Max Keon's "anisotropic gravity".

Apologies for breaking the thread but MS OE produces
reference lines that violate the protocol and the
only way round is to cut & paste into a new thread.
I have taken the opportunity to change the subject
line as well. Followups trimmed to relevant groups.


"Max Keon" wrote in message
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"George Dishman" wrote in message
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"Max Keon" wrote in message
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most snipped - see other reply

On the subject of math, the manner in which you worded a reply to
another poster "Chris L Peterson", regarding my proposed gravity
anisotropy, strongly suggests that I was wrong. If you do have
anything to add to that thread, feel free to do so.

Sorry for the delay in posting this.

The points on this are straightforward. You say that
Pioneer shows the drag effect of anisotropic gravity
and that the effect of the Sun applies only to the
radial component. That would be true so consider
what effect it would have on an eccentric orbit like
that of Mercury. A full dynamic analysis might be
complex but as a first approximation, think of the
orbit as being circular with a cyclic radial
perturbation. That radial component would be damped
by the anisotropy so the most obvious effect should
be an exponential reduction in the eccentricity and
the orbit should tend to become circular.

The perihelion advance of Mercury you mention is
perpendicular to that so you would have to show the
maths to convince me your equations predict it.

Think of Pioneer's trajectory as part of the climb to its orbit
aphelion around the Sun. You recently gave a distance from the
Sun where Pioneer would come to a halt due to the anomalous
acceleration, but it wouldn't come to a halt of course because it
would still posses transverse motion as it rides over the high
point of its orbit.

True.

Pioneer was noted to be shifting from its
predicted trajectory in the direction of the Sun as it climbed
the hill. Whether it was noted or not, that had to be the case.
It's the only direction the anomaly could take.

Not true, the direction depends on the cause. Thermal
radiation would push the craft along the spin axis.

That action was
advancing the orbit aphelion.

The gravity anisotropy on the climb to the aphelion increases
resistance to the outward motion and that shifts its orbit path
slightly toward the Sun.

Correct.

Pioneer's transverse motion is now
faster than it would be if it had continued along its old path.

Careful, that's not correct. Since the forces are
radial, the transverse speed is unaffected. Howver,
since the radius is reduced, the angular velocity
is increased.

The slowing effect of the gravity anisotropy has been offset by
the direction shift.

Not offset, the slowing still has the effect of
reducing the radius but a change in angular
velocity is a further consequence.

As for Mercury, the slowing effect of the anisotropy is also
neutralized by a shift in orbit direction.

No, not neutralized.

Mercury's maximum trajectory angle relative the Sun is around 11
degrees, so the average for the entire orbit is 7.8 degrees to
the Sun, which gives an average radial velocity of 6500 m/sec.

The gravity anisotropy is generated according to;
Outward leg = ((c+v)^2/c^2)^.5*(G*M/r^2)-(G*M/r^2)
Inward leg = ((c-v)^2/c^2)^.5*(G*M/r^2)-(G*M/r^2)

Try instead:

((c-v*cos(theta))^2/c^2)^.5*(G*M/r^2)-(G*M/r^2)

where v is the magnitude of the orbital speed and
theta is the angle between the actual velocity and
the Sun-Mercury line, i.e. theta would always be
zero for a circular orbit.

r = 6E+10 meters (average orbit radii).
Gravity anisotropy = 8E-7 and -8E-7 m/sec^2

The square root of that figure brings it into the ball park
of Mercury's perihelion advance, which is 3.7E-3 m/sec.

Hold, on, you've missed a lot. You need to integrate
the anisotropic acceleration to find how much the
radius deviates from the Newtonian path, then use
the unaffected transverse speed to find the angular
speed. Find how much that deviates from Newtonian
value and you get a figure for the mean angular rate
of displacement of the perihelion which is the
published figure.

I don't
know whether or not that action can be justified,

No, see the outline above of what you need to do.

but perhaps
that's how the radial anisotropy is converted to transverse
motion. The transformation takes place in a 3D realm after all.

No need to worry about that, you can work in 2D using
the plane of Mercury's orbit.

The perihelion of Mercury's orbit advances as the effect of the
gravity anisotropy is counteracted, so the orbit eccentricity
remains intact.

No, the advance doesn't counteract the reduction in
radius, it depends on it. Nor does the anisotropy
correct the situation on the inward leg after aphelion.
When moving outwards, the speed is slowed due to the
drag as as you say Mercury is closer than it would be
in Newtonian mechanics and aphelion is reduced. As it
falls back in the drag reduces its speed of approach
to the Sun so it is then farther away than would be
expected for the new aphelion value but (I think) still
closer than expected from the original orbit. The key
point though is that this is still reducing the radial
speed. After a complete orbit, the planet is nearly
where it started but the radial speed is much smaller,
the effect of the drag is cumulative.

You may object to that reasoning, but the
Sun-Mercury relationship is a closed system and there is no
mechanism in place with which to transfer energy between them.

The drag force itself must dissipate energy in some way
so energy is not conserved if gravity is anisotropic.

Apart from tidal effects, gravity has no such mechanism. Instead
of breaking conservation laws, Mercury just changes course a
little.

Sorry, your equation above loses energy.

As did Pioneer.

Pioneer has reduced kinetic energy as a result
of the anomaly.

Picture a ball on the end of an elastic rope being whizzed around
in an eccentric orbit. While it's moving in the outward direction
the rotation axis is pulled in the opposite direction. The ball
will change course and will reach the limit of its outward
movement at a later stage of the orbit cycle. But the maximum
distance between the axis and the ball won't have changed.

The energy is stored in the elastic like in a spring
and is returned as the elastic rebounds and the ball
gets closer. Include anisotropy and you have frictional
loss in the elastic which reduces the energy in the
radial oscillation of the ball and turns it into heat
in the elastic. Where the energy goes in your theory
is unspecified.

Now separately think of the effect of the "rest of
the universe" (ABCD) on the circular orbit of a
planet P around the Sun S:


\ C /


A P B
S

/ D \


I recently stumbled across the claim that almost all matter in
the visible universe is in the plane of our galaxy, and is thus
in the plane of Pioneer's path. You promptly rejected it of
course.

This is a very nice site showing a seies of maps:

http://www.atlasoftheuniverse.com/galaxy.html

That starter shows the galaxy with the plane horizontal.
Click the "Zoom out ..." button at the bottom left three
times and look at the distribution. It still appears to
have some preference for the same plane. Now click once
more and you can see the distribution of superclusters
is much more even. Click a final time to see the visible
universe and it is obviously anisotropic.

The CMBR was a good indication that it was wrong anyway.
Mass estimates for the visible universe are somewhere around
1E+56 kg. My calculations required a 1E+53 kg universe, but it
was necessary for all of that mass to be in the plane of
Pioneer's travels. If the mass of the universe is almost
isotropic in all directions it would need to total 1E+106 kg,

That can't be right, there shouldn't be more than an
order of magnitude between them. The mean of cos()^2
is 0.5.

which is impossible to justify. Using a 1E+56 kg isotropic
universe, results in a universe generated gravity anisotropy for
Pioneer of 1.18E-34 m/sec^2. I don't think that has too much of
a future.

You are 52 orders of magnitude wrong above so
you need to recalculate that.

In the diagram the planet is moving to the left
towards distant galaxies at A and away from those
at B. The symbols A, B, C and D represent the
combined effect of all the matter in the four
quadrants separated by the obliques.

Matter at A and B will both act to produce a drag
force on P while galaxies in quadrants C and D
have little effect since the motion is primarily
transverse. Of course quarter of an orbit later it
C and D that are most significant, and for a
symmetrical distribution of distant galaxies the
drag is constant throughout the orbit. That would
not be true for the effect of our own galaxy though.

The effect of this would be to reduce the kinetic
energy of the planet causing it to spiral slowly
in towards the Sun. As it does so the speed must
increase as the inverse square root of the radius
and the drag would thus increase too increasing
the rate of orbital decay.

I think you claimed the effect of the rest of the
universe was comparable to that of the Sun but you
tossed around several sets of numbers so I can't
be sure.

Bottom line is that you need to explain why radial
drag from the Sun at the level of the Pioneer
anomaly hasn't made the orbits of the planets
circular and why the effect of the rest of the
universe hasn't caused them to spiral into the
Sun.

Some of us seem to forget that the Pioneer anomaly is not an
anomaly in nature it's the failure of mankind to understand the
universe.

Not necessarily, more likely it is a failure to
understand some aspect of the craft design.

It's a failing in the mathematics that presumes to
describe our universe. Something is clearly missing and that
problem must be resolved before any of us can claim to have a
proper understanding of the universe. So start resolving.

Start by making sure your maths correctly models the
planets. I've given you the roadmap to calculating
Mercury's perihelion advance but it relies on a
matching reduction in eccentricity so let's see what
you get when you complete the two calculations. If you
can show your value for the perihelion advance matches
observation but the rate of change of eccentricity is
within measured bounds then your theory survives the
test, otherwise we rule it out.

George