Guarino, and by extention Harshman, et al, are not considering a real isolated system of bodies

[T Pagano]

On Wed, 9 May 2012 19:23:27 -0700 (PDT), "g...@risky-biz.com"
<gdgu...@gmail.com> wrote:

>On May 9, 9:18 pm, T Pagano <not.va...@address.net> wrote:
>> On Tue, 8 May 2012 19:43:06 -0700 (PDT), "g...@risky-biz.com"
>
>>
>> <gdguar...@gmail.com> wrote:
>> >On May 8, 5:05 pm, T Pagano <not.va...@address.net> wrote:
>> >> On Sun, 6 May 2012 18:40:34 -0700 (PDT), "g...@risky-biz.com"
>>
>> >> <gdguar...@gmail.com> wrote:
>> >> >On May 6, 8:43 pm, T Pagano <not.va...@address.net> wrote:
>>
>> >Firstly, thank you for your reply. I mean that sincerely. It should
>> >have been in the original thread, but you have made a reasonable
>> >facsimile of a regular newsgroup response and I commend you for it.
>> >Keep it up.
>>

snip for brevity


>
>OK. Then take a system of separate bodies (with some distance between
>them) that are distributed in a spherical shape. If we calculate the
>gravitational forces on any one of them that is say 1/3 of the way out
>from the center, there will be other masses in all directions. The
>pull toward the center will necessarily be less than it would be if
>all of the (rest of the) mass was concentrated at the center.

Again, I concede that in calculating the gravitational force vector on
any body in an isolated system one must perform the vector addition
for each two body pairing in a system and not by simplifying matters
by assuming the mass of the system is at the COM.

Nonetheless the net gravitational force vector on any body in an
isolated system ALWAYS points to the COM. And any body located at the
COM will never have any net force applied to it. So far Guarino, et
al have effectively denied this.


snip for brevity


>> >>         a.  Harshman ignored all of the other two body pair forces on
>> >> the Earth from the billions of galaxies scattered in spherical shells
>> >> around the Earth.  The neoTychoan system is made up of every body in
>> >> the universe.  Find us a physicist who'll agree with that.
>>
>> >He didn't ignore them, and neither do I. We use the equation to gauge
>> >how much mass would be needed to counterbalance the Sun at various
>> >distances. The results tell us that the effect of those distant masses
>> >is infinitesimal by comparison.
>>
>> 1.  I only realized yesterday that Harshman, et al, weren't
>> criticizing the neoTychoan Model as proposed,  but were, in effect,
>> attacking the initial conditions of the model.  Specifically Harshman
>> was attacking the initial condition that the Earth was located at the
>> COM of that System.
>
>I answered this elsewhere. I'll let John confirm this for himself, but
>that is not what he is claiming. To be sure, he does not believe that
>the Earth is at the Universe's CoM, or even that the Universe has a
>CoM. Likewise, I'm sure he does not believe that the Sun could make a
>1AU orbit by any known physics. But he has decided to show that a
>stationary Earth cannot be squared with Newtonian physics even if we
>assume all of those things.
>
>> 2.  If the Earth "is" colocated at COM of the universe all of the
>> radial gravitational force vectors from the Earth to each of the
>> bodies in the Universe (including the Sun) would balance to zero.
>
>No they wouldn't. Try two stars of unequal masses and a peanut at the
>CoM between them. Use the Law of Universal Gravitation. If the ratio
>between the stars' masses is 2:1, the ration of their gravitational
>forces on the peanut will be 8:1, in other words, unbalanced. A 3:1
>mass ratio would produce a 27:1 ratio of forces. The only ratio that
>allows a balance of forces at the CoM is 1:1.

The biggest flaw in this analysis is that Guarino fails to
comprehend----with regard to the Third Law----that it is applicable to
the system as a whole and NOT the individual particles (or bodies) in
the system. If the system is genuinely isolated all the forces "in
the system" balance to zero. The system cannot apply a net force to
itself. Which effectively means no net force is ever appled at the
COM. It is irrelevent whether a body is located at that special point
or not.




__________________________________________________________________
WHY GUARINO'S EXAMPLE IS NOT ANALOGUOUS TO THE NEOTYCHOAN MODEL
--------------------------------------------------------------------------------------------
1. In the absence of specifics Guarino's example implies that the two
stars are fixed-and-held-in-place (and at rest relative to one
another) and in a gravitational tugging match on the peanut which
apparently is not held in place. And that the peanut will be
accelerated by an unbalanced match. Under these conditions the system
is NOT isolated and the Third Law of Motion doesn't apply. Some
outside force is holding the two sun's fixed and stationary. On the
other hand the neoTychoan model is an isolated system.

2. Another possible interpretation of Guarino's conditions is that he
is mistakenly assuming that Sun M and the peanut are an isolated
system and Sun 2M and the peanut is an isoloated system. He then
applies Newton's Law of Gravitation to each isolated system. And
finally he conjoins the two isolated systems and argues that the
peanut will be accelerated. In this situation the peanut is not at
the center of mass in either of the two isolated systems and certianly
not in the inappropriately conjoining of the two.

3. The example is not analogous to the neoTychoan model.


_________________________________________________________
ACCORDING TO THE THIRD LAW
-------------------------------------------------------------------------------
1. The gravitational forces between star M and the peanut are equal
and opposite; likewise between star 2M and the peanut. They balance
at the COM where the peanut happens to be located. The COM is a
special location and that's where the peanut is located. In any
system of particles no net force will be appled "at" the COM. Draw
all the vectors; they balance to zero.

2. Furthermore the two stars are NOT fixed-and-held-in-place and in
a tugging match with the peanut at the COM; they would be accelerating
towards the COM. And according to the Third Law their accelerations
would be such that the COM will not change. They will collide at the
COM.


snipped


Regards,
T Pagano

[Greg Guarino]

This is a more important concept than you realize. "Simplifying" is the
correct word here. It is a useful approximation that we can employ when
the system in question is (effectively) all in the same direction and
(effectively) all at the same distance from us. So the Andromeda galaxy
qualifies. The difference in direction between the "left" and "right"
sides of Andromeda are negligible at this distance, as are the distances
between the near edge and far edge of that galaxy.

Recognize mostly that it is a useful approximation rather than reality.
Every star, planet and rock in the Milky Way exerts a (small)
gravitational force on every one of its counterparts in Andromeda.
Because of the distance between them, we can render the calculation
easier by pretending the forces are applied to the center of mass of
each galaxy, but that is not actually what is going on.

Jupiter's gravity distorts the shape of its moons precisely because the
gravitation between them cannot be reduced to forces applied to their
respective CoMs. It attracts the near side of the moon more strongly
than the far side, stretching it in the process. Earth's tides work the
same way.

> Nonetheless the net gravitational force vector on any body in an
> isolated system ALWAYS points to the COM. And any body located at the
> COM will never have any net force applied to it. So far Guarino, et
> al have effectively denied this.

I agree. We have done so, and effectively.

True

Which effectively means no net force is ever appled at the
> COM.

Not true. We can in certain circumstances pretend that an external force
applied to a system is applied to its center of mass, but that's not
what is actually happening. This may be your biggest misunderstanding.

It is irrelevent whether a body is located at that special point
> or not.

> __________________________________________________________________
> WHY GUARINO'S EXAMPLE IS NOT ANALOGUOUS TO THE NEOTYCHOAN MODEL
> --------------------------------------------------------------------------------------------
> 1. In the absence of specifics Guarino's example implies that the two
> stars are fixed-and-held-in-place

That is certainly not what I meant, although I may not have made it
clear. Lets assume two stars orbiting around their mutual center of mass.

(and at rest relative to one
> another) and in a gravitational tugging match on the peanut which
> apparently is not held in place. And that the peanut will be
> accelerated by an unbalanced match. Under these conditions the system
> is NOT isolated and the Third Law of Motion doesn't apply. Some
> outside force is holding the two sun's fixed and stationary.

I assure you the idea of two stars being "held in place" never entered
my mind. Nor would it.

On the
> other hand the neoTychoan model is an isolated system.
>
> 2. Another possible interpretation of Guarino's conditions is that he
> is mistakenly assuming that Sun M and the peanut are an isolated
> system and Sun 2M and the peanut is an isoloated system.

Again , not so. For the moment let's assume the three proposed bodies
are the entire universe.

He then
> applies Newton's Law of Gravitation to each isolated system. And
> finally he conjoins the two isolated systems and argues that the
> peanut will be accelerated. In this situation the peanut is not at
> the center of mass in either of the two isolated systems and certianly
> not in the inappropriately conjoining of the two.

None of that bears any resemblance to the example I intended.

>
> 3. The example is not analogous to the neoTychoan model.
>
>
> _________________________________________________________
> ACCORDING TO THE THIRD LAW
> -------------------------------------------------------------------------------
> 1. The gravitational forces between star M and the peanut are equal
> and opposite; likewise between star 2M and the peanut.

True.

They balance
> at the COM where the peanut happens to be located.

Untrue, unless the Law of Universal Gravitation is wrong. Is it? That's
part of what you snipped. Do the calculations. Newton intended for his
equations to be consistent. You can't just throw this one out.

The COM is a
> special location and that's where the peanut is located. In any
> system of particles no net force will be appled "at" the COM. Draw
> all the vectors; they balance to zero.

A net force will indeed be applied to an *object* at the center of mass,
unless the two stars are of equal mass. Newton's equation demands it.
Try it for yourself.

> 2. Furthermore the two stars are NOT fixed-and-held-in-place and in
> a tugging match with the peanut at the COM; they would be accelerating
> towards the COM. And according to the Third Law their accelerations
> would be such that the COM will not change. They will collide at the
> COM.

True enough. If they were not in orbit the two stars would eventually
collide, but not until after the peanut had already collided with the
more massive star.

[Rolf]

T Pagano wrote:
> On Wed, 9 May 2012 19:23:27 -0700 (PDT), "g...@risky-biz.com"

[snip snip]

I just wonder, how does the geostationary model explain the existence of
Earth's magnetic field, and the way it moves over time?

Rolf

> Regards,
> T Pagano

[John Harshman]

Of course we've denied this, because it isn't true. You have been shown
clear examples demonstrating that it isn't true and in fact can't be
true except under very special circumstances. (Oddly, those special
circumstances are present in the only concrete example you've ever
tried, so I suspect you have at least some inkling of your problem here.)

The third law applies to any subset of bodies in the system. We can
agree that at least two bodies are needed, though. And yes, an net force
can indeed be applied at the CoM. You have always ignored examples,
again I suspect because you realize on some level that if you didn't
ignore them they would sink your boat.

So here's one again, so you can ignore it. Consider an isolated system
consisting of planet A with mass equal to the earth, planet B with mass
twice earth's, in stable, circular orbits about each other, with a
distance of 300,000 miles. And a peanut at the center of mass (200,000
miles from A and 100,000 from B). What is the ratio of forces on the
peanut from planet A and planet B? According to you that ratio must be
1. According to Newton it's 1/8. Who's right, you or Newton?

Your objections below are of course irrelevant.

> WHY GUARINO'S EXAMPLE IS NOT ANALOGUOUS TO THE NEOTYCHOAN MODEL
> --------------------------------------------------------------------------------------------
> 1. In the absence of specifics Guarino's example implies that the two
> stars are fixed-and-held-in-place (and at rest relative to one
> another) and in a gravitational tugging match on the peanut which
> apparently is not held in place.

No, in fact the example implies nothing about current motion, which is
irrelevant to the instantaneous force calculation.

> And that the peanut will be
> accelerated by an unbalanced match. Under these conditions the system
> is NOT isolated and the Third Law of Motion doesn't apply.

Why is the system not isolated? You need to look at the definitions
again. "Isolated" says nothing about all parts of the system being free
from accelleration. What a bizarre notion.

> Some
> outside force is holding the two sun's fixed and stationary. On the
> other hand the neoTychoan model is an isolated system.

No outside force is necessary or implied.

> 2. Another possible interpretation of Guarino's conditions is that he
> is mistakenly assuming that Sun M and the peanut are an isolated
> system and Sun 2M and the peanut is an isoloated system. He then
> applies Newton's Law of Gravitation to each isolated system. And
> finally he conjoins the two isolated systems and argues that the
> peanut will be accelerated. In this situation the peanut is not at
> the center of mass in either of the two isolated systems and certianly
> not in the inappropriately conjoining of the two.

This is not a possible interpretation unless you're a weasel desperately
trying to find a way out. He clearly states that both bodies and the
peanut constitute a single system.

> 3. The example is not analogous to the neoTychoan model.

In what way, exactly? The question is whether there is any net force on
an object at the center of mass of the system. You say no, his example
shows that you're wrong. What's special about your system that alters
Newton's laws?

> ACCORDING TO THE THIRD LAW
> -------------------------------------------------------------------------------
> 1. The gravitational forces between star M and the peanut are equal
> and opposite; likewise between star 2M and the peanut. They balance
> at the COM where the peanut happens to be located.

Whoops, sorry. No balance. M-peanut forces balance, but that ends up
with both bodies moving toward each other. 2M-peanut forces also
balance, but again both bodies move toward each other. But M-peanut and
2M-peanut forces most certainly do not balance each other, since the
2M-peanut force has 8 times the strength of the M-peanut force. So the
peanut is going to accelerate toward 2M.

> The COM is a
> special location and that's where the peanut is located. In any
> system of particles no net force will be appled "at" the COM. Draw
> all the vectors; they balance to zero.

You draw the vectors. They balance to zero only in that the CoM itself
doesn't move. The peanut moves, though.

> 2. Furthermore the two stars are NOT fixed-and-held-in-place and in
> a tugging match with the peanut at the COM; they would be accelerating
> towards the COM. And according to the Third Law their accelerations
> would be such that the COM will not change. They will collide at the
> COM.

True if the masses were initially stationary. But the peanut will
collide with 2M long before M and 2M collide.

[Inez]

> _________________________________________________________
> ACCORDING TO THE THIRD LAW
> --------------------------------------------------------------------------- ----
> 1.   The gravitational forces between star M and the peanut are equal
> and opposite; likewise between star 2M and the peanut.  They balance
> at the COM where the peanut happens to be located.  The COM is a
> special location and that's where the peanut is located.   In any
> system of particles no net force will be appled "at" the COM.  Draw
> all the vectors; they balance to zero.
>

It always surprises me how things that are obvious are so non-obvious
to you. If two objects of unequal mass are orbiting each other the
CoM is closer to the heavier one, right? If a peanut is at that
point, according to you the heavier and closer object exerts the same
force as the lighter and further away one. Lighter objects therefore
must exert more gravity than heavy ones in your special universe.

[Mark Isaak]

On 5/21/12 10:48 AM, T Pagano wrote:
>
> Nonetheless the net gravitational force vector on any body in an
> isolated system ALWAYS points to the COM. And any body located at the
> COM will never have any net force applied to it. So far Guarino, et
> al have effectively denied this.

Do the math, and you will deny it, too. Go ahead: For an isolated
system, try the Sun, Earth, and the last orbit of the Space Shuttle.
Try it once with the Shuttle between the Sun and Earth and once with the
Shuttle one quarter orbit from there.

Show your work:











--
Mark Isaak eciton (at) curioustaxonomy (dot) net
"It is certain, from experience, that the smallest grain of natural
honesty and benevolence has more effect on men's conduct, than the most
pompous views suggested by theological theories and systems." - D. Hume

[Walter Bushell]

Tony would fail physics for football players at Whatsamatter U.

--
This space unintentionally left blank.

[Charles Brenner]

That's brilliant.

[Mitchell Coffey]

On May 22, 7:37 am, Walter Bushell <pr...@panix.com> wrote:
> Tony would fail physics for football players at Whatsamatter U.

It kind'a makes you feel discouraged.

Mitchell

[T Pagano]

On Mon, 21 May 2012 15:38:09 -0400, Greg Guarino <gdgu...@gmail.com>
wrote:

This example is not illustrative of the error I was making.

>
>Jupiter's gravity distorts the shape of its moons precisely because the
>gravitation between them cannot be reduced to forces applied to their
>respective CoMs. It attracts the near side of the moon more strongly
>than the far side, stretching it in the process. Earth's tides work the
>same way.

This isn't illustrative of my error. If one does the gravitational
vector addition upon any particular particle it will point towards the
COM and NOT the center of the larger body. In the Heliocentric model
the planets do NOT revolve around the center of the Sun. The sun
revolves around the COm of the heliocentric model.

>
>> Nonetheless the net gravitational force vector on any body in an
>> isolated system ALWAYS points to the COM. And any body located at the
>> COM will never have any net force applied to it. So far Guarino, et
>> al have effectively denied this.
>
>I agree. We have done so, and effectively.

So far this hasn't been shown.
>
>> snip for brevity

snip for brevity

>>>> 2. If the Earth "is" colocated at COM of the universe all of the
>>>> radial gravitational force vectors from the Earth to each of the
>>>> bodies in the Universe (including the Sun) would balance to zero.
>>>
>>> No they wouldn't. Try two stars of unequal masses and a peanut at the
>>> CoM between them. Use the Law of Universal Gravitation. If the ratio
>>> between the stars' masses is 2:1, the ration of their gravitational
>>> forces on the peanut will be 8:1, in other words, unbalanced. A 3:1
>>> mass ratio would produce a 27:1 ratio of forces. The only ratio that
>>> allows a balance of forces at the CoM is 1:1.
>>
>> The biggest flaw in this analysis is that Guarino fails to
>> comprehend----with regard to the Third Law----that it is applicable to
>> the system as a whole and NOT the individual particles (or bodies) in
>> the system. If the system is genuinely isolated all the forces "in
>> the system" balance to zero. The system cannot apply a net force to
>> itself.
>
>True
>
>Which effectively means no net force is ever appled at the
>> COM.
>
>Not true. We can in certain circumstances pretend that an external force
>applied to a system is applied to its center of mass, but that's not
>what is actually happening. This may be your biggest misunderstanding.

The Third Law applies to an isolated system where no external force is
applied.

>
>It is irrelevent whether a body is located at that special point
>> or not.
>
>> __________________________________________________________________
>> WHY GUARINO'S EXAMPLE IS NOT ANALOGUOUS TO THE NEOTYCHOAN MODEL
>> --------------------------------------------------------------------------------------------
>> 1. In the absence of specifics Guarino's example implies that the two
>> stars are fixed-and-held-in-place
>
>That is certainly not what I meant, although I may not have made it
>clear. Lets assume two stars orbiting around their mutual center of mass.

No, let's stick with your example with my understanding of it
corrected.

>
>(and at rest relative to one
>> another) and in a gravitational tugging match on the peanut which
>> apparently is not held in place. And that the peanut will be
>> accelerated by an unbalanced match. Under these conditions the system
>> is NOT isolated and the Third Law of Motion doesn't apply. Some
>> outside force is holding the two sun's fixed and stationary.
>
>I assure you the idea of two stars being "held in place" never entered
>my mind. Nor would it.

Fair enough. Let's stick with your original example now that my
understanding of your example is corrected.

>
> On the
>> other hand the neoTychoan model is an isolated system.
>>
>> 2. Another possible interpretation of Guarino's conditions is that he
>> is mistakenly assuming that Sun M and the peanut are an isolated
>> system and Sun 2M and the peanut is an isoloated system.
>
>Again , not so. For the moment let's assume the three proposed bodies
>are the entire universe.

Fair enough. Let's stick with your original example now that my
understanding of your example is corrected.

>
> He then
>> applies Newton's Law of Gravitation to each isolated system. And
>> finally he conjoins the two isolated systems and argues that the
>> peanut will be accelerated. In this situation the peanut is not at
>> the center of mass in either of the two isolated systems and certianly
>> not in the inappropriately conjoining of the two.
>
>None of that bears any resemblance to the example I intended.

Fair enough. Let's stick with your original example now that my
understanding of your example is corrected.

>>
>> 3. The example is not analogous to the neoTychoan model.
>>
>>
>> _________________________________________________________
>> ACCORDING TO THE THIRD LAW
>> -------------------------------------------------------------------------------
>> 1. The gravitational forces between star M and the peanut are equal
>> and opposite; likewise between star 2M and the peanut.
>
>True.
>
>They balance
>> at the COM where the peanut happens to be located.
>
>Untrue, unless the Law of Universal Gravitation is wrong. Is it? That's
>part of what you snipped. Do the calculations. Newton intended for his
>equations to be consistent. You can't just throw this one out.

The only way for the peanut to reside exactly at the COM in this
example is for the peanut to be massless. Calculating the COM only
requires the four basic operations. Let's look at Guarino's example
again more carefully with my corrected understanding:


[Guarino's thought experiment]

>No they wouldn't. Try two stars of unequal masses and a peanut at the
>CoM between them. Use the Law of Universal Gravitation. If the ratio
>between the stars' masses is 2:1, the ration of their gravitational
>forces on the peanut will be 8:1, in other words, unbalanced. A 3:1
>mass ratio would produce a 27:1 ratio of forces. The only ratio that
>allows a balance of forces at the CoM is 1:1.

[End thought experiment]

1. Guarino's initial conditions are that there are two suns with
unequal masses at some unspecified distance between them with an
attendent COM (1). Both are along one dimenstion (let's say the x
axis).

2. Then Guarino inserts the peanut at the x coordinate of COM (1).
Unfortunately the COM of this new system has changed ever-so-slightly
and no longer resides at the coordinate of COM (1) but at the x
coordinate of a new COM (2).

3. The net gravitiational vector on the peanut will be directed at
the new COM (2) and its acceleration (along with that of the two suns)
will be such that the new COM (2) will not be accelerated.
If COM (2) was at rest it will remain at rest.

4. All three bodies will collide at COM (2).


And this example doesn't lay a glove on the neoTychoan model. It also
doesn't demonstrate that a body genuinely at the COM of an isolated
system of particles will be accelerated by another body in the
isolated system. Such would violate the Third Law.

Try as you might you will not solve this problem with a simple one
dimensional example with three bodies.

>
>The COM is a
>> special location and that's where the peanut is located. In any
>> system of particles no net force will be appled "at" the COM. Draw
>> all the vectors; they balance to zero.
>
>A net force will indeed be applied to an *object* at the center of mass,
>unless the two stars are of equal mass. Newton's equation demands it.
>Try it for yourself.

You inserted the peanut at the x coordinate of COM (1) but adding that
new mass to the isolated system altered the COM of that new "three"
body system ever so slightly such that it was no longer at COM (1).

You're going have to devise a thought experiment where a body is
actually located at the COM of some isolated system.

>
>> 2. Furthermore the two stars are NOT fixed-and-held-in-place and in
>> a tugging match with the peanut at the COM; they would be accelerating
>> towards the COM. And according to the Third Law their accelerations
>> would be such that the COM will not change. They will collide at the
>> COM.
>
>True enough. If they were not in orbit the two stars would eventually
>collide, but not until after the peanut had already collided with the
>more massive star.

The initial conditions are not terribly clear. My understanding is
this:

1. You have a binary star system of two stars of unequal masses at
some unspecified distance between the two revolving around their
COM (1) in a two dimensional plane.

2. Then you place a peanut, at rest, at the (x,y) coordinates of
COM (1). The addition of the new mass will alter the COM of the
system ever so slightly to COM (2).

3. The calcualtion isn't terribly easy, but looking at the vectors at
various points in the orbit of the binary stars it appears that the
peanut will be pulled into an orbit around COM (2) and will not be
accelerated towards the larger sun.

4. And the question for Harshman who denies Centrifugal forces in non
inertial frames: what keeps the smaller sun from accelerating towards
the larger sun? Harshman has asserted that Mercury is not accelerated
towards the Sun in the Heliocentric model due to the gravitational
forces of the eight other planets. Care to defend that claim?


Regards,
T Pagano

[Greg Guarino]

Excellent.

> Lighter objects therefore
> must exert more gravity than heavy ones in your special universe.

It's even more special than that. A peanut half the distance between the
CoM and the more massive object will be drawn *away* from it, toward the
CoM, eventually colliding with the first peanut.

[John Harshman]

Not true. If the center of mass of the peanut is placed at the center of
mass of the system, that doesn't affect the position of the center of
mass of the system. Try the math.

> 3. The calcualtion isn't terribly easy, but looking at the vectors at
> various points in the orbit of the binary stars it appears that the
> peanut will be pulled into an orbit around COM (2) and will not be
> accelerated towards the larger sun.

Even if this supposed calculation is right, your ideas are shown to be
wrong if the peanut moves at all, since it's been your contention that
there can be no net force on the peanut. And as your extensive work with
Newton has shown, an object subject to no net force won't move. And let
me point out that the peanut *is* accelerated toward the larger sun. It
might miss, given its lateral velocity with regard to that sun (consider
a coordinate system in which the sun is stationary), but the same is
true of most objects falling around our sun.

> 4. And the question for Harshman who denies Centrifugal forces in non
> inertial frames: what keeps the smaller sun from accelerating towards
> the larger sun?

Nothing. They are both accelerating toward each other. They just miss
because of their lateral velocity.

> Harshman has asserted that Mercury is not accelerated
> towards the Sun in the Heliocentric model due to the gravitational
> forces of the eight other planets. Care to defend that claim?

No, I have asserted that Mercury is accelerated toward the sun. Its
acceleration vector always points toward the sun. But its lateral
velocity makes it always miss the sun as it falls.

[Greg Guarino]

In fact, it is. You equate "net force applied to the system" with "net
force applied to the CoM". I am telling you that we can in certain
circumstances *pretend* that is the case to simplify a calculation, but
it is not actually what is going on. The examples below demonstrate that.

>> Jupiter's gravity distorts the shape of its moons precisely because the
>> gravitation between them cannot be reduced to forces applied to their
>> respective CoMs. It attracts the near side of the moon more strongly
>> than the far side, stretching it in the process. Earth's tides work the
>> same way.

The inability of a system to apply a net force to itself says nothing
whatever about the ability of bodies within the system to apply forces
to each other. They can, and the magnitude of that force is determined
by the dreaded equation, wherever the bodies might be, including at the
CoM of the system.

> This isn't illustrative of my error. If one does the gravitational
> vector addition upon any particular particle it will point towards the
> COM and NOT the center of the larger body. In the Heliocentric model
> the planets do NOT revolve around the center of the Sun. The sun
> revolves around the COm of the heliocentric model.

>>> Nonetheless the net gravitational force vector on any body in an
>>> isolated system ALWAYS points to the COM. And any body located at the
>>> COM will never have any net force applied to it. So far Guarino, et
>>> al have effectively denied this.
>>
>> I agree. We have done so, and effectively.
>
> So far this hasn't been shown.

The equation shows it nicely. Care to give it a try?

<snip>

> Fair enough. Let's stick with your original example now that my
> understanding of your example is corrected.
>>>
>>> 3. The example is not analogous to the neoTychoan model.
>>>
>>>
>>> _________________________________________________________
>>> ACCORDING TO THE THIRD LAW
>>> -------------------------------------------------------------------------------
>>> 1. The gravitational forces between star M and the peanut are equal
>>> and opposite; likewise between star 2M and the peanut.
>>
>> True.
>>
>> They balance
>>> at the COM where the peanut happens to be located.
>>
>> Untrue, unless the Law of Universal Gravitation is wrong. Is it? That's
>> part of what you snipped. Do the calculations. Newton intended for his
>> equations to be consistent. You can't just throw this one out.
>
> The only way for the peanut to reside exactly at the COM in this
> example is for the peanut to be massless.

Why? We calculate the Center of Mass by multiplying each mass by its
distance from the center of mass. If that distance is zero....?

Calculating the COM only
> requires the four basic operations. Let's look at Guarino's example
> again more carefully with my corrected understanding:
>
>
> [Guarino's thought experiment]
>> No they wouldn't. Try two stars of unequal masses and a peanut at the
>> CoM between them. Use the Law of Universal Gravitation. If the ratio
>> between the stars' masses is 2:1, the ration of their gravitational
>> forces on the peanut will be 8:1, in other words, unbalanced. A 3:1
>> mass ratio would produce a 27:1 ratio of forces. The only ratio that
>> allows a balance of forces at the CoM is 1:1.
> [End thought experiment]
>
> 1. Guarino's initial conditions are that there are two suns with
> unequal masses at some unspecified distance between them with an
> attendent COM (1). Both are along one dimenstion (let's say the x
> axis).
>
> 2. Then Guarino inserts the peanut at the x coordinate of COM (1).
> Unfortunately the COM of this new system has changed ever-so-slightly
> and no longer resides at the coordinate of COM (1) but at the x
> coordinate of a new COM (2).

This is not true, but I think it demonstrates another of your
misconceptions; to wit, that the precise location of the peanut at the
CoM is of relevance to the question. The gravitational forces between
each of the large masses and the peanut will indeed balance at some
location of the peanut, but it is nowhere near the CoM. Thus an angstrom
give or take (or even a much greater distance) is of no consequence.

> 3. The net gravitiational vector on the peanut will be directed at
> the new COM (2) and its acceleration (along with that of the two suns)
> will be such that the new COM (2) will not be accelerated.
> If COM (2) was at rest it will remain at rest.

I refer you again to the equation. Are you sure that you don't already
understand that it falsifies your argument?

<snip>

> Try as you might you will not solve this problem with a simple one
> dimensional example with three bodies.

I'm demonstrating that it is simply untrue that no force can be applied
to an object at the CoM. A one-dimensional model works fine for that
purpose.

>> The COM is a
>>> special location and that's where the peanut is located. In any
>>> system of particles no net force will be appled "at" the COM. Draw
>>> all the vectors; they balance to zero.
>>
>> A net force will indeed be applied to an *object* at the center of mass,
>> unless the two stars are of equal mass. Newton's equation demands it.
>> Try it for yourself.
>
> You inserted the peanut at the x coordinate of COM (1) but adding that
> new mass to the isolated system altered the COM of that new "three"
> body system ever so slightly such that it was no longer at COM (1).

That's not true, but what if it was? Put the peanut at your "new " CoM
then. Plug a ratio of 2.00000000001:.9999999999 into the equation rather
than 2:1 if you like. See if it balances then. Or better yet, refer to
Inez' post, which is quite elegant in its simplicity.

<snip>

>
> 4. And the question for Harshman who denies Centrifugal forces in non
> inertial frames: what keeps the smaller sun from accelerating towards
> the larger sun? Harshman has asserted that Mercury is not accelerated
> towards the Sun in the Heliocentric model due to the gravitational
> forces of the eight other planets. Care to defend that claim?

The answer to this has been repeated ad nauseam. Harshman argues nothing
of the sort. He says, correctly, that Mercury is in fact accelerated in
the direction of the center of the Sun; that's what makes its trajectory
an orbit rather than a straight line. Its tangential velocity is great
enough to keep it from hitting the Sun, but not great enough for it to
escape orbit.

[Friar Broccoli]

On Tue, 22 May 2012 12:46:05 -0400, Greg Guarino <gdgu...@gmail.com>
wrote:

Typical evolutionist nonsense. THINK! What are the chances of two
peanuts colliding in space?

--
Friar Broccoli (Robert Keith Elias), Quebec Canada
I consider ALL arguments in support of my views

[Greg Guarino]

On 5/22/2012 1:10 PM, John Harshman wrote:

> an object subject to no net force won't move

Of course you mean "won't accelerate". It could continue on a straight
line path if already in motion.

[Charles Brenner]

On May 22, 9:37 am, T Pagano <not.va...@address.net> wrote:

> On Mon, 21 May 2012 15:38:09 -0400, Greg Guarino <gdguar...@gmail.com>
> wrote:

> The only way for the peanut to reside exactly at the COM in this
> example is for the peanut to be massless.

Bizarrely confused, or random invention? I vote for door #2.

>  Calculating the COM only
> requires the four basic operations.  Let's look at Guarino's example
> again more carefully with my corrected understanding:
>
> [Guarino's thought experiment]>No they wouldn't. Try two stars of unequal masses and a peanut at the
> >CoM between them. Use the Law of Universal Gravitation. If the ratio
> >between the stars' masses is 2:1, the ration of their gravitational
> >forces on the peanut will be 8:1, in other words, unbalanced. A 3:1
> >mass ratio would produce a 27:1 ratio of forces. The only ratio that
> >allows a balance of forces at the CoM is 1:1.
>
> [End thought experiment]
>
> 1.  Guarino's initial conditions are that there are two suns with
> unequal masses at some unspecified distance between them with an
> attendent COM (1).  Both are along one dimenstion (let's say the x
> axis).
>
> 2.  Then Guarino inserts the peanut at the x coordinate of COM (1).
> Unfortunately the COM of this new system has changed ever-so-slightly

changed? Baldfaced invention.

> and no longer resides at the coordinate of COM (1) but at the x
> coordinate of a new COM (2).

And even if that were true would it matter? No, but Tony doesn't know
or care; he's just stalling for time.

For that matter, if putting the peanut at COM (1) really did perturb
the system as he wrongly invents, and moreover if the perturbation
were significant as he imaginatively pretends to assume, then the
rebuttal would still be trivial: Just slightly change the description
of the conditions such that the peanut position be adjusted as
necessary to reside at the COM.

> 3.  The net gravitiational vector on the peanut will be directed at
> the new COM (2) and its acceleration (along with that of the two suns)
> will be such that the new COM (2) will not be accelerated.
> If COM (2) was at rest it will remain at rest.

What's the point of this blather? It's not an argument -- it's just a
claim essentially equivalent to the same mistaken claim he's been
making all along involving confusing the COM (a balance point, a
position with respect to which the first moment of mass is 0) with a
"center of gravity" (a point at which the -2 moment of mass is 0).

It seems to me that Tony's personal (insincere) rule for "victory"
etc. is that as long as he's still writing any words at all, he's
analogous to a boxer who's still on his feet.

> 4.  All three bodies will collide at COM (2).
>
> And this example doesn't lay a glove on the neoTychoan model.  It also
> doesn't demonstrate that a body genuinely at the COM of an isolated
> system of particles will be accelerated by another body in the
> isolated system.  Such would violate the Third Law.

Obviously wrong, but in particular 100% bluffing.

> Try as you might you will not solve this problem with a simple one
> dimensional example with three bodies.

Reminiscent of Nixon's secret plan for victory in Vietnam. Tony's
bluffing that he has some math up his sleeve.

> >The COM is a
> >> special location and that's where the peanut is located.   In any
> >> system of particles no net force will be appled "at" the COM.  Draw
> >> all the vectors; they balance to zero.
>
> >A net force will indeed be applied to an *object* at the center of mass,
> >unless the two stars are of equal mass. Newton's equation demands it.
> >Try it for yourself.
>
> You inserted the peanut at the x coordinate of COM (1) but adding that
> new mass to the isolated system altered the COM of that new "three"
> body system ever so slightly such that it was no longer at COM (1).
>
> You're going have to devise a thought experiment where a body is
> actually located at the COM of some isolated system.

If this were an actual sincere mistake, the reply would be as I wrote
above. But it's not -- it's just words to fill the page.

> 3.  The calcualtion isn't terribly easy, but looking at the vectors at
> various points in the orbit of the binary stars it appears that the
> peanut will be pulled into an orbit around COM (2) and will not be
> accelerated towards the larger sun.

In summary, it is time to stop giving Tony credit for being a sentient
being where math is concerned. The simple examples about gravitational
force of two unequal large bodies are totally beyond him. His
intelligence is completely limited to words; no math sense at all and
he full well knows it (unless he doesn't know that there is any
reasoning beyond mere words). In writing "calculation isn't terribly
easy" he is merely parroting an expression. His intimation that he
could himself understand such a calculation, let alone do it, is 100%
consciously dishonest.