Perihelion of Mercury with classical mechanics ?

Nicolaas Vroom wrote:

schreef in bericht
...
[...]

See problem 12.4 of Lightman et al., _Problem book in relativity
and gravitation_, for a simple derivation. For a speed of gravity
of 300c within Newtonian gravity, the Earth's orbit is unstable
enough that it would have been at the edge of the Sun about
120,000 years ago.

My simulations of the stability of the Earth show that for
a speed of gravity equal c the distance of the Earth
increases with 1 km out of a distance of 149600000 km
for each revolution (1 year)

If

(1) you're looking at Newtonian gravity in the "force" description
(F = GMm/r^2 = ma), but with the direction and magnitude of the
force depending on the retarded position of the gravitating mass;
and
(2) you're looking at a two-body problem,

then the problem can be analyzed analytically, and gives a result that
is drastically different from your claim. If this is the case, then
there's something wrong with your simulation.

If you are looking at Newtonian gravity in the "potential" description,
with a potential that depends on the retarded position of the gravitating
mass, then the effect is suppressed. Even then, I suspect that you will
get in trouble with the Lunar orbit, and you will certainly run into
contradictions with pulsar observations. For that model, Mercury's
perihelion advance can also be computed analytically, and disagrees with
observation.

Or are you doing neither of these things?

Steve CArlip

On Thu, 3 Feb 2005 19:14:24 +0000 (UTC),
wrote:

greywolf42 wrote:
wrote in message
...

[...]

A related question to aberration... If there IS an aberrative
vector that tends to cause a Star & its Planet to soon be parted,
where in the universe does the energy to do so come from?

To gain radii doesn't REAL energy have to be expended???

What about if we stop thinking so linearly. Say there are two
bodies (the Star & its Planet) whos real position is like so,

[S] (P)

Thus, for JUST a center point vector these would be - -

Who are actually aberrated so as to look to each other as,

(P)
[S]

and INSTEAD of a leading vector, the arrow does point to the
baricenter as a curve. Thus the pointing vectors at each body
points so that the remains a central radial acceleration
only. The energy of the system remains conserved, AND, at
each differential point along the curved path, the vector
always remains center pointing?

Why is this not possible?

Nicolaas Vroom wrote:

schreef in bericht
...

[...]
If

(1) you're looking at Newtonian gravity in the "force" description
(F = GMm/r^2 = ma), but with the direction and magnitude of the
force depending on the retarded position of the gravitating mass;
and
(2) you're looking at a two-body problem,

then the problem can be analyzed analytically, and gives a result that
is drastically different from your claim. If this is the case, then
there's something wrong with your simulation.

That is what I have done.
What should be the result (increase in distance) for Jupiter
after one revolution with speed of gravity equal to c?
The same but for 300*c ?

To a very good approximation, for nearly circular orbits the radius
at time t will satisfy

r^2 - (r_0)^2 = (4GM/c_g)(t-t_0)

where r_0 is the radius at time t_0 , M is the mass of the Sun, and
c_g is the speed of (Newtonian) gravity. Take r_0 to be the radius of
the Sun and r the present radius of the Earth's orbit, and you can
use this to compute t-t_0, the time in the past that the Earth must
have been at r_0. If c_g=c, this comes out to about 400 years. The
time is directly proportional to c_g, so for c_g=300c, this becomes
about 120,000 years.

Again, the computation is fairly simple; see the Lightman reference
I gave before. All you really have to do is to note that the effect
of propagation delay in Newtonian gravity is to impart a tangential
acceleration equal to v/c_g times the radial acceleration, and
compute the change in energy.

Steve Carlip

Paul Stowe wrote:
[...]

A related question to aberration... If there IS an aberrative
vector that tends to cause a Star & its Planet to soon be parted,
where in the universe does the energy to do so come from?

If your theory is just Newtonian gravity with time delay stuck in,
then energy isn't conserved. The energy doesn't come from anywhere;
it just appears.

If you want to look at a model in which energy is conserved, the answer
will depend on the details of the model. In models having only a
gravitational field, the field itself can carry energy in the form of
gravitational radiation, and a consistent theory has to automatically
balance field energy and orbital kinetic energy. You can use this to
get estimates of the effect of aberration by assuming self-consistency;
typically, you find that there must be other interactions (velocity-
dependent forces) that at least partially counteract the effect of
finite-velocity propagation. Of course, this argument doesn't tell you
what those interactions are -- that will again depend on the specific
model. But this is no different than most arguments appealing to
conservation, which typically tell you that something must happen
but don't in themselves tell you exactly what.

In a theory with more than just gravitational fields -- a LeSage model,
for instance, or a model describing gravity in terms of fluid flows --
the extra stuff in the theory (LeSagean particles, fluid,...) can carry
energy as well. You can still appeal to energy conservation, if you've
checked that your model really does conserve energy. But to draw any
real conclusions, you also need a fairly detailed understanding of the
rate of energy transfer between the gravitating objects and whatever
else is in the model.

Steve Carlip

wrote in message
...
greywolf42 wrote:
wrote in message
...

[...]

Laplace considered the effect of a finite speed of gravity in
Newtonian mechanics in 1805, and showed that observations of the
orbit of the Moon required a speed of at least 7x10^6 c.

Steve is being deliberately dishonest, here. He is attempting to
"motivate" you, so that you don't "waste your time" with theories
that Steve does not support.

That is not true.

Well, that was been your stated purpose for this very same deliberate
distortion in the past. I see you continue your deliberate distortion in
your parallel post to Nicolaas Vroom.

[...]

Steve attempts to avoid the fact that he has made this same deception many
times. Replacing the snip:
======================
(This is not inadverntent. He has done it before, and been called
on it, several times.)
======================

In this immediate response, Steve has mixed two counteracting
forces (aberration: Lightman, and drag: Laplace) in such a way
as to make you think that they are addressing the same force.

This is simply wrong. Go back and read Laplace, _Celestial Mechanics_,
section X.VII.22. It's true that elsewhere in X.VII, Laplace deals with
drag. But this section, which contains the limit that I quoted, deals
*explicitly* with aberration, *not* drag.

My apologies for not checking the section number.

So, instead of deceiving Nicolaas about drag *and* aberration, you are
simply deceiving Nicolaas about the very existence of drag.

There are five components to this deliberate distortion.

Of which you list four?

Bad numbering system. The first was addressed immediately above.

1) Steve is not telling you the name or type of the gravitational theory
that Laplace was addressing. The theory is called Le Sagian gravity,
and was proffered by Georges Louis Le Sage, in 1782. This theory
derives Newton's gravitational law (actually it derives the weak-field
limit of GR) from the partial absorption of 'ultra-mundane corpuscles'
by mass. {A search on Le Sage or Lesage will bring up quite a few
recent discussions on the theory.}

It may be that Laplace had LeSage in mind. I don't know.

And it is irrelevant. For the point is not whether Laplace had Le Sage
specifically in mind. But that Laplace was (and you are) addressing Le
Sage-type theories.

In particular, I
have been unable to find any reference to LeSage in section X.VII of
Laplace's _Celestial Mechanics_. Perhaps it's elsewhere -- I haven't
read the whole book. Would you care to provide a specific citation?

I haven't read the whole thing for years now, either. Nor do I have a
copy. Nor is it relevant to the issue of your deception -- keeping Nicolaas
ignorant of the type of theory being discussed. At issue is not simply a
single section of Laplace, but the essence of the argument of Laplace,
Lightman, and yourself.

2) The 'drag' effect mentioned by Steve is based on the drag of a matter
body as it moves through a *medium.* It is not the speed of gravity --
per se -- that would cause the Earth to shrink its orbit; it is the
impact of those 'ultra-mundane corpuscles.'

That is incorrect. The issue in this thread has been the effect of finite
propagation speed in Newtonian gravity, and that's what I addressed.

Which is why I accurately described your action as deliberate deception, and
not an outright lie. Your statements are quite literally true -- and also
deliberately deceptive.

I did not say, or imply, anything about "drag."

That *is* the deception on your part. You are well aware that theories of
the sort that you (and Laplace and Lightman) were addressing *also* have a
drag component. But knowing this -- and knowing the possibility exists of a
balance -- you did not tell Nicolaas about this.

Contrary to your claim, the limit
I quoted from Laplace also had nothing to do with drag, but came from the
effect of putting a finite propagation speed into Newtonian gravity.

But Laplace *does* have a section on drag. From which, you are attempting
to divert.

3) The effect that arises in *any* gravitational theory with a finite
speed of gravity (including GR) is gravitational aberration. And
gravitational aberration will tend to *increase* the radius of an orbit.

Right. That's what I said. "For a speed of gravity of 300c within
Newtonian gravity, the Earth's orbit is unstable enough that it would
have been at the edge of the Sun about 120,000 years ago."
That's an increase in the radius of the orbit, right?

Yep. As I noted. Your statement about orbital increase is specifically
true -- and deliberately deceptive. Because you are assuming zero drag
effect. (I believe the value in your calculation may be in error by about a
factor of 1 million. What aberration factor did you use for the Earth?)
With a drag effect, you can't make the above claim. That is the deception.

[...]

Here is what Steve snipped:

Steve did a
paper on just this effect -- to try to save GR from the issue.

And this is unavoidable. Steve knows that GR suffers from *precisely* the
same "problem" of aberration. But aberration never acts alone. That is
Steve's deception. For GR, Steve discussed "miraculous" (and non-specific)
back-action.

4) Laplace (and just about everyone since, including Feynman and
Poincare) determined their "requirement" for high speed on the basis
of drag, alone. And never considered the potential balancing of the
two forces. In fact, Steve will tell you that the aberration term will
*always* overpower the drag term (for the Earth).

Steve apparently has confirmed this last sentence. Both by not
contradicting it, and by trying to remove all consideration of balancing
drag forces from this post.

Once again: Laplace, _Celestial Mechanics_, section X.VII.22, is about
finite propagation speed, not drag.

But the *other* sections contain drag calculations.

Steve will likely tell you that such is done simply to avoid
"confusion."

No, I will say that greywolf wrote a fictional account that had nothing to
do with what I said.

But that is simply a false statement, Steve. Unlike your prior distortion
(which was explicitly true, but deceptive), this statement is demonstrably
false. My statements have everything to do with what you've said -- both on
this post and on prior exchanges.

Unlike him, I will not charge "deliberate distortion"

But Steve will continue to deliberately distort the physical situation.

or accuse him of "deliberate dishonesty."

Because Steve knows that nothing in my post is either a distortion, or
dishonest.

He may have misremembered Laplace,
or only read someone else's description, and leapt to conclusions without
actually paying much attention to the post he was responding to.

So, Steve will continue to try to deliberately deceive Nicolaas about the
*fact* that all orbital dynamical calculations contain both drag and
aberration terms. But Steve will pretend to be noble and professional.


Steve, all you have to do to be honest and professional is to mention that
there are two competing forces in real, physical, causative theories. Drag
and aberration. And that *IF* one of these two forces overpowers the other,
then the planet will either spiral in or out. But you can't honestly
continue to claim that either approach -- alone -- demonstrates that
physical theories of gravity don't work.

Of course, that acknowledges the issue that you wish to avoid.

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}

greywolf42 wrote:
wrote in message
...

[A good deal of ad hominem snipped...]

I did not say, or imply, anything about "drag."

That *is* the deception on your part. You are well aware that theories of
the sort that you (and Laplace and Lightman) were addressing *also* have a
drag component. But knowing this -- and knowing the possibility exists of a
balance -- you did not tell Nicolaas about this.

The question in this thread was *explicitly* about Newtonian gravity with
a propagation delay. Period. If you need clarification on this, see
http://groups-beta.google.com/group/...c024f0ce180044.

Since this was the question, this is what I responded to.

[more ad hominem snipped...]

So, Steve will continue to try to deliberately deceive Nicolaas about the
*fact* that all orbital dynamical calculations contain both drag and
aberration terms. But Steve will pretend to be noble and professional.

Nicolaas knows perfectly well that there are other models in which additional
forces act. You should not insult him by assuming such ignorance. In this
thread, those other models were not at issue. Go back and read a little!

Steve Carlip

wrote in message
...
Nicolaas Vroom wrote:

schreef in bericht
...

[...]

If

(1) you're looking at Newtonian gravity

But, Steve, at issue is not simply "Newtonian gravity." Nicolaas was
responding to Greg's claims about "classical" theories of gravity:

"Attempts to calculate the precession of the perihelion of Mercury by purely
classical means have taken into account any number of influences, including
of course the motion of the Sun."

Why do you continue to try to divert solely into Newton's empirical formula
.... then change the formula?

in the "force" description
(F = GMm/r^2 = ma), but with the direction and magnitude of the
force depending on the retarded position of the gravitating mass;
and
(2) you're looking at a two-body problem,

then the problem can be analyzed analytically, and gives a result that
is drastically different from your claim. If this is the case, then
there's something wrong with your simulation.

That is what I have done.
What should be the result (increase in distance) for Jupiter
after one revolution with speed of gravity equal to c?
The same but for 300*c ?

To a very good approximation, for nearly circular orbits the radius
at time t will satisfy

r^2 - (r_0)^2 = (4GM/c_g)(t-t_0)

where r_0 is the radius at time t_0 , M is the mass of the Sun, and
c_g is the speed of (Newtonian) gravity. Take r_0 to be the radius of
the Sun and r the present radius of the Earth's orbit, and you can
use this to compute t-t_0, the time in the past that the Earth must
have been at r_0. If c_g=c, this comes out to about 400 years. The
time is directly proportional to c_g, so for c_g=300c, this becomes
about 120,000 years.

Again, the computation is fairly simple; see the Lightman reference
I gave before. All you really have to do is to note that the effect
of propagation delay in Newtonian gravity is to impart a tangential
acceleration equal to v/c_g times the radial acceleration, and
compute the change in energy.

But this is simply trying to hack an empirical formula (Newton's). Equation
mining is not generally useful. A real theory includes a cause, that gives
rise to a finite speed of gravity. Not simply trying to slap a new term
into an equation.

The fact that the orbit is not stable simply indicates that your crude
approach has failed to accurately (or completely) model the process. Not
that gravity does not have a finite speed.

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}

On Sun, 6 Feb 2005 00:07:40 +0000 (UTC),
wrote:

Paul Stowe wrote:
[...]

A related question to aberration... If there IS an aberrative
vector that tends to cause a Star & its Planet to soon be parted,
where in the universe does the energy to do so come from?

If your theory is just Newtonian gravity with time delay stuck
in, then energy isn't conserved. The energy doesn't come from
anywhere; it just appears.

Therein lies the problem of using a single mathematical correlation
as 'a theory'. It is not. No more or less than Coulomb's inverse
square mathematical correlation. These are both simple expressions
of observational correlation and say nothing, one way or the other
as to the speed of propagation of the underlying processes. Both
equations are vacant of and time derivative components.

Second, it would seem to me that the violation of basic conservation
of momentum/energy would be a big red flag pointing out that you have
missed something vital in modeling. It may mean that the speed of
propagation is infinite, but, to conclude this would require exhaustion
of all other possibilities. Since the problem also exists in E&M, AND
we can definitely rule out infinite propagation, I think it is a safe
bet that it can also be ruled out for Newtonian Gravity. We are talking
about Newtonian physics here, for which the cornerstone IS the
conservation laws.

If you want to look at a model in which energy is conserved, the
answer will depend on the details of the model.

That is always the case...

In models having only a gravitational field, the field itself can carry
energy...

And in Newtonian Gravity the field has energy, doesn't it? In the form
of so-called potential energy?

in the form of gravitational radiation, and a consistent theory has to
automatically balance field energy and orbital kinetic energy.

I would think that, based upon observations to date, nature ultimately
requires conservation.

You can use this to get estimates of the effect of aberration by assuming
self-consistency; typically, you find that there must be other interactions
(velocity-dependent forces) that at least partially counteract the effect
of finite-velocity propagation.

Indeed, isn't that what I was proposing in this thread, narratively?

Of course, this argument doesn't tell you what those interactions are

Of course. But IT DOES allow one to rule out irrational proposals LIKE
aberrative fling with its gross violation of the conservation laws.

-- that will again depend on the specific model. But this is no different
than most arguments appealing to conservation, which typically tell you
that something must happen but don't in themselves tell you exactly what.

Right. One must dig into the details to find those.

In a theory with more than just gravitational fields -- a LeSage model,
for instance, or a model describing gravity in terms of fluid flows --
the extra stuff in the theory (LeSagean particles, fluid,...) can carry
energy as well. You can still appeal to energy conservation,

I wouldn't think it an appeal, but a requirement set by observations of
nature. Therein lies my biggest hangup with so-called "Dark Energy".

if you've checked that your model really does conserve energy. But to
draw any real conclusions, you also need a fairly detailed understanding
of the rate of energy transfer between the gravitating objects and whatever
else is in the model.

Absolutely, the devil is always in the details...

Paul Stowe

Paul Stowe wrote:
On Sun, 6 Feb 2005 00:07:40 +0000 (UTC),
wrote:

[...]
If you want to look at a model in which energy is conserved, the
answer will depend on the details of the model.

That is always the case...

In models having only a gravitational field, the field itself can carry
energy...

And in Newtonian Gravity the field has energy, doesn't it? In the form
of so-called potential energy?

I was too terse... In Newtonian gravity, the gravitational field
doesn't have *independent* energy. In electromagnetism, a light wave
can carry energy that exists independent of the source of the light;
once you've turned on a flashlight, the light's energy doesn't disappear
if you turn it off. Potential energy in Newtonian gravity, on the other
hand, has no independent existence; it is determined entirely by the
instantaneous locations of the sources. There are no energy-carrying
gravitational waves in Newtonian gravity.

in the form of gravitational radiation, and a consistent theory has to
automatically balance field energy and orbital kinetic energy.

I would think that, based upon observations to date, nature ultimately
requires conservation.

You can use this to get estimates of the effect of aberration by assuming
self-consistency; typically, you find that there must be other interactions
(velocity-dependent forces) that at least partially counteract the effect
of finite-velocity propagation.

Indeed, isn't that what I was proposing in this thread, narratively?

Of course, this argument doesn't tell you what those interactions are

Of course. But IT DOES allow one to rule out irrational proposals LIKE
aberrative fling with its gross violation of the conservation laws.

Not necessarily. This depends on the details of the interaction, and, in
particular, on how easy it is to transfer energy between gravitating bodies
and the field/medium/whatever else accounts for conservation. If you look
at the analysis in general relativity, for example, it's not just that
energy is conserved. It's a three-step argument:

1. Total energy (matter plus gravitational radiation) is conserved
(at least to a good enough approximation);
2. Matter couples only weakly to gravitational radiation -- specifically,
only the third and higher time derivatives of the quadrupole and higher
moments can radiate. This means that the power carried by gravitational
radiation is smaller than the Newtonian power (F times v) by a factor of
order (v/c)^5;
3. Therefore, the gravitating system can exchange energy only weakly with
gravitational radiation -- specifically, the net non-Newtonian forces
involved in gain or loss of energy must be smaller than the Newtonian
gravitational force by a factor of order (v/c)^5.

If you carry out the same analysis for electromagnetism, you find a smaller
suppression, of order (v/c)^3. If you had a model with monopole coupling
to radiation/medium/whatever -- that is, if an object could gain or lose
energy by exchanging mass with a field or medium -- this argument would
only give you a suppression only of order v/c, which is the usual factor
in aberration.

(Push a ball in a bathtub. Energy is conserved, but if you looked at the
energy of the ball alone you'd find changes that were *much* larger than
anything anyone has ever attributed to aberration. I am *not* suggesting
this as an analog for any particular model -- this is not intended as a swipe
at LeSagean gravity, for instance -- but just using it to point out that
energy conservation doesn't help if you don't have an independent limit on
the exchange of energy between an object and its surroundings.)

-- that will again depend on the specific model. But this is no different
than most arguments appealing to conservation, which typically tell you
that something must happen but don't in themselves tell you exactly what.

Right. One must dig into the details to find those.

Agreed.

Steve Carlip

On Tue, 8 Feb 2005 19:36:14 +0000 (UTC),
wrote:

Paul Stowe wrote:
On Sun, 6 Feb 2005 00:07:40 +0000 (UTC),
wrote:

[...]
If you want to look at a model in which energy is conserved, the
answer will depend on the details of the model.

That is always the case...

In models having only a gravitational field, the field itself can
carry energy...

And in Newtonian Gravity the field has energy, doesn't it? In the
form of so-called potential energy?

I was too terse... In Newtonian gravity, the gravitational field
doesn't have *independent* energy. In electromagnetism, a light
wave can carry energy that exists independent of the source of the
light; once you've turned on a flashlight, the light's energy doesn't
disappear if you turn it off. Potential energy in Newtonian gravity,
on the other hand, has no independent existence; it is determined
entirely by the instantaneous locations of the sources.

I would say that for potential energy to exist it must be 'real'.
To be 'real' it cannot magically appear and/or disappear. In
what is called 'Newtonian Gravity' [NG] everything revolves around
one correlational equation. That equation says nothing about
anything except instantaneous 'snapshots' of one primary effect.
In fact, it has no derivational foundation contained within the
theory.

I think we can agree that NG as you present it is whoefully
inadequate and too incomplete to be used to describe the processes
of gravitation. Thirring-Lenze is another process that immediately
springs to mind.

Let's take your flashlight example. If the Sun were to 'magically'
dissappear when would the Earth straighten it path? By your
desciption of NG, instantaneously. That's NOT a prediction of NG
since the propagational speed isn't found in the equation. It is
instead, a rather naive interpretation. I know that you don't think
for a second that the Earth's path would immediately straighten.
Thus, like your flashlight example, the field potential would
continue to propagate (radiating outward) even IF we 'shut off' the
Sun. This would argue for an existence independent of the source.

There are no energy-carrying gravitational waves in Newtonian
gravity.

As presented I'd say that NG is simply mute on this. It can't
say, because it is too incomplete.

in the form of gravitational radiation, and a consistent theory
has to automatically balance field energy and orbital kinetic
energy.

I would think that, based upon observations to date, nature
ultimately requires conservation.

You can use this to get estimates of the effect of aberration by
assuming self-consistency; typically, you find that there must be
other interactions (velocity-dependent forces) that at least
partially counteract the effect of finite-velocity propagation.

Indeed, isn't that what I was proposing in this thread, narratively?

Of course, this argument doesn't tell you what those interactions
are

Of course. But IT DOES allow one to rule out irrational proposals
LIKE aberrative fling with its gross violation of the conservation
laws.

Not necessarily. This depends on the details of the interaction,
and, in particular, on how easy it is to transfer energy between
gravitating bodies and the field/medium/whatever else accounts for
conservation. If you look at the analysis in general relativity,
for example, it's not just that energy is conserved. It's a
three-step argument:

1. Total energy (matter plus gravitational radiation) is conserved
(at least to a good enough approximation);

A nit, I agree total energy, but there is more there than matter &
gravitational radiation, the either a potential or curvature. Both
act to 'bend' the path of massive bodies and therefore whether a
field or 'fabric' it too has energy.

2. Matter couples only weakly to gravitational radiation -- specifically,
only the third and higher time derivatives of the quadrupole and higher
moments can radiate. This means that the power carried by gravitational
radiation is smaller than the Newtonian power (F times v) by a factor of
order (v/c)^5;

3. Therefore, the gravitating system can exchange energy only weakly with
gravitational radiation -- specifically, the net non-Newtonian forces
involved in gain or loss of energy must be smaller than the Newtonian
gravitational force by a factor of order (v/c)^5.

If you carry out the same analysis for electromagnetism, you find a smaller
suppression, of order (v/c)^3. If you had a model with monopole coupling
to radiation/medium/whatever -- that is, if an object could gain or lose
energy by exchanging mass with a field or medium -- this argument would
only give you a suppression only of order v/c, which is the usual factor
in aberration.

May I ask, what mass?

(Push a ball in a bathtub. Energy is conserved, but if you looked at the
energy of the ball alone you'd find changes that were *much* larger than
anything anyone has ever attributed to aberration. I am *not* suggesting
this as an analog for any particular model -- this is not intended as a swipe
at LeSagean gravity, for instance -- but just using it to point out that
energy conservation doesn't help if you don't have an independent limit on
the exchange of energy between an object and its surroundings.)

I agree and this is the crux of the problem. The basic interaction for
aberration is a two body problem. It is not simply the exchange of energy
of one object but at least three. The two bodies and the field that binds
them.

[Snip...]

Paul Stowe