Gravitational Doppler

On 4 Aug 2006 21:11:16 -0700, wrote:


Lester Zick wrote:
On 4 Aug 2006 13:03:52 -0400, (Steve Willner)
wrote:

In article ,
Lester Zick writes:
In the case of friction if we ignore slippage the magnitude of the
deceleration (counterceleration?) can only be a function of velocity:
proportionately stronger at greater velocities, zero at zero velocity,
and reversing direction at velocities in opposite directions.

I don't know what you mean by "ignore slippage,"

"Ignoring slippage" just means assuming friction is maintained evenly
throughout. There are occasions when friction is not maintained evenly
throughout as when brake pads are worn unevenly or the brakepad has
oil residue.

but mechanical
friction is generally greatest at low speeds (just above zero) and
nearly constant independent of speed at higher speeds.

At very low speeds you have a mixture of first order friction effects
and second order elastic molecular forces in operation. When second
order elastic molecular forces are very slight in comparison to first
order friction effects the net force exerted by the latter depends on
how much friction is generated and that depends in turn on velocity.

Of course its
direction is always opposite the direction of motion.

Of course. That marks it as a first order force.

It's not hard to think of other examples where force depends on
velocity. Air resistance and magnetic force on a moving charge are
two that come to mind.

Air resistance is certainly a first order force but magnetic force is
a second order quadratic effect in that the interaction of magnetic
fields is positive and inverse square. I think what you might mean is
that a magnetic field is a linear function of velocity.But interaction
of the fields is inverse square if the fields are present. However for
what it's worth I'd prefer not to argue magnetic effects because their
underlying mechanics are so complicated in dynamic terms that they
don't admit of readlily apparent analysis and illustrations.

Lester Zick
~v~~

xxein: Given your post, you have no idea of a physic or how to obtain
one.

Good. There's certainly no reason to discuss what you don't
understand. I don't know where you go but I generally purchase
physic's at the drugstore.

Lester Zick
~v~~

Lester Zick wrote:
On Sat, 05 Aug 2006 08:27:11 GMT, Odysseus
wrote:

In article ,
Lester Zick wrote:

On Fri, 04 Aug 2006 06:48:27 GMT, Odysseus
wrote:

In article ,
Lester Zick wrote:

snip

Rocket thrust as a constant force in this context is what I would call
a second order nonlinear force whereas friction is what I would term a
first order linear force. In other words an ordinary retro rocket
causes an absolute acceleration while friction brakes can only cause a
relative acceleration (deceleration in my own vernacular) in direct
proportion to underlying velocity. Hence constant retro rocket
acceleration will not vary directly as a function of velocity while
friction brake deceleration will.

Why should the latter be the case? Air resistance is a function of
velocity (quadratic IIANM), but a caliper brake exerting a constant
force on a wheel will produce a constant frictional force and therefore
a constant deceleration, to a first approximation at least, until the
speed becomes very low and the transition between sliding and static
friction takes place.

Are you suggesting "air resistance" and "friction braking" are
different? They look pretty much the same to me. I'm not sure I
understand the point you're trying to make. You ask "why should the
latter be the case?" without suggesting any alternative that I can
see.

I certainly am; they're not at all the same. Sliding friction between
two solid surfaces is independent of speed; it's just the product of the
normal force with the coefficient of friction.

Here you say sliding friction between two solid surfaces is
independent of speed but below you indicate the effect is linear.

There is a little ambiguity in the wording later but
no contradiction.

I don't mind being corrected on the subject but now I'm confused. In any
event I acknowledged to George that my reading on the Pioneer anomaly
is incorrect so I'm not sure the issue matters much at the moment.

Where the normal force is
provided by the weight of the object on a level surface (as for the
train, if its wheels stop turning and slide on the rails) the
deceleration is just k*g, where k is the relevant coefficient of
friction (here for steel on steel) and g is the acceleration of gravity.
No velocity parameter required.

Air resistance is very different, the force being strongly dependent on
the speed. This has to do with the effects of pressure and turbulence,
which are quite complicated. At very low speeds or in a viscous fluid,
drag is roughly proportional to the velocity, but at high speeds in air
it's a function of velocity squared.

Sure. My mistake. With air we're dealing with a compressible fluid.

Going back to the spacecraft, consider the drag
effect of dust. The dust is so thin each particle is
independent so no viscosity. The impact of each
dust particle imparts a small change of momentum
to the craft given by p=mv where m is the mass of
the particle and v is its speed relative to the craft.
If the particle is in a circular orbit with speed small
compared to that of the craft we can ignore the
transverse effect and the momentum is proportional
to the speed. However, there is a second factor. As
the craft moves, it sweeps out some volume. The
faster the craft moves, the greater the volume it
sweeps in a given time and hence for some dust
density it encounters more particles. Hence the
force (rate of change of momentum) is proportional
to the square of the speed.

Were the braking proportional to velocity, the train would never quite
come to a halt; instead its speed would approach zero asymptotically,
like the amount of radioactive material in a sample, decaying
exponentially. Cf. also Newton's law of cooling.

Sure. Friction braking is asymptotic until sufficiently slowing is
effected to bring elastic electrostatic forces into play which stop
motion.

It is not in fact asymptotic, but linear; simple experiments, requiring
little in the way of apparatus, will readily demonstrate that. I
performed several such in my high-school and first-year physics classes.

Hmm. Linear as a function of velocity?

No, the speed is linear as a function of time because
the frictional braking is independent of speed.

Wouldn't the make the approach
to v=0 asymptotic?

If the braking force were a linear function of speed then
speed would decrease asymptotically as an exponential
function of time. However, the braking force is constant
generally until they start to bind at low speeds.

George

On 7 Aug 2006 05:31:49 -0700, "George Dishman"
wrote:


Lester Zick wrote:
On Sat, 05 Aug 2006 08:27:11 GMT, Odysseus
wrote:

[. . .]

Going back to the spacecraft, consider the drag
effect of dust. The dust is so thin each particle is
independent so no viscosity. The impact of each
dust particle imparts a small change of momentum
to the craft given by p=mv where m is the mass of
the particle and v is its speed relative to the craft.
If the particle is in a circular orbit with speed small
compared to that of the craft we can ignore the
transverse effect and the momentum is proportional
to the speed. However, there is a second factor. As
the craft moves, it sweeps out some volume. The
faster the craft moves, the greater the volume it
sweeps in a given time and hence for some dust
density it encounters more particles. Hence the
force (rate of change of momentum) is proportional
to the square of the speed.

George, are you trying to make a case here for a dust drag scenario
for the Pioneer anomaly?

Were the braking proportional to velocity, the train would never quite
come to a halt; instead its speed would approach zero asymptotically,
like the amount of radioactive material in a sample, decaying
exponentially. Cf. also Newton's law of cooling.

Sure. Friction braking is asymptotic until sufficiently slowing is
effected to bring elastic electrostatic forces into play which stop
motion.

It is not in fact asymptotic, but linear; simple experiments, requiring
little in the way of apparatus, will readily demonstrate that. I
performed several such in my high-school and first-year physics classes.

Hmm. Linear as a function of velocity?

No, the speed is linear as a function of time because
the frictional braking is independent of speed.

Wouldn't the make the approach
to v=0 asymptotic?

If the braking force were a linear function of speed then
speed would decrease asymptotically as an exponential
function of time. However, the braking force is constant
generally until they start to bind at low speeds.

Please forgive my obtuseness, George, but assuming constant pad
pressure, isn't braking deceleration a linear function of the amount
of friction generated and the amount of friction generated a linear
function of speed? Besides your comment above "linear as a function of
time" appears to assume we have some other measure of time than speed.
This is the difficulty I have with a dust drag or even ether drag
scenario for the anomaly:it still somehow seems related to speed.

Lester Zick
~v~~

Lester Zick writes:

On 7 Aug 2006 05:31:49 -0700, "George Dishman"
wrote:


Lester Zick wrote:
On Sat, 05 Aug 2006 08:27:11 GMT, Odysseus
wrote:

[. . .]

Going back to the spacecraft, consider the drag
effect of dust. The dust is so thin each particle is
independent so no viscosity. The impact of each
dust particle imparts a small change of momentum
to the craft given by p=mv where m is the mass of
the particle and v is its speed relative to the craft.
If the particle is in a circular orbit with speed small
compared to that of the craft we can ignore the
transverse effect and the momentum is proportional
to the speed. However, there is a second factor. As
the craft moves, it sweeps out some volume. The
faster the craft moves, the greater the volume it
sweeps in a given time and hence for some dust
density it encounters more particles. Hence the
force (rate of change of momentum) is proportional
to the square of the speed.

George, are you trying to make a case here for a dust drag scenario
for the Pioneer anomaly?

The impulse on a spacecraft due to an individual dust particle is
equal to
I = m v if the dust is captured, or
I = 2 m v if the dust bounces elastically
where m is the dust grain mass and v is the spacecraft speed

This is basic conservation of momentum. The mean number of collisions
in a given time t is equal to the product of the density of dust
grains, n, times the volume swept up by the spacecraft in that time,
N = n * V
= n * (A * v * t)
where N is the number of collisions and A is the spacecraft area

Thus, the total impulse in time t is, at most,
I = (2 m v) * (n * A * v * t)

Using the definition of impulse, as the integral of force (so F =
dI/dt), and acceleration being a = F / M, where M is the spacecraft
mass, the acceleration is,
a = 2 m n A v^2 / M

or half of that if the dust is captured. Thus, the acceleration due
to non-interacting dust is proportional to the square of the
spacecraft velocity. If there is a distribution of dust grain masses,
then
a = 2 m n A v^2 / M

where m is the mean dust grain mass.

That is all basic classical mechanics. The nature of dust in the
solar system is pretty well known:

[ Markwardt, , Nov 2003: ]
: Dust properties in the outer solar system have been measured, in
: some cases by quantitative dust instruments on Pioneers 10 and
: 11 themselves (Landgraf et al 2002; Gurnett et al 1997). The there
: is a continuous density distribution. According to the above
: equation, the acceleration is heavily weighted to large dust
: particles, but these are extremely rare. The net densities are of
: order 2 x 10^{-17} cm^{-3}, with dust masses ~0.1 ug, leaving the net
: acceleration due to dust to be safely less than a few times 10^{-12}
: cm s^{-2}, far less than the quoted anomalous acceleration.

Thus, dust acceleration of the Pioneers is neglible.

CM


References
D. A. Gurnett, J. A. Ansher, W. S. Kurth, and L. J. Granroth 1997,
Geophys. Res. Lett., 24, 3125
M. Landgraf, J.-C. Liou, H. A. Zook, and E. Gr\"un 2002,
Astrophys. J., 123, 2857

"Lester Zick" wrote in message
...
On Sun, 6 Aug 2006 20:17:30 +0100, "George Dishman"
wrote:


"Lester Zick" wrote in message
. ..
...
George, it seems I've been winging it a little too carelessly. My
calculations only imply that v/V is the same as V/c for 2004 and do
not imply v/V is constant.

In that case all the previous discussion is
really moot. However I hope you now have a
lot more information at your disposal.

Apart from the calculations for 2004 apparently so. I doubt a lot more
information is going to help without the underlying mechanical theory
to act as a framework.In fact one of the disappointing features of the
original paper was far too much information. My personal perspective
was that it should have started off discussing the anomaly and its
measurement and other relevant characteristics then gone into space
craft construction, propulsion, and mechanical subsystems which might
have had a bearing on the anomaly. As it was I couldn't see the forest
for the trees.

You have to remember that a priori there is
no concrete evidence that the anomaly arises
from motion of the craft. I think it entirely
appropriate that they first explained the
method by which the speed is measured and then
say there was a residual after everything known
was taken into account. As an engineer in a
communications firm, my initial focus was on
the effects of the circular polarisation of
the radio beam from a spinning craft on the
frequency counters.

Obviously I've been sloppy in my comments
but this still stikes me as a remarkable coincidence and I'm convinced
gravitational doppler is what underlies the phenomenon, at least for
2004, whether or not I can link it all up.

Well the key I think is the formula for your
"gravitational doppler". If it is a multiplier
onto the normal gravitational acceleration as
it appeared earlier in the thread then the
cruial test is how the anomaly varies with
range. At constant speed, the anomaly from
gravitational doppler would vary as the
inverse square of the distance from the Sun
but the observed anomaly is constant,
independent of range. That seems to rule it
out but correct me if I'm assuming too much.

I'm not sure. This is really the point I was interested in exploring a
little further. I'm personally convinced the effect is there. At least
an analogous effect manifests itself when magnets sitting apart on a
rest surface are pulled rapidly away from each other.

But no such effect is seen. Moving a magnet will
induce eddy currents in nearby metal, another
magnet for example, and eddy currents can provide
a braking effect, but that is not a Doppler
variation of the magnetic force.

The problem is
that I don't quite know how to characterize that effect as a function
of velocity or acceleration.In my estimation it's certainly a function
of motion away from the sources and some kind of doppler effect.

Your description as Doppler means there would be a
speed-dependent factor applied to the basic force.
A craft moving at a speed of 10^-6 of the speed of
light produces a Doppler shift of roughly 10^-6
times the signal so 2kHz on a 2GHz carrier or 1kHz
on a 1GHz carrier. If the same applied to Pioneer
then since the radial speed is almost constant at
about 12.5 km/s, the anomaly should be a constant
fraction of the basic Newtonian force of GM/r^2.

The same is true of gravitationally bound systems as I believe we've
touched on before. I'm convinced that because Pioneer and other probes
are moving away from the sun there has to be an anomalous acceleration
toward the sun and I believe the underlying mechanics have to be some
kind of doppler effect. But whether the effect is linear as a function
of velocity or something else is not so apparent.

It doesn't matter what the behaviour as a function
of speed is, the speed is constant. What does matter
is the behaviour with distance since the craft moved
from 40AU to 60AU without any reduction in the anomaly.

As loathe as I am to
get into the subject maybe we have to consider properties of whatever
spatial plenum is involved (shudder!). But the effect has to be there
because there is no other way to communicate anomalous motion toward
or away from mutually attracting sources.

Unfortunately I've pretty much reached the limits of my understanding
of longitudinal doppler mechanics. I suppose what will happen now is
that I'll try converting measurements into cm. and try looking up the
solar gravitational constant and start playing around with the numbers
again. Maybe I'll get lucky once more. But it certainly strikes me as
incredibly serendipitous that the calculations for 2004 worked out as
accurately as they did.

Yes but look at the nature of the coincidence, if
the same article had been published the year before
the numbers would not have matched. The anomaly is
a speed proportional to time (constant acceleration)
while you calculated one particular speed, 8000 miles
per year. As a result there must be some year when
the anomaly matches and it is a coincidence that the
Times happened to choose that year to print the
article. It isn't a scientific coincidence but one of
publishing dates.

For comparison consider this coincidence. If the
anomaly was caused by drag from dust particles the
density of the dust needed to produce the anomaly
is 3*10^-19 g/cm^3. That is considered unreasonable
because the upper limit on dust from various optical
measurements is lower. Hower this paper was published
just a few weeks ago:

http://www.arxiv.org/abs/astro-ph/0606197

The upper limit they put on dark matter in the Solar
system, which wouldn't be detected by optical means,
is ........ 3*10^-19 g/cm^3 !

Now that's a coincidence ;-)

One thing I was trying to work around was the anomalous frequency
drift of -6x10^-9 hz/sec reported in the original paper. This at least
I can understand given the doppler mechanics of speed measurement for
Pioneer. Given the retrograde ..

I think you mean radial.

.. nature of the anomaly I think we really
have to acknowledge that the mechanical likelihood is that it only
occurs because Pioneer is moving away from the sun.

No we don't, that's a dangerous and possibly
misleading assumption. If the craft turned to
face the back of the dish towards Earth we have
no idea which way the acceleration would go.

But why it is
constant and independent of distance remains a mystery.

Definitely.

So I'll have to rethink the
problem. For the time being I'll just have to let the issue rest. But
I certainly appreciate your interest and comments.

That's OK, I've been scratching this itch for
5 years now ;-)

Good luck with the hunt.

Thanks, George. Maybe a more appropriate title for this thread would
have been "The Mechanics of Gravitational Doppler". At least I can
hope for further serious discussion of mechanics of action at a
distance and principles related to changes in distance. (You know for
what it's worth if the anomaly is not internal we might try assigning
it to some kind of ether drag but even so how could that drag not be
some kind of function of velocity?)

Aether isn't needed, just dark matter particles,
but it would be proportional to the square of
the speed anyway. That doesn't rule it out though
because the speed is constant so it could have any
relationship, we only know the value at one speed.

George

On 07 Aug 2006 14:36:12 -0400, Craig Markwardt
wrote:


Lester Zick writes:

On 7 Aug 2006 05:31:49 -0700, "George Dishman"
wrote:


Lester Zick wrote:
On Sat, 05 Aug 2006 08:27:11 GMT, Odysseus
wrote:

[. . .]

Going back to the spacecraft, consider the drag
effect of dust. The dust is so thin each particle is
independent so no viscosity. The impact of each
dust particle imparts a small change of momentum
to the craft given by p=mv where m is the mass of
the particle and v is its speed relative to the craft.
If the particle is in a circular orbit with speed small
compared to that of the craft we can ignore the
transverse effect and the momentum is proportional
to the speed. However, there is a second factor. As
the craft moves, it sweeps out some volume. The
faster the craft moves, the greater the volume it
sweeps in a given time and hence for some dust
density it encounters more particles. Hence the
force (rate of change of momentum) is proportional
to the square of the speed.

George, are you trying to make a case here for a dust drag scenario
for the Pioneer anomaly?

The impulse on a spacecraft due to an individual dust particle is
equal to
I = m v if the dust is captured, or
I = 2 m v if the dust bounces elastically
where m is the dust grain mass and v is the spacecraft speed

This is basic conservation of momentum. The mean number of collisions
in a given time t is equal to the product of the density of dust
grains, n, times the volume swept up by the spacecraft in that time,
N = n * V
= n * (A * v * t)
where N is the number of collisions and A is the spacecraft area

Thus, the total impulse in time t is, at most,
I = (2 m v) * (n * A * v * t)

Using the definition of impulse, as the integral of force (so F =
dI/dt), and acceleration being a = F / M, where M is the spacecraft
mass, the acceleration is,
a = 2 m n A v^2 / M

or half of that if the dust is captured. Thus, the acceleration due
to non-interacting dust is proportional to the square of the
spacecraft velocity. If there is a distribution of dust grain masses,
then
a = 2 m n A v^2 / M

where m is the mean dust grain mass.

That is all basic classical mechanics. The nature of dust in the
solar system is pretty well known:

[ Markwardt, , Nov 2003: ]
: Dust properties in the outer solar system have been measured, in
: some cases by quantitative dust instruments on Pioneers 10 and
: 11 themselves (Landgraf et al 2002; Gurnett et al 1997). The there
: is a continuous density distribution. According to the above
: equation, the acceleration is heavily weighted to large dust
: particles, but these are extremely rare. The net densities are of
: order 2 x 10^{-17} cm^{-3}, with dust masses ~0.1 ug, leaving the net
: acceleration due to dust to be safely less than a few times 10^{-12}
: cm s^{-2}, far less than the quoted anomalous acceleration.

Thus, dust acceleration of the Pioneers is neglible.

I assume you mean the dust acceleration is negligible as a fraction of
the anomaly?

You know, Craig, it would be helpful at least to me if you would state
your thesis ahead of calculations so I can tell where you're going
with them. Personally I have a hard time just reading calculations
without some understanding what they're supposed to be in aid of. I
don't necessarily doubt what you say but don't really have the
expertise to judge the issue accurately in numerical terms. It might
be interesting to calculate the amount of dust needed to effect the
Pioneer anomaly.

Lester Zick
~v~~

"Lester Zick" wrote in message
...
On 7 Aug 2006 05:31:49 -0700, "George Dishman"
wrote:


Lester Zick wrote:
On Sat, 05 Aug 2006 08:27:11 GMT, Odysseus
wrote:

[. . .]

Going back to the spacecraft, consider the drag
effect of dust. The dust is so thin each particle is
independent so no viscosity. The impact of each
dust particle imparts a small change of momentum
to the craft given by p=mv where m is the mass of
the particle and v is its speed relative to the craft.
If the particle is in a circular orbit with speed small
compared to that of the craft we can ignore the
transverse effect and the momentum is proportional
to the speed. However, there is a second factor. As
the craft moves, it sweeps out some volume. The
faster the craft moves, the greater the volume it
sweeps in a given time and hence for some dust
density it encounters more particles. Hence the
force (rate of change of momentum) is proportional
to the square of the speed.

George, are you trying to make a case here for a dust drag scenario
for the Pioneer anomaly?

No. My position is quite simple, we do not yet
know what causes it. What I was doing was to
try to show you that the assumption you are
making is unjustifiable on the basis of the
available data. I took dust as a counterexample
which fits the observations and would produce a
constant acceleration but would be ruled out by
your assumption the the anomaly is proportional
to the speed. Dust is ruled out on other grounds
so I am not suggesting that as a cause, only
that you need to keep an open mind and only rule
things out when the data force it. For example
we can rule out the idea that the solar radiation
pressure is less than anticipated because that
would produce an inverse square reduction with
distance.

Were the braking proportional to velocity, the train would never
quite
come to a halt; instead its speed would approach zero
asymptotically,
like the amount of radioactive material in a sample, decaying
exponentially. Cf. also Newton's law of cooling.

Sure. Friction braking is asymptotic until sufficiently slowing is
effected to bring elastic electrostatic forces into play which stop
motion.

It is not in fact asymptotic, but linear; simple experiments, requiring
little in the way of apparatus, will readily demonstrate that. I
performed several such in my high-school and first-year physics
classes.

Hmm. Linear as a function of velocity?

No, the speed is linear as a function of time because
the frictional braking is independent of speed.

Wouldn't the make the approach
to v=0 asymptotic?

If the braking force were a linear function of speed then
speed would decrease asymptotically as an exponential
function of time. However, the braking force is constant
generally until they start to bind at low speeds.

Please forgive my obtuseness, George, but assuming constant pad
pressure, isn't braking deceleration a linear function of the amount
of friction generated and the amount of friction generated a linear
function of speed?

Nothing obtuse about that Lester, it's a perfectly
sensible question. The answer is that the amount of
frictional force is independent of the speed but
a linear function of the pressure applied to the pads.

Besides your comment above "linear as a function of
time" appears to assume we have some other measure of time than speed.

Just being explicit to remove an ambiguity. Compare
these sentences "At constant acceleration, speed is
a linear function of time." and "Braking force is a
linear function of pad pressure."

Odysseus wrote "It is not in fact asymptotic, but
linear" meaning the speed was a linear function of
time but you took it to mean force was a linear
function of speed. I have seen many conversations
descend into flame wars due to that sort of simple
misunderstanding and try to highlight the problem
where I can. Even if _I_ have misunderstood, it at
least gets the subject aired and clarified.

This is the difficulty I have with a dust drag or even ether drag
scenario for the anomaly:it still somehow seems related to speed.

Dust drag is proportional to the square of the speed,
see what I said above or Craig's post, but you might
as well forget about speed dependence, the speed of
the Pioneer craft was nearly constant so any
dependence on speed is immeasurable.

HTH

George

"Lester Zick" wrote in message
...
On 07 Aug 2006 14:36:12 -0400, Craig Markwardt
wrote:


Lester Zick writes:

On 7 Aug 2006 05:31:49 -0700, "George Dishman"
wrote:


Lester Zick wrote:
On Sat, 05 Aug 2006 08:27:11 GMT, Odysseus
wrote:

[. . .]

Going back to the spacecraft, consider the drag
effect of dust. The dust is so thin each particle is
independent so no viscosity. The impact of each
dust particle imparts a small change of momentum
to the craft given by p=mv where m is the mass of
the particle and v is its speed relative to the craft.
If the particle is in a circular orbit with speed small
compared to that of the craft we can ignore the
transverse effect and the momentum is proportional
to the speed. However, there is a second factor. As
the craft moves, it sweeps out some volume. The
faster the craft moves, the greater the volume it
sweeps in a given time and hence for some dust
density it encounters more particles. Hence the
force (rate of change of momentum) is proportional
to the square of the speed.

George, are you trying to make a case here for a dust drag scenario
for the Pioneer anomaly?

The impulse on a spacecraft due to an individual dust particle is
equal to
I = m v if the dust is captured, or
I = 2 m v if the dust bounces elastically
where m is the dust grain mass and v is the spacecraft speed

This is basic conservation of momentum. The mean number of collisions
in a given time t is equal to the product of the density of dust
grains, n, times the volume swept up by the spacecraft in that time,
N = n * V
= n * (A * v * t)
where N is the number of collisions and A is the spacecraft area

Thus, the total impulse in time t is, at most,
I = (2 m v) * (n * A * v * t)

Using the definition of impulse, as the integral of force (so F =
dI/dt), and acceleration being a = F / M, where M is the spacecraft
mass, the acceleration is,
a = 2 m n A v^2 / M

or half of that if the dust is captured. Thus, the acceleration due
to non-interacting dust is proportional to the square of the
spacecraft velocity. If there is a distribution of dust grain masses,
then
a = 2 m n A v^2 / M

where m is the mean dust grain mass.

That is all basic classical mechanics. The nature of dust in the
solar system is pretty well known:

[ Markwardt, , Nov 2003: ]
: Dust properties in the outer solar system have been measured, in
: some cases by quantitative dust instruments on Pioneers 10 and
: 11 themselves (Landgraf et al 2002; Gurnett et al 1997). The there
: is a continuous density distribution. According to the above
: equation, the acceleration is heavily weighted to large dust
: particles, but these are extremely rare. The net densities are of
: order 2 x 10^{-17} cm^{-3}, with dust masses ~0.1 ug, leaving the net
: acceleration due to dust to be safely less than a few times 10^{-12}
: cm s^{-2}, far less than the quoted anomalous acceleration.

Thus, dust acceleration of the Pioneers is neglible.

I assume you mean the dust acceleration is negligible as a fraction of
the anomaly?

You know, Craig, it would be helpful at least to me if you would state
your thesis ahead of calculations so I can tell where you're going
with them.

Craig is a professional and currently involved in
the processing of the data from SWIFT mission. He's
explaining the stuff to you about as simply as it
is possible to do but there's a gulf between your
levels of understanding.

Personally I have a hard time just reading calculations
without some understanding what they're supposed to be in aid of. I
don't necessarily doubt what you say but don't really have the
expertise to judge the issue accurately in numerical terms. It might
be interesting to calculate the amount of dust needed to effect the
Pioneer anomaly.

Here is the formula from above:

a = 2 m n A v^2 / M

where m is the mean dust grain mass.

The number of dust grains per unit volume is n and
their mean mass is m so the product m n is the
mean mass per unit volume, i.e. the mean density
so if we call that s and lose the factor of 2 by
assuming the dust sticks then

a = s A v^2 / M

The area swept by the craft is given in the paper
as predominantly that of the dish which has a
radius of 1.73 m (see page 28). The speed v is
about 12.5 km/s and the mass M is about 241 kg
(also on page 28) and we know the acceleration
is 8.74*10^-10m/s^2 so I'll leave you with the
exercise of finding the density.

I had posted the answer in another reply before I
saw this so you can cheat if you like, assuming I
didn't make a mistake of course ;-)

George

Lester Zick wrote:
On 4 Aug 2006 21:11:16 -0700, wrote:


Lester Zick wrote:
On 4 Aug 2006 13:03:52 -0400, (Steve Willner)
wrote:

In article ,
Lester Zick writes:
In the case of friction if we ignore slippage the magnitude of the
deceleration (counterceleration?) can only be a function of velocity:
proportionately stronger at greater velocities, zero at zero velocity,
and reversing direction at velocities in opposite directions.

I don't know what you mean by "ignore slippage,"

"Ignoring slippage" just means assuming friction is maintained evenly
throughout. There are occasions when friction is not maintained evenly
throughout as when brake pads are worn unevenly or the brakepad has
oil residue.

but mechanical
friction is generally greatest at low speeds (just above zero) and
nearly constant independent of speed at higher speeds.

At very low speeds you have a mixture of first order friction effects
and second order elastic molecular forces in operation. When second
order elastic molecular forces are very slight in comparison to first
order friction effects the net force exerted by the latter depends on
how much friction is generated and that depends in turn on velocity.

Of course its
direction is always opposite the direction of motion.

Of course. That marks it as a first order force.

It's not hard to think of other examples where force depends on
velocity. Air resistance and magnetic force on a moving charge are
two that come to mind.

Air resistance is certainly a first order force but magnetic force is
a second order quadratic effect in that the interaction of magnetic
fields is positive and inverse square. I think what you might mean is
that a magnetic field is a linear function of velocity.But interaction
of the fields is inverse square if the fields are present. However for
what it's worth I'd prefer not to argue magnetic effects because their
underlying mechanics are so complicated in dynamic terms that they
don't admit of readlily apparent analysis and illustrations.

Lester Zick
~v~~

xxein: Given your post, you have no idea of a physic or how to obtain
one.

Good. There's certainly no reason to discuss what you don't
understand. I don't know where you go but I generally purchase
physic's at the drugstore.

Lester Zick
~v~~

xxein: That isn't a bad idea. We need more guesses than one gets from
a bus schedule to determine the real and innate identity of mass and
energy.

On Mon, 7 Aug 2006 21:16:16 +0100, "George Dishman"
wrote:


"Lester Zick" wrote in message
.. .
On Sun, 6 Aug 2006 20:17:30 +0100, "George Dishman"
wrote:


"Lester Zick" wrote in message
...
...
George, it seems I've been winging it a little too carelessly. My
calculations only imply that v/V is the same as V/c for 2004 and do
not imply v/V is constant.

In that case all the previous discussion is
really moot. However I hope you now have a
lot more information at your disposal.

Apart from the calculations for 2004 apparently so. I doubt a lot more
information is going to help without the underlying mechanical theory
to act as a framework.In fact one of the disappointing features of the
original paper was far too much information. My personal perspective
was that it should have started off discussing the anomaly and its
measurement and other relevant characteristics then gone into space
craft construction, propulsion, and mechanical subsystems which might
have had a bearing on the anomaly. As it was I couldn't see the forest
for the trees.

You have to remember that a priori there is
no concrete evidence that the anomaly arises
from motion of the craft. I think it entirely
appropriate that they first explained the
method by which the speed is measured and then
say there was a residual after everything known
was taken into account.

But that analysis didn't happen until page 20. Preceeding that there
was an interminable description of space craft structure and function
that isn't really relevant until mechanical explanations for the
anomaly are entertained.

As an engineer in a
communications firm, my initial focus was on
the effects of the circular polarisation of
the radio beam from a spinning craft on the
frequency counters.

Well as I say anything relevant to meaurement mechanics and techniques
would certainly be critical.

Obviously I've been sloppy in my comments
but this still stikes me as a remarkable coincidence and I'm convinced
gravitational doppler is what underlies the phenomenon, at least for
2004, whether or not I can link it all up.

Well the key I think is the formula for your
"gravitational doppler". If it is a multiplier
onto the normal gravitational acceleration as
it appeared earlier in the thread then the
cruial test is how the anomaly varies with
range. At constant speed, the anomaly from
gravitational doppler would vary as the
inverse square of the distance from the Sun
but the observed anomaly is constant,
independent of range. That seems to rule it
out but correct me if I'm assuming too much.

I'm not sure. This is really the point I was interested in exploring a
little further. I'm personally convinced the effect is there. At least
an analogous effect manifests itself when magnets sitting apart on a
rest surface are pulled rapidly away from each other.

But no such effect is seen. Moving a magnet will
induce eddy currents in nearby metal, another
magnet for example, and eddy currents can provide
a braking effect, but that is not a Doppler
variation of the magnetic force.

Not what I'm suggesting. It may be possible to jury rig explanations
for moving magnets but consider the sun-earth system or even the
earth-moon graviational systems. If the sun were moved suddenly
radially away from the earth the earth would have to follow to some
extent to conserve angular momentum. Gravitational doppler just
explains the coupling of changes in gravitation between attractive
bodies. And conversely if the sun moved suddenly toward the earth
conservation of angular momentum would require the earth to extend its
orbit. I'm not suggesting the effect isn't novel but we need some
mechanism to explain how such changes are accommodated in what
otherwise would be a constant gravitational field.

The problem is
that I don't quite know how to characterize that effect as a function
of velocity or acceleration.In my estimation it's certainly a function
of motion away from the sources and some kind of doppler effect.

Your description as Doppler means there would be a
speed-dependent factor applied to the basic force.

That's the problem my calculations were designed to deal with however
it doesn't explain the constant acceleration.

A craft moving at a speed of 10^-6 of the speed of
light produces a Doppler shift of roughly 10^-6
times the signal so 2kHz on a 2GHz carrier or 1kHz
on a 1GHz carrier. If the same applied to Pioneer
then since the radial speed is almost constant at
about 12.5 km/s, the anomaly should be a constant
fraction of the basic Newtonian force of GM/r^2.

Oh well we'll just have to wait and see. I don't have the answer yet
and don't expect it soon.

The same is true of gravitationally bound systems as I believe we've
touched on before. I'm convinced that because Pioneer and other probes
are moving away from the sun there has to be an anomalous acceleration
toward the sun and I believe the underlying mechanics have to be some
kind of doppler effect. But whether the effect is linear as a function
of velocity or something else is not so apparent.

It doesn't matter what the behaviour as a function
of speed is, the speed is constant. What does matter
is the behaviour with distance since the craft moved
from 40AU to 60AU without any reduction in the anomaly.

Well if the anomaly is really constant acceleration as it appears it
really has to come from the space craft because no external effect not
proportional to V in some respect appears mechanically plausible to
me.

As loathe as I am to
get into the subject maybe we have to consider properties of whatever
spatial plenum is involved (shudder!). But the effect has to be there
because there is no other way to communicate anomalous motion toward
or away from mutually attracting sources.

Unfortunately I've pretty much reached the limits of my understanding
of longitudinal doppler mechanics. I suppose what will happen now is
that I'll try converting measurements into cm. and try looking up the
solar gravitational constant and start playing around with the numbers
again. Maybe I'll get lucky once more. But it certainly strikes me as
incredibly serendipitous that the calculations for 2004 worked out as
accurately as they did.

Yes but look at the nature of the coincidence, if
the same article had been published the year before
the numbers would not have matched.

Yes but on the plus side I wouldn't have made a successful calculation
either and gotten into this mess. A cruel jest indeed on the part of
the gods.

The anomaly is
a speed proportional to time (constant acceleration)
while you calculated one particular speed, 8000 miles
per year.

I didn't calculate it. That was I'm sure provided by JPL to the Times
whoever did the actual calculation.

As a result there must be some year when
the anomaly matches and it is a coincidence that the
Times happened to choose that year to print the
article.

Yeah, yeah, some coincidence. Another grand mal jest on the part of
the gods.

It isn't a scientific coincidence but one of
publishing dates.

Well we shall just have to see what we shall see. Perhaps the gods
have just given us an unrecognized opportunity to figure out what we
haven't imagined before.

For comparison consider this coincidence. If the
anomaly was caused by drag from dust particles the
density of the dust needed to produce the anomaly
is 3*10^-19 g/cm^3. That is considered unreasonable
because the upper limit on dust from various optical
measurements is lower. Hower this paper was published
just a few weeks ago:

http://www.arxiv.org/abs/astro-ph/0606197

The upper limit they put on dark matter in the Solar
system, which wouldn't be detected by optical means,
is ........ 3*10^-19 g/cm^3 !

Now that's a coincidence ;-)

But a very mundane coincidence regardless. Dark matter drag? Please
pardon my skepticism but I think the whole dark matter nonsense was
concocted out of whole cloth just to explain anomalous galactic
rotation speed on the part of people too inept to explain the effect
in mechancial terms. And I think dark matter will likely be explained
much sooner in terms of gravitational doppler than the Pioneer anomaly
will ever be in terms of dark matter. Dark matter sounds like the
worst kind of ad hoc special pleading to me.

One thing I was trying to work around was the anomalous frequency
drift of -6x10^-9 hz/sec reported in the original paper. This at least
I can understand given the doppler mechanics of speed measurement for
Pioneer. Given the retrograde ..

I think you mean radial.

No. So far we only know the effect is radially directed towards the
sun opposed to V. Perhaps I'm misuing the term "retrograde" in this
context but that's what it suggests to me.

.. nature of the anomaly I think we really
have to acknowledge that the mechanical likelihood is that it only
occurs because Pioneer is moving away from the sun.

No we don't, that's a dangerous and possibly
misleading assumption.

Well it's certainly a speculative assumption but I have to start
somewhere. Obviously platoons of engineers are looking at internal
explanations and if I or somebody else can't jury rig some kind of V
related dependency for the anomaly undoubtedly we'll just wind up
assuming the anomaly represents some kind of mechanical malfunction.

If the craft turned to
face the back of the dish towards Earth we have
no idea which way the acceleration would go.

Don't understand this last remark.

But why it is
constant and independent of distance remains a mystery.

Definitely.

So I'll have to rethink the
problem. For the time being I'll just have to let the issue rest. But
I certainly appreciate your interest and comments.

That's OK, I've been scratching this itch for
5 years now ;-)

Good luck with the hunt.

Thanks, George. Maybe a more appropriate title for this thread would
have been "The Mechanics of Gravitational Doppler". At least I can
hope for further serious discussion of mechanics of action at a
distance and principles related to changes in distance. (You know for
what it's worth if the anomaly is not internal we might try assigning
it to some kind of ether drag but even so how could that drag not be
some kind of function of velocity?)

Aether isn't needed, just dark matter particles,

Well dark matter is every bit as ad hoc an explanation as Lorentz's
ether drift was for Michelson-Morley. And believe it or not last night
I was even starting to think some kind of ether drift might explain
the Pioneer anomaly. Just shows what fevered imaginations might
hearken back to.

but it would be proportional to the square of
the speed anyway. That doesn't rule it out though
because the speed is constant so it could have any
relationship, we only know the value at one speed.

You know, George, just your way of putting it as "the speed is
constant" makes me think what if the speed of the drift is taken as
constant in relation to the speed of light? Something to ponder. In
any event toying with the gods is proving rather frustrating.

Lester Zick
~v~~