Gravitational Doppler

Lester Zick wrote:
On 21 Aug 2006 06:15:07 -0700, "George Dishman"
wrote:
Lester Zick wrote:

.. If you can't make your
own arguments there's nothing much to criticize except technique.

OK, if you want me to make my own arguments try this.

You first suggested that globular clusters were amongst the
youngest objects in the galaxy and later changed to say you
were interested in the relative ages.

Yeah, George, look I have absolutely no further interest in your
misrepresentations of the issue I raised.

I've shown you the quote of the issue you raised
several times so there is no misrepresentation on
my part, but I understand you were never really
interested in relative ages of anything, you just
wanted to have an argument.

You seem interested in
pursuing a problem I've long since given up clarifying and doing so in
highly prejudicial terms.

Not at all, I carefully wrote the last post just to include
the factual measurements without criticism of you or
your questions. You are the one trying to turn it back
into a dispute.

The age of the stars in NGC 6397, as determined by means
of stellar evolution models, is 13400 +/- 800 million years.

Well goodie. That's just swell.

Just a simple fact, that is the age the current best
measurement gives.

The relative ages of the Milky Way and NGC 6397 has been
determined by measuring Beryllium content and is found to
be about a 200 million year difference making the age of the
galaxy 13600 +/- 800, i.e. the galaxy is very slightly older
than the cluster.

And what about the age of the Milky Way as determined by measuring its
Alka Seltzer content?

Carry on Lester, I don't need to use "prejudicial
terms" when you demonstrate your attitude so
effectively yourself.

The age of NGC 6397 is therefore 98.5% of the age of the
galaxy and since there are other younger structures in the
galaxy that makes the cluster "one of the oldest structures
in the galaxy".

Well the problem here is that even given these particular relative
ages that doesn't make globular clusters older than the galaxy ..

Why do you think that is a problem? When you asked
about the relative ages of the Milky way and clusters, a
week ago, I gave you the link to the page that said that
relatively the galaxy was 200 million years older. You
chose not to read the page and assumed I was disagreeing
with you as any troll would.

.. and
certainly not one of the oldest objects in the universe in any
categorical priority sense of oldest objects.

I said nothing of the universe above, that comes next.

The age of the universe is 13700 million years measured by
the WMAP mission.

The age of the universe is not an issue in Newtonian mechanics. We've
already established that.

We have established that indeed. The reason it isn't
an issue is that Newtonian mechanics gives a similar
age.

This is nothing but an ad hoc assertion akin
to dark matter which should read "if all our assumptions, assertions,
and fantasies regarding CMBR and the Hubble redshift should turn out
to be true we might then be able to chronicle the age of the universe
otherwise not".

More unsubstantiated ranting Lester? If you want
to query the age, there are a raft of measurements
on which it relies from the calibration of distances
using local parallax onwards that you could examine,
but I don't think that's your style.

The age of NGC 6397 is therefore 97.8% of the age of the
universe and since there are other younger structures in
the universe that makes the cluster "one of the oldest
structures in the universe".

And not even in your wildest dreams does it make it categorically
older than the galaxy.

Right, it categorically makes it younger as I
pointed out to you last weekend, and as you
would have known if you had bothered to read
the page, or maybe you did but clearly all you
wanted was an argument so the fact that I had
agreed with you was a problem for you. That is
the second time I have agreed with you against
the posts of others in the group and both times
you have simply argued with me for my pains.
It's called trolling, Lester, and I'm not interested
if that's all you are looking for.

None of the above ages relies on the dynamics of cluster
structure so your comments on that aspect are not
relevant.

And none of your assertions makes anything older or younger than
anything else in categorical terms.

On the contrary, the beryllium measurement
categorically makes the galaxy older than the
cluster as I pointed out over a week ago.

Oh and it's easy to validate my assertion that
those are the measured values, just look at
the ESO page I cited.

George

On 22 Aug 2006 01:20:38 -0700, "George Dishman"
wrote:

Yes, yes, George, it's good to see we've finally reached agreement on
the fundamental issue I raised initially. I agree that the virial
theorem supports my view on the relative age of globular clusters.

The problem has always been that those who disagree with my analysis
have looked at the problem backward, initially trying to grasp the
motions of individual stars within a globular cluster instead of the
cluster as a whole. The fact seems to be that globular clusters have
no net angular momentum themselves. Consequently we must infer that
motions of individual stars within the cluster are completely nugatory
and that angular momenta within the cluster cancel each other and
centers of gravity for those angular momenta must be stationary with
respect to the cluster or the cluster itself would have angular
momentum.

The result of all this is that globular clusters must be collapsing
along the lines of those stationary centers of gravity. This much of
course should be intuitively obvious to the casual observer of
Newtonian mechanics however difficult it may be to grasp by the
average student of astronomy. Perhaps it is the case that average
students of astronomy are just average students to begin with and only
take astronomy in the first place because they're too lazy or stupid
to cope with actual celestial mechanics.

In any event in the interests of full discolsure I've enclosed a link
to you where if they're interested the halt and lame can further
research your views on various aspects of the problem which read more
like a couple of turbid chapters from Tolstoy than any kind of
effective mechanical analysis of the issues under consideration.

Lester Zick
~v~~

Lester Zick writes:

On 21 Aug 2006 03:25:34 -0400, Craig Markwardt
wrote:


Lester Zick writes:
On 19 Aug 2006 14:19:24 -0400, Craig Markwardt
wrote:


Lester Zick writes:
... snip ...
It means I think the sky is falling in gc's just the way it does in
every celestial object whose centers of gravity are stationary with
respect to one another.
... snip ...

What exactly do you mean by,
* "centers of gravity", and that they
* "stationary with respect to one another"

Perfectly reasonable questions.

I'm not asking for an "it's obvious" answer, but rather, what exactly
you think the terms you used mean in terms of geometry and perhaps
mathematics.

I take the term "centers of gravity" to mean the centers through which
universal gravitational attraction operates. Each star in a globular
cluster has its own local internal center of gravity and each star in
various cominations with other stars has a non local center of gravity
presumably lying somewhere between or among them through which
gravitational attraction for the combination acts in relation to
centers of gravity for other combinations.And these centers of gravity
exist for every possible combination of stars within the cluster. And
every possible combination of stationary and moving stars within a
cluster has to be reckoned in terms of all centers of gravity among
all the combinations and not just exclusively between each pair of
stars within the cluster or for the cluster as a whole in calculating
net angular momentum for the cluster.

Wouldn't it be more straightforward to calculate the cluster angular
momentum about a given axis based on a sum of the individual stars'
angular momenta?[*] After all, that is the formal definition of
angular momentum, isn't it?

Regardless of how you add them up the sum is still roughly zero
provided you add them all up and not just a few in relation to a
specific axis.

However, since classical total angular momentum is not defined in the
manner which you describe, you would need to substantiate your claim
with extensive theoretical work, which you have not done.

[*] By that I mean, L_total = Sum[ L_i ] = Sum[ r_i x p_i ], where
r_i and p_i are the ith star's distance from the axis and linear
momentum, and "x" indicates a vector cross product.

And secondly, on what evidence do you claim that "centers of gravity
are stationary with respect to one another?"

Well this may not appear obvious however in calculating net angular
momentum for the cluster as a whole we know two basic things: first
the motion of various stars in the cluster individually and second the
net angular momentum for the cluster as a whole of approximately zero.

Thus we can easily construct an equation where the sum of all angular
momenta for all possible combinations of stars in a globular cluster
equals zero. So regardless how we take various combinations of angular
momenta for various centers of gravity within the cluster we have to
recognize that their sum must be zero for the cluster itself to have a
net angular mometum approximately zero. Which means in turn that all
combinations must offset one another in aggregate. Hence even though
some combinational centers may not offset one another directly, all
centers of gravity within the cluster have to be roughly stationary
with respect to all other centers of gravity regardless of a presence
of non zero angular momentum for certain combinations within the
cluster.

How does your conclusion follow?

Because the net angular momentum for the cluster as a whole is roughly
zero. Consequently regardless of individual angular momenta considered
in isolation the aggregate of all angular momenta must be roughly zero
too. Otherwise the cluster itself must have non zero angular momentum.

Your original conclusion still does not follow. Even if the total sum
angular momentum of an ensemble is zero, one cannot conclude that the
individual components of the sum must be zero. Hence one cannot
conclude that the individual components are "stationary."

First, you've been writing about angular momentum, so what step of
logic allows one to translate from the domain of angular momentum to
"roughly stationary" points? For example, the total angular momentum
of a system can be zero when the total energy or linear momentum is not.

I'm not talking about linear momentum here.As far as different domains
of angular momentum are concerned we're just adding them up. They have
to equal zero whether or not isolated domains have energy or linear
momentum. It's quite possible for moving bodies with kinetic energy
and linear momentum to possess offsetting angular momenta with respect
to various centers of gravity.

You claimed that something was "stationary." In classical mechanics
if a body is stationary, it is not moving. A body cannot have
"kinetic energy and linear momentum" and also be stationary.


Second, it is easy to construct a sum of two functions which is zero
but whose individual values are not.

Sure. The problem is that we have to wind up with centers of gravity
stationary with respect to each other or the angular momentum of the
object as a whole will have some net angular momentum.

For example, consider three identical stars arranged along the X axis
at positions (-1 pc), (0 pc), (+1 pc),[*] with the outer two stars
moving apart and the center star held fixed (with respective
velocities: (-1 pc/yr), (0 pc/yr), (+1 pc/yr)). By any definition,
the total linear and angular momentum of this system is zero. And
yet, the stars are moving apart. The "centers of gravity" as you
define them are also moving apart from each other and thus not
"stationary." Thus, your conclusion is not rigorous.

Which centers of gravity? That for the stars individually considered
in isolation or the center of gravity for the system as a whole? The
fact that the stars themselves are moving apart is irrelevant. The
center of gravity for the system itself is stationary. The centers of
gravity as I define them are only moving apart for the individual
stars and not for the system as a whole.

You claimed that one must consider *all* possible combinations of
"centers of gravity." For the triplet of stars mentioned, there are
three possible pairs of stars, three possible 2-1 combinations, and a
sum of all three, for a total of seven combinations. All of those
"centers of gravity" are moving with respect to each other, even
though the total linear and angular momenta are zero. Thus, your
claim leads to a contradiction.

If you are now changing your claim to only discuss the angular
momentum of the center of mass alone, that is a different matter, but
it is not what you originally claimed.

.... snip ...
Of course I maintain that given such an analysis with effectively
stationary centers of gravity overall we're faced with a de facto
necessity for collapse along lines of stationary centers of gravity.
It's what I call the Chicken Little Hypothesis. In other words the sky
is falling.

How does that follow either? Even if, for the sake of argument, the
"centers of gravity" were "stationary," you have defined them as
imaginary points.

It's not a question of how I've defined them.They're defined by Newton
as much as anyone as the centers through which universal gravitational
attraction works. And they're no more imaginary than the local centers
of attraction through which gravitational attraction works inside
stars. Just because you can't associate any material element with them
outside a star doesn't mean they don't actually exist.

That is not relevant. "Centers of gravity" are still imaginary
points. Therefore, they are not attracted to each other by gravity,
nor do they have angular momentum or energy. They do not necessarily
"collapse" by themselves. As you defined them, they merely exist as
points defined by the various stars in the cluster. Thus your
conclusion does not follow. The relevant question is regards the
motions of the individual stars. Then any follow-on discussion of
"centers of gravity" can be computed immmediately.


.... snip ...
Let's try a simple example. Suppose we have a globular cluster with
roughly zero net angular momentum. And let's suppose through the magic
of TV we can define opposing centers of gravity in respective
hemispheres A and B around which all stars in those hemispheres have
roughly equal and opposite aggregate angular momentum.

The question then is can A and B be moving with respect to each other?
Obviously not. They have to be stationary with respect to one another.

Your example is not well enough defined. If your "A" and "B" are
defined in terms of a fixed set of stars, initially in two
hemispheres; then of course, as the stars move, the centers of mass of
the two sets of stars will move in some complicated pattern. If your
"A" and "B" are always defined in terms of the two fixed hemispheres,
then of course the hemispheres will not move since you have defined
them to be fixed. Stars will pass between the boundaries of the two
hemispheres, thus blurring the concept of "center of gravity." Thus,
your example is not sufficient.

....snip...

CM

Lester Zick wrote:
On 22 Aug 2006 01:20:38 -0700, "George Dishman"
wrote:

my entire post snipped by Lester

Yes, yes, George, it's good to see we've finally reached agreement on
the fundamental issue I raised initially.

Nice to see we have cleared up that clusters are
some of the oldest objects in the galaxy.

I agree that the virial
theorem supports my view on the relative age of globular clusters.

It doesn't, the virial theorem was not relevant to that
determination at all. The relative difference in ages
was determined by beryllium abundances and has
never been in contention. You would have known that
if you had read the ESO web page I posted when you
first asked that question. We never disagreed on that.
In fact it is quite likely that the formation of the galaxy
took some time and was probably ongoing when the
cluster formed but the ESO measurement confirms
what you said on their relative ages.

The problem has always been that those who disagree with my analysis
have looked at the problem backward, initially trying to grasp the
motions of individual stars within a globular cluster instead of the
cluster as a whole. The fact seems to be that globular clusters have
no net angular momentum themselves. Consequently we must infer that
motions of individual stars within the cluster are completely nugatory
and that angular momenta within the cluster cancel each other

Essentially that is correct, the net is small compared
to the sum of the individual stars' momenta though it
is not exactly zero.

and
centers of gravity for those angular momenta must be stationary with
respect to the cluster or the cluster itself would have angular
momentum.

No, the angular momenta of individual stars can
be high as long as they cancel as you say above.
That is where the virial theorem comes in. For a
globular cluster, it gives:

KE = -1/2 PE

or the average kinetic energy for individual stars is
half of their average negative gravitational potential
energy. Since the directions of the individual stars
motions are randomised by the gravitational
interactions, they are also random and that gives
a random distribution of angular momenta about
the cluster's centre of momentum even though
the total is near to zero.

The result of all this is that globular clusters must be collapsing
along the lines of those stationary centers of gravity.

Nope, it says the opposite. Since the individual
stars have a distribution of angular momenta, it is
thefore a result of Newtonian mechanics that the
stars do not all rush directly to the centre.

The distribution of kinetic energies also includes
a tail so there will be a few stars whose kinetic
energy is greater than is required for escape so
the cluster "evaporates" over long time scales.
Since the highest velocity stars also have the
highest momentum, that doesn't alter the
conclusion that the cluster won't collapse to a
disc. They do undergo core collapse of course
but that's not what you are describing.

more childish attempts at insults snipped.

George

On 23 Aug 2006 01:04:20 -0700, "George Dishman"
wrote:


Lester Zick wrote:
On 22 Aug 2006 01:20:38 -0700, "George Dishman"
wrote:

Well, George, I didn't snip your entire post as you claim; I just
didn't see anything worth saving. I imagine it's still out there lost
in cyberspace which is pretty much just where it belongs. It's true
that the virial theorem support my interpretation of globular cluster
collapse and I'm glad to know you concur that globular clusters are
some of the youngest objects in the universe.

As for your analysis of the exchange of PE and KE in inverse square
conic section orbits. It's totally irrelevant and about as original as
the rest of your many and varied misconceptions being hoary with age
since the days of Kepler and Newton. But keep plodding along. It's
what the British do.

Lester Zick
~v~~

"Lester Zick" wrote in message
...
On 23 Aug 2006 01:04:20 -0700, "George Dishman"
wrote:
Lester Zick wrote:
On 22 Aug 2006 01:20:38 -0700, "George Dishman"
wrote:

Well, George, I didn't snip your entire post as you claim; I just
didn't see anything worth saving.

Of course you didn't Lester, but then what
you see is seldom what I write.

... It's true
that the virial theorem support my interpretation of globular cluster
collapse and I'm glad to know you concur that globular clusters are
some of the youngest objects in the universe.

ROFL, so you have been reduced to telling
a pack of lies Lester. That's not what your
supposed to achieve if you are going to
become an effective troll.

plonk

On Wed, 23 Aug 2006 20:18:41 +0100, "George Dishman"
wrote:

There's nothing much to what you write, George. It's out there if
anyone wants to look. You complain that I tell lie after lie whereas
you just tell the same lie over and over. And if I ever want to become
a troll I'll be sure to ask your help.

Lester Zick
~v~~

On 22 Aug 2006 14:43:22 -0400, Craig Markwardt
wrote:


Lester Zick writes:

On 21 Aug 2006 03:25:34 -0400, Craig Markwardt
wrote:


Lester Zick writes:
On 19 Aug 2006 14:19:24 -0400, Craig Markwardt
wrote:


Lester Zick writes:
... snip ...
It means I think the sky is falling in gc's just the way it does in
every celestial object whose centers of gravity are stationary with
respect to one another.
... snip ...

What exactly do you mean by,
* "centers of gravity", and that they
* "stationary with respect to one another"

Perfectly reasonable questions.

I'm not asking for an "it's obvious" answer, but rather, what exactly
you think the terms you used mean in terms of geometry and perhaps
mathematics.

I take the term "centers of gravity" to mean the centers through which
universal gravitational attraction operates. Each star in a globular
cluster has its own local internal center of gravity and each star in
various cominations with other stars has a non local center of gravity
presumably lying somewhere between or among them through which
gravitational attraction for the combination acts in relation to
centers of gravity for other combinations.And these centers of gravity
exist for every possible combination of stars within the cluster. And
every possible combination of stationary and moving stars within a
cluster has to be reckoned in terms of all centers of gravity among
all the combinations and not just exclusively between each pair of
stars within the cluster or for the cluster as a whole in calculating
net angular momentum for the cluster.

Wouldn't it be more straightforward to calculate the cluster angular
momentum about a given axis based on a sum of the individual stars'
angular momenta?[*] After all, that is the formal definition of
angular momentum, isn't it?

Regardless of how you add them up the sum is still roughly zero
provided you add them all up and not just a few in relation to a
specific axis.

However, since classical total angular momentum is not defined in the
manner which you describe, you would need to substantiate your claim
with extensive theoretical work, which you have not done.

What do you mean classical angular momentum is not defined in the
manner I describe? I don't define angular momentum at all classical or
otherwise. Classical angular momentum is defined as the vector cross
product L=r x p. Do you actually mean to tell me that you really don't
understand how to resolve and add vectors in three dimensions without
extensive theoretical work on my part?

[*] By that I mean, L_total = Sum[ L_i ] = Sum[ r_i x p_i ], where
r_i and p_i are the ith star's distance from the axis and linear
momentum, and "x" indicates a vector cross product.

And secondly, on what evidence do you claim that "centers of gravity
are stationary with respect to one another?"

Well this may not appear obvious however in calculating net angular
momentum for the cluster as a whole we know two basic things: first
the motion of various stars in the cluster individually and second the
net angular momentum for the cluster as a whole of approximately zero.

Thus we can easily construct an equation where the sum of all angular
momenta for all possible combinations of stars in a globular cluster
equals zero. So regardless how we take various combinations of angular
momenta for various centers of gravity within the cluster we have to
recognize that their sum must be zero for the cluster itself to have a
net angular mometum approximately zero. Which means in turn that all
combinations must offset one another in aggregate. Hence even though
some combinational centers may not offset one another directly, all
centers of gravity within the cluster have to be roughly stationary
with respect to all other centers of gravity regardless of a presence
of non zero angular momentum for certain combinations within the
cluster.

How does your conclusion follow?

Because the net angular momentum for the cluster as a whole is roughly
zero. Consequently regardless of individual angular momenta considered
in isolation the aggregate of all angular momenta must be roughly zero
too. Otherwise the cluster itself must have non zero angular momentum.

Your original conclusion still does not follow. Even if the total sum
angular momentum of an ensemble is zero, one cannot conclude that the
individual components of the sum must be zero. Hence one cannot
conclude that the individual components are "stationary."

I didn't say the individual components of the sum must be zero. I said
they have to aggregate to zero.That means that various angular momenta
taken in whatever combinations have to offset each other. And if the
individual components of all combinations are not roughly stationary
with respect to one another the sum of angular momenta for the cluster
as a whole will certainly not be roughly zero.

First, you've been writing about angular momentum, so what step of
logic allows one to translate from the domain of angular momentum to
"roughly stationary" points? For example, the total angular momentum
of a system can be zero when the total energy or linear momentum is not.

I'm not talking about linear momentum here.As far as different domains
of angular momentum are concerned we're just adding them up. They have
to equal zero whether or not isolated domains have energy or linear
momentum. It's quite possible for moving bodies with kinetic energy
and linear momentum to possess offsetting angular momenta with respect
to various centers of gravity.

You claimed that something was "stationary." In classical mechanics
if a body is stationary, it is not moving. A body cannot have
"kinetic energy and linear momentum" and also be stationary.

Why not? We're discussing angular momentum here not linear momentum
and kinetic energy. Two bodies of equal mass in opposing orbits have
zero net angular momentum because their vector cross products L=r x p
offset one another and yet they still have net kinetic energy in gross
linear terms because kinetic energy is not a vector.

Second, it is easy to construct a sum of two functions which is zero
but whose individual values are not.

Sure. The problem is that we have to wind up with centers of gravity
stationary with respect to each other or the angular momentum of the
object as a whole will have some net angular momentum.

For example, consider three identical stars arranged along the X axis
at positions (-1 pc), (0 pc), (+1 pc),[*] with the outer two stars
moving apart and the center star held fixed (with respective
velocities: (-1 pc/yr), (0 pc/yr), (+1 pc/yr)). By any definition,
the total linear and angular momentum of this system is zero. And
yet, the stars are moving apart. The "centers of gravity" as you
define them are also moving apart from each other and thus not
"stationary." Thus, your conclusion is not rigorous.

Which centers of gravity? That for the stars individually considered
in isolation or the center of gravity for the system as a whole? The
fact that the stars themselves are moving apart is irrelevant. The
center of gravity for the system itself is stationary. The centers of
gravity as I define them are only moving apart for the individual
stars and not for the system as a whole.

You claimed that one must consider *all* possible combinations of
"centers of gravity." For the triplet of stars mentioned, there are
three possible pairs of stars, three possible 2-1 combinations, and a
sum of all three, for a total of seven combinations. All of those
"centers of gravity" are moving with respect to each other, even
though the total linear and angular momenta are zero. Thus, your
claim leads to a contradiction.

So how is it the vector sum of all those angular momenta around all
those centers of gravity add up to zero?

If you are now changing your claim to only discuss the angular
momentum of the center of mass alone, that is a different matter, but
it is not what you originally claimed.

And it's not what I mean. It doesn't really matter whether the vector
sum of all angular momenta is taken with respect to the center of the
mass alone. The fact is their vector sum is roughly zero.

... snip ...
Of course I maintain that given such an analysis with effectively
stationary centers of gravity overall we're faced with a de facto
necessity for collapse along lines of stationary centers of gravity.
It's what I call the Chicken Little Hypothesis. In other words the sky
is falling.

How does that follow either? Even if, for the sake of argument, the
"centers of gravity" were "stationary," you have defined them as
imaginary points.

It's not a question of how I've defined them.They're defined by Newton
as much as anyone as the centers through which universal gravitational
attraction works. And they're no more imaginary than the local centers
of attraction through which gravitational attraction works inside
stars. Just because you can't associate any material element with them
outside a star doesn't mean they don't actually exist.

That is not relevant. "Centers of gravity" are still imaginary
points. Therefore, they are not attracted to each other by gravity,
nor do they have angular momentum or energy. They do not necessarily
"collapse" by themselves. As you defined them, they merely exist as
points defined by the various stars in the cluster. Thus your
conclusion does not follow. The relevant question is regards the
motions of the individual stars. Then any follow-on discussion of
"centers of gravity" can be computed immmediately.

As Newton defined them centers of gravity are merely points through
which gravitation acts. The center of gravity for a star is no more or
less real than the center of gravity between stars.

... snip ...
Let's try a simple example. Suppose we have a globular cluster with
roughly zero net angular momentum. And let's suppose through the magic
of TV we can define opposing centers of gravity in respective
hemispheres A and B around which all stars in those hemispheres have
roughly equal and opposite aggregate angular momentum.

The question then is can A and B be moving with respect to each other?
Obviously not. They have to be stationary with respect to one another.

Your example is not well enough defined. If your "A" and "B" are
defined in terms of a fixed set of stars, initially in two
hemispheres; then of course, as the stars move, the centers of mass of
the two sets of stars will move in some complicated pattern. If your
"A" and "B" are always defined in terms of the two fixed hemispheres,
then of course the hemispheres will not move since you have defined
them to be fixed.

I haven't "defined" them to be any such thing. I've said either they
are fixed in relation to one another or the cluster as a whole must
have non zero angular momentum.

Stars will pass between the boundaries of the two
hemispheres, thus blurring the concept of "center of gravity." Thus,
your example is not sufficient.

Yeah, look, Craig, I don't know where you get your ideas on vector
arithmetic and blurred centers of gravity. You seem sincere yet these
are or should be basic mechanical concepts in first year collegiate
math. And what I'm seeing so far is a pretty gross deficiency on the
part of almost everyone in sci.astro in basic vector mechanics. And
I'm really beginning to regret having broached the topic at all. It's
such a simple proposition that I couldn't begin to conceive of all the
ridiculous mental constipation and rationalization it's generated.

Lester Zick
~v~~

On 1 Aug 2006 01:03:54 -0700, "George Dishman"
wrote:

Lester Zick wrote:
On 31 Jul 2006 00:52:19 -0700, wrote:


Lester Zick wrote:
On Mon, 24 Jul 2006 00:34:14 -0700, Lester Zick
wrote:


Gravitational Doppler
~v~~

We are well aware of gravitational lensing but there is another EM
analog associated with Newtonian universal gravitation as well:
gravitational doppler. In other words with latency extensions to
Newtonian universal gravitation we can explain planetary orbital
perihelion anomalies and calculate the Pioneer anomaly in simple,
direct terms.

To do this we only need to calculate Pioneer's velocity away from the
sun as a fraction of the speed of light and recognize that the effect
of the sun's gravitation will increase in proportion:

(Numbers used here were drawn from a column 1 article in the L. A.
Times of 12/21/2004 and are not exact)

Yearly distance traveled by Pioneer = 219,000,000 miles

Yearly discrepancy in distance = 8,000 miles

Ratio = ~ 27,375

speed of light = 186,289 miles per
second

Yearly distance traveled by light in one year=

186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr

Divided by yearly distance traveled by Pioneer

Ratio = ~ 26,825

A difference between the two ratios of 2% (27375 - 26,825 / 27,375)

QED

~v~~

In other words Pioneer travels about 7 miles per second away from the
sun and in doing so gravitation waves lengthen and their attractive
intensity is experienced longer in each wave. (In this respect unlike
repulsive waves like EM radiation, the effect of attraction increases
in gravitation with longer waves and decreases with shorter waves.)
And conversely the attraction of gravitation should decrease as the
sun is approached.

Clearly the Pioneer Anomaly is caused by what I call gravitational
doppler. This mechanical principle of gravitational doppler latency
added to Newtonian universal gravitation also underlies planetary
perihelion orbital anomalies except in such cases where a roughly
constant orbital distance is maintained there is no net change in
gravitational attraction: there is only an eccentric locus of force
offset to the receding hemisphere of the sun according to its own
rotational speed and density distribution. I have only been able to
estimate this degree of eccentricity to account for the anomalous
perihelion advance of the planet Mercury to a an order of magnitude of
2 however the rotational characteristics of the sun and distribution
of mass are extremely complex and difficult to estimate accurately.


[. . .]

D=219,000,000 miles d=8,000 miles discrepancy
V=219,000,000 mi/yr v=8,000 mi/yr discrepancy

We find that:

d/D=D/c*sec/yr and

v/V=V/c

From which we can conclude:

V^2=cv or v=V^2/c

[. . .]

For the years covered by the original study:

d D d/D V V/c
270 2.52E+08 1.07E-06 2.51E+08 4.27E-05
810 2.50E+08 3.24E-06 2.50E+08 4.25E-05
1351 2.49E+08 5.43E-06 2.48E+08 4.23E-05
1891 2.48E+08 7.63E-06 2.47E+08 4.20E-05
2431 2.47E+08 9.86E-06 2.46E+08 4.19E-05
2971 2.46E+08 1.21E-05 2.45E+08 4.17E-05
3511 2.45E+08 1.43E-05 2.44E+08 4.15E-05
4052 2.44E+08 1.66E-05 2.43E+08 4.14E-05

Between 1987 and 1994, the values of D, V and
V/c fell by only 3.07% while the value of d/D
increased by a factor of over 15.

As you can see V/c is almost constant while
d/D is increasing quadratically and around
2004 the values would be roughly equal.

George, a quick question from six months ago: are the data values in
your table for d cumulative and are all the variables heliocentric?

~v~~