even now, the Earth is bathed in an external magnetic field, that
of the Sun. The solar magnetic field is expelled from the Earth by
the Earth's own field, anmd of course, the same fate would befall
the proposed Jupiter-Saturn combined field. Since this field would
not penetrate the Earth at all, it's hard to imagine a process whereby
the torque might be applied.
Still, even if one did find such a strange torque provider, would
it be 100% efficient in converting magnetic energy into mechanical
torque? I think not. There needs to be a description of the torque
mechanism, and how much of the magnetic field energy winds up as
torque, and how much as heat deposited in the depths of the Earth?
What affect would the deposited heat have on the biosphere, or on
the thermal history of the Earth? What about coupling mechanisms
between the core (where Earth's magnetic field is generated, and where
the torque is presumably applied) and the mantle/crust? After all,
if the torque is applied to the core, as seems reasonable, it would
be very difficult for such a torque to overcome the very large moment
of inertia of the rest of the rotating Earth, even if there was a 100%
efficient couple.
The magnetic torque propose has all the earmarks of being just as
physically impossible as the rest of the model.
FIVE
The paper is as sloppy as hell. While this may be a less severe blow
to the model in principle, it indicates sloppy and careless writing by
the author, and a careless eye of the editor and/or any reviewers of
the paper.
For instance, all orbits should be around a barycenter for the
system, not the center of Jupiter. I complained about this before
and received the rebuke that it was really impolite to suggest that a
man of Grubaugh's experience didn't know what a barycenter was. Well,
all I can say is that if he knew it, why did he leave it out of his
model? It's not as if it were a major complication.
Another example: compare the numerical results listed at the end
of Appendix E, page 48 (Aeon III, 3), and table 3, on page 41. Table 3
is supposed to be a list of the numbers calculated in appendix E
Appendix E Table 3
---------- ----------
a = ------ a = 1.0 (No value shown explicitly in App. E)
b = 0.473 b = 0.475
c = 0.054 c = 0.0553
d = 0.06 d = 0.0611
The attentive reader will notice that the values for 'b' and 'c' do
not agree. This may amount to no more than an egregious typo, but
it certainly does not move one to confidence in the numbers. It is
also a noteworthy peculiarity that the numbers tabulated in table 3
are given to more significant figures than are the numbers in appendix
E, where they were actually calculated.
---
---------------------------------------------------------------
Timothy J. Thompson, Jet Propulsion Laboratory.
Earth & Space Sciences Division ...
Advanced Spaceborne Thermal Emission and Reflectance Radiometer
Board of Directors, Los Angeles Astronomical Society ...
Vice President, Mount Wilson Observatory Association ...
INTERnet/BITnet: t...@lithos.jpl.nasa.gov
NSI/DECnet: jplsc8::tim
SCREAMnet: YO!! TIM!!
GPSnet: 118:10:22.85 W by 34:11:58.27 N
Everett Cochrane
Frankly, I cannot believe the incredible statement by Tim Thompson that
Newton's equations are "static" and not applicable for determining
nominal equilibrium distances of orbiting bodies. Does Thompson mean
that if two bodies are in motion relative to each other, Newton's laws
do not apply? That is absurd. When were Newton's laws repealed?
I can use two of Newton's laws, Gm1m2/R2 and mV2/R, to find the
equilibrium orbital distance between the earth and the Sun, knowing that
the orbital period is 365 1/4 days. Now what else does Thompson want?
Surely he does not mean to say that another method of calculation will
produce a significantly different answer! All of this is too elementary
to require debate.
I can also find the RATIO of the equilibrium distances from Earth to Moon
and from Earth to Sun using only the two cited Newton equations, knowing
only that the Moon orbits the Earth 12 and a fraction times per year, and
that the two bodies are in equilibrium. If the math works, what more is
needed?
It would appear that Thompson has missed the whole idea of my model.
I have simply demonstrated that, using the two Newtonian equations, you
can produce a theoretical system in which the four planets, Saturn, Venus,
Mars and Earth orbit Jupiter synchronously, IN LINE AND IN EQUILIBRIUM.
Perhaps one of the reasons for Thompson's confusion is that the system
is not a familiar one. The participating planets revolve once around
each other with each revolution around the Sun. To show that this system
is not mathematically sound, one must show either that Newton's laws
will not yield equilibrium distances, or that I slipped on a calculation.
When we calculate the nominal orbital equilibrium positions, why should
we be surprised to find that the equations give no absolute distances
until we establish one of the distances, or the orbital period? That the
equations are dimensionless is as it should be. David Talbott asked for
figures enabling him and his co-researchers to visualize a planetary
configuration from an earthbound perspective, when placing the configuration
at different positions between the present orbits of Venus and Earth.
(In other words, the "boundaries" Thompson said are missing were already
provided and are, in fact, more narrow than theoretically necessary).
Beyond this general parameter, absolute distances of the stack from the
Sun are not stated, so that Talbott and his group can look at the effects
of variations in distances.
As in the case of the Moon and Earth, the absolute distance cannot be
determined knowing only the ratio of orbital periods. (That does not
alter the fact that the moon and Earth are in equilibrium!) Similarly,
the equilibrium positions in the model can be stated as ratios without
stating any absolute distances. I'm aghast that this requires explanation.
Thompson suggests that my "simplistic" method of calculation negates the
model. I insist, then, that he demonstrate his point by a more sophisticated
analysis to show either, (1) that the stack is not or cannot be in
equilibrium, as stated; (2) that the equilibrium distances (in ratios
to the Saturn/Jupiter distance) are significantly different from what I
have calculated. Until he provides such a demonstration, it is his
confused generalizations that are too simplistic.
Let me help him out a little. Reduce the problem to three bodies: Sun,
Jupiter and Saturn. Place Jupiter and Saturn on a line oriented 90 degrees
to the line from the Sun to the two planets' center of gravity, with
Saturn in the trailing position. In calculating equilibrium positions
I found that the ratio of the DISTANCE BETWEEN SATURN AND JUPITER to the
DISTANCE FROM THE CENTER OF GRAVITY TO THE SUN is .1074 So place the CG
at a distance to the Sun of 149.6 million kilometers (one AU). You will
see that the equilibrium distance between Saturn and Jupiter is 16.067
million kilometers, using elementary math which, to the best of my
knowledge, has not been refuted. You will also see that the angle of
Jupiter to Saturn-to-Sun is 85.255 degrees. The planets are in
equilibrium. The angle does not change. If you wish, use a different
distance to the Sun, but apply the same ratio and angle, and you will
find the equilibrium conditions at that new distance also. That is the
obvious value of dimensionless equations: Change a given condition and you
can easily calculate the effects on the system. But is it really
necessary to state the obvious?
If Thompson doubts that one can add an additional planet "in line" and
in equilibrium, I will be happy to show him where to put it to make it
work.
I am more than a little surprised discussion has stumbled along this way.
Even after making it clear that we are dealing with equilibrium positions,
not with complex orbits or changing conditions requiring time-dependent
analyses, Thompson still treats the issue as if the system is "underdescribed"
and not in equilbrium (not to mention his continuing irrelevant citations
of Kepler). Tell us, Tim, what mysterious force will intervene to
immediately unravel the synchronous orbits, or tell us in what way they
violate Kepler? And if the orbits are synchronous in the sense that I
have defined, why do you keep talking about changing conditions? All
you need to do is show why the simple three-body system is not mathematically
in equilbrium, or show why it would move from equilbrium to non-equilibrium.
I was asked by Talbott whether the system might be analogous to defining
the equilibrium of a postcard standing on end - mathematically correct,
but unworkable in the real world. What I found, however, was a natural
tendency of the system to correct itself (a tendency of all known
synchronous systems in the solar system). For example, if you disrupt
the in-line positions of the planets by a degree, you will see that the
forces change slightly, and in the direction of correction, eventually
restoring the equilibrium positions.
I would be happy to consider any criticism based on an independent
analysis.
Bob Grubaugh
May 21, 1994
Tim Thompson
>Bob Grubaugh responds to Tim Thompson:
>
>Frankly, I cannot believe the incredible statement by Tim Thompson that
>Newton's equations are "static" and not applicable for determining
>nominal equilibrium distances of orbiting bodies. Does Thompson mean
>that if two bodies are in motion relative to each other, Newton's laws
>do not apply? That is absurd. When were Newton's laws repealed?
>
"Static' implies to me something that sits around, and does not move.
Since there was nothing in your paper which dealt with motion, and there
were no quantities allowed to vary either temporally, or spatially, then
"static" sounds pretty appropriate to me. You cannot ever analyze an orbit
while ignoring both temporal and spatial variation, no matter whose
equations you ise, including Newton and Einstein. You did a lot of algebra,
but you solved no physically meaningful problem.
you seem to be under the delusion that if your system had actually been
an impossible configuration, then Newton's force law would have revealed
this fact, but that is not true. Newton's equation, as you used it, is just
another algebraic expression, and if you solve it it will give you an
answer, but interpreting the answer, and setting up the problem in the first
place is where the physics is done. You did no physics.
>I can use two of Newton's laws, Gm1m2/R2 and mV2/R, to find the
>equilibrium orbital distance between the earth and the Sun, knowing that
>the orbital period is 365 1/4 days. Now what else does Thompson want?
>Surely he does not mean to say that another method of calculation will
>produce a significantly different answer! All of this is too elementary
>to require debate.
>
Too elementary indeed. No, you cannot use Newton's laws to solve that
problem, unless you first define "equilibrium distance", which means nothing
to me, and then allow for time variation in both R and V.
[ ... ]
>
>It would appear that Thompson has missed the whole idea of my model.
>I have simply demonstrated that, using the two Newtonian equations, you
>can produce a theoretical system in which the four planets, Saturn, Venus,
>Mars and Earth orbit Jupiter synchronously, IN LINE AND IN EQUILIBRIUM.
No you have not, unless you want your planets to sit in one place, as
still as can be.
>Perhaps one of the reasons for Thompson's confusion is that the system
>is not a familiar one. The participating planets revolve once around
>each other with each revolution around the Sun. To show that this system
>is not mathematically sound, one must show either that Newton's laws
>will not yield equilibrium distances, or that I slipped on a calculation.
>
Its mathematical soundness is irrelevant, but its physical soundness
counts. Your maodel has already been run through dynamic programs by both
Dehner and Ellenberger, and it evaporated at once in both cases. How can
you continue to insist that this iis a stable configuration, when every
attempt to impart motion fails? Perhaps if Dehner is still following this,
he can remind you of his results, I did not hang onto the mesage.
>When we calculate the nominal orbital equilibrium positions, why should
>we be surprised to find that the equations give no absolute distances
>until we establish one of the distances, or the orbital period? That the
>equations are dimensionless is as it should be.
>
Do you intend to imply that *any* distance between Jupiter and Saturn will
produce a synchronous system, if the orbits are spaced proportionally as
you have described? For the purpose of answering this question, ignore any
outside influences, so that the Jupiter-Saturn distance can be expanded to
arbitrary size without introducing outside perturbations.
[ ... ]
>Thompson suggests that my "simplistic" method of calculation negates the
>model. I insist, then, that he demonstrate his point by a more sophisticated
>analysis to show either, (1) that the stack is not or cannot be in
>equilibrium, as stated; (2) that the equilibrium distances (in ratios
>to the Saturn/Jupiter distance) are significantly different from what I
>have calculated. Until he provides such a demonstration, it is his
>confused generalizations that are too simplistic.
>
This has already been done, as I noted above. both of the attempts I am
aware of to impart motion to this system have resulted in instant
catastrophe. I see no reason to add to the list. You may feel free to
explain why your system fails the dynamic test.
[ ... ]
>I am more than a little surprised discussion has stumbled along this way.
>Even after making it clear that we are dealing with equilibrium positions,
>not with complex orbits or changing conditions requiring time-dependent
>analyses,
This is absolute garbage. You can never, ever, under any circumstances
analyze an orbit in this way, period, end of sentence.
>Thompson still treats the issue as if the system is "underdescribed"
You had more unknowns than you had equations, and that fits the definition
for underdescribed last I heard. mathematicians may feel free to correct me
if necessary.
>and not in equilbrium (not to mention his continuing irrelevant citations
>of Kepler).
Kepler's laws are not irrelevant if you want to do physics instead of
algebra.
>Tell us, Tim, what mysterious force will intervene to
>immediately unravel the synchronous orbits, or tell us in what way they
>violate Kepler?
>
As already twice indicated, the mysterious force of gravity will
destroy the system in a "heart-beat".
[ ... ]
>
>I would be happy to consider any criticism based on an independent
>analysis.
>
then you will be happy to explain why the system is dynamically unstable,
as noted above.
Richard...@ccmail.jpl.nasa.gov
Thompson) wrote: (Responding to an article abput Bob Grubaugh's PC model)
> >Perhaps one of the reasons for Thompson's confusion is that the system
> >is not a familiar one. The participating planets revolve once around
> >each other with each revolution around the Sun. To show that this system
> >is not mathematically sound, one must show either that Newton's laws
> >will not yield equilibrium distances, or that I slipped on a calculation.
> >
> Its mathematical soundness is irrelevant, but its physical soundness
> counts. Your maodel has already been run through dynamic programs by both
> Dehner and Ellenberger, and it evaporated at once in both cases. How can
> you continue to insist that this iis a stable configuration, when every
> attempt to impart motion fails? Perhaps if Dehner is still following this,
> he can remind you of his results, I did not hang onto the mesage.
#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*
I believe that Ellenberger used a graphical program called 'Gravity' - I
don't know what Dehner used.
I have been doing some modeling with a program that I am developing. I
have been advised that it is typical for such programs to have an inherent
error that must be corrected: The incremental points computed for the
paths of modeled orbits tend to make an orbit more "open" than it should be
( the more elliptical the orbit, the more obvious the error).
Is it possible that either or both of their programs do not have the
necessary correction designed in? If so, how does that affect the dynamic
modeling referred to above?
Benjamin T. Dehner
>In article ecoc...@delphi.com, Everett Cochrane <ecoc...@delphi.com> () writes:
>>Bob Grubaugh responds to Tim Thompson:
...[some stuff]
>>Perhaps one of the reasons for Thompson's confusion is that the system
>>is not a familiar one. The participating planets revolve once around
>>each other with each revolution around the Sun. To show that this system
>>is not mathematically sound, one must show either that Newton's laws
>>will not yield equilibrium distances, or that I slipped on a calculation.
>>
> Its mathematical soundness is irrelevant, but its physical soundness
>counts. Your maodel has already been run through dynamic programs by both
>Dehner and Ellenberger, and it evaporated at once in both cases. How can
>you continue to insist that this iis a stable configuration, when every
>attempt to impart motion fails? Perhaps if Dehner is still following this,
>he can remind you of his results, I did not hang onto the mesage.
Yes, I'm still around. I'm sending a copy of the paper off to
Grubaugh RSN, but, in short, here is the problem:
I'll assume the analysis is correct that there is a net zero gravi-
tational forces on the planets *to begin with*. However, the initial
conditions require that the entire configuration move in such a way as to
have constant angular velocity around the sun, to retain the polar-
configuration form. Thus, after a VERY short time, the planets have moved
away from the statically balanced configuration, and the interplanetary
interaction are no longer balanced. Then the entire ``zero sum'' stability
is gone.
...[more stuff]
Ben
--
-----------------------------------------------------------------------------
Benjamin T. Dehner Dept. of Physics and Astronomy PGP public key
b...@iastate.edu Iowa State University available on request
Ames, IA 50011
Benjamin T. Dehner
>In article <2rr685$m...@grover.jpl.nasa.gov>, t...@scn1.jpl.nasa.gov (Tim
>Thompson) wrote: (Responding to an article abput Bob Grubaugh's PC model)
>> >Perhaps one of the reasons for Thompson's confusion is that the system
>> >is not a familiar one. The participating planets revolve once around
>> >each other with each revolution around the Sun. To show that this system
>> >is not mathematically sound, one must show either that Newton's laws
>> >will not yield equilibrium distances, or that I slipped on a calculation.
>> >
>> Its mathematical soundness is irrelevant, but its physical soundness
>> counts. Your maodel has already been run through dynamic programs by both
>> Dehner and Ellenberger, and it evaporated at once in both cases. How can
>> you continue to insist that this iis a stable configuration, when every
>> attempt to impart motion fails? Perhaps if Dehner is still following this,
>> he can remind you of his results, I did not hang onto the mesage.
>#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*#*
>I believe that Ellenberger used a graphical program called 'Gravity' - I
>don't know what Dehner used.
I wrote my own N-body code (in Fortran), using a ordinary
differential equation initial value problem integrator called 'DEABM' from
a library called DEPAC. I also hacked together a quick X-windows program
in C to graphically display the results. The source for all 3 are available
on request.
>I have been doing some modeling with a program that I am developing. I
>have been advised that it is typical for such programs to have an inherent
>error that must be corrected: The incremental points computed for the
>paths of modeled orbits tend to make an orbit more "open" than it should be
>( the more elliptical the orbit, the more obvious the error).
>Is it possible that either or both of their programs do not have the
>necessary correction designed in? If so, how does that affect the dynamic
>modeling referred to above?
I haven't done a complete analysis, but I did notice a dependance
on the error tolerances used in the integrator. Under no conditions,
however, did the configuration seem stable. As I explained in another post,
this is basically do to the fact that the initial condition of constant
angular velocity about the Sun quickly carries the planets out of the
`zero sum' positions.
Richard...@ccmail.jpl.nasa.gov
(Benjamin T. Dehner) wrote:
>
> I haven't done a complete analysis, but I did notice a dependance
> on the error tolerances used in the integrator. Under no conditions,
> however, did the configuration seem stable. As I explained in another post,
> this is basically do to the fact that the initial condition of constant
> angular velocity about the Sun quickly carries the planets out of the
> `zero sum' positions.
>
Ben
A quick way to check is to set up a "sun" with a "planet" in a long
elliptical orbit. If the code is uncorrected, the planet's orbit will
"precess".
Rick Smith
Boucher David
#Bob Grubaugh responds to Tim Thompson:
#
#Frankly, I cannot believe the incredible statement by Tim Thompson that
#Newton's equations are "static" and not applicable for determining
#nominal equilibrium distances of orbiting bodies. Does Thompson mean
#that if two bodies are in motion relative to each other, Newton's laws
#do not apply? That is absurd. When were Newton's laws repealed?
#
#I can use two of Newton's laws, Gm1m2/R2 and mV2/R, to find the
#equilibrium orbital distance between the earth and the Sun, knowing that
#the orbital period is 365 1/4 days. Now what else does Thompson want?
#Surely he does not mean to say that another method of calculation will
#produce a significantly different answer! All of this is too elementary
#to require debate.
If the bodies are in motion, the value of "R" can and does CHANGE; the
"equilibrium orbital distance" between the earth and the sun changes
throughout the year, as does the equilibrium distance between the
earth and moon (which is why the eclipse we just had was annular instead
of total). As the relative position, velocity, and acceleration of
bodies are interdependent variables, Grumbaugh's calculation of a
single "equilibrium orbital distance" while neglecting tangential
acceleration is naive and unworkable.
#I can also find the RATIO of the equilibrium distances from Earth to Moon
#and from Earth to Sun using only the two cited Newton equations, knowing
#only that the Moon orbits the Earth 12 and a fraction times per year, and
#that the two bodies are in equilibrium. If the math works, what more is
#needed?
But if you include terms for the tangential accelerations produced by
the interactions of the bodies, the math does NOT work. Are you even
aware that the orbits of the earth and moon are elliptical, not
circular? That means that the orbital velocities and distances from
sun to earth and from earth to moon are NOT CONSTANT!
- db
--
****** "It is a capital mistake to theorise before one has data. ******
****** Insensibly one begins to twist facts to suit theories ******
****** instead of theories to suit facts." - Sherlock Holmes ******
*************************************************************************
Richard...@ccmail.jpl.nasa.gov
> I wrote my own N-body code (in Fortran), using a ordinary
> differential equation initial value problem integrator called 'DEABM' from
> a library called DEPAC. I also hacked together a quick X-windows program
> in C to graphically display the results. The source for all 3 are available
> on request.
>
I would appreciate seeing the source code(s). You can use the following
mail address: Richard...@ccmail.jpl.nasa.gov.
Ken Smith
garbage (to be polite) which arrived at this site today.
In article <RMzMdT3....@delphi.com> Everett Cochrane <ecoc...@delphi.com> writes:
>Bob Grubaugh responds to Tim Thompson:
>
>Frankly, I cannot believe the incredible statement by Tim Thompson that
>Newton's equations are "static" and not applicable for determining
>nominal equilibrium distances of orbiting bodies. Does Thompson mean
^
In the subsequent argument Grubaugh assumes that the word "two" is
inserted here.
>that if two bodies are in motion relative to each other, Newton's laws
^^^
>do not apply? That is absurd. When were Newton's laws repealed?
>
>I can use two of Newton's laws, Gm1m2/R2 and mV2/R, to find the
^^^^^^^^ ^^^^^
>equilibrium orbital distance between the earth and the Sun, knowing that
>the orbital period is 365 1/4 days. Now what else does Thompson want?
>Surely he does not mean to say that another method of calculation will
>produce a significantly different answer! All of this is too elementary
>to require debate.
The first of these is Newton's law of universal gravitation.
It gives the force between *two* bodies.
If there are more than *two* bodies in the system you *must* include
the forces between all of them.
In your system, in which you claim that four planets were in orbit
around Jupiter there are *six* bodies involved: Sun, Jupiter, Saturn,
Earth, Venus and Mars, in order of decreasing mass.
This gives 15 different pairs of bodies, and so 15 different forces
*must* be included.
The second one derives from the formula a = (V^2)/R, which is the
acceleration of a body moving *with constant speed V* about a *fixed
point*, in a *circle of radius R*
Now the Earth does not move with constant speed V (have you heard of
Kepler's 2nd law?), nor does it move about a the fixed Sun (it moves
about the centre of the solar system), nor does it move in a circle
(have you heard of Kepler's 1st law?)
However the orbit is not too far from a circle, and the mass of the
Sun is so much greater than the mass of the Earth that assuming a
fixed center is not too bad, but they are both only approximations.
You should read Isaac Asimov's title essay in his book _The Relativity
of Wrong_; some things are more wrontg than others.
But the orbit of the Earth changes over time due to the influence of
the other planets. Does the name Milankovich mean anything to you?
If not, can I suggest that you should learn something about orbital
mechanics before posting any more drivel?
I don't know what your background is, but a first year student at this
institution who put forward this stuff in our *introductory* mechanics
course would fail miserably.
[deletions]
>I would be happy to consider any criticism based on an independent
>analysis.
Consider the above "an independent analysis" - I haven't communicated
with any of the other critics in any way.
>Bob Grubaugh
>May 21, 1994
Ken Smith
--
Dr. Ken Smith | snailmail: Department of Mathematics,
email: k...@maths.uq.oz.au | The University of Queensland,
Mathematician by profession; | St Lucia, Qld. 4072.
reason sometimes rules. | Australia.
Tom Swanson
>You should read Isaac Asimov's title essay in his book _The Relativity
>of Wrong_; some things are more wrontg than others.
>
Tom (Chris) Swanson
University of Ediacara
Professor of Darwin Physics
Larson Chair of Creative Drawing