Anom Accel of Pioneer 10 for v>(GM/r)^1/2

The Anomalous Acceleration of Pioneer 10 toward the sun of
about 10^-8cm/sec^2
at various distances r from the sun can be associated with
the fact that the velocity of the spacecraft is greater than the
orbital velocity the
spacecraft would have in a circular orbit at the same distance.
A rationale for this coincidence is given below.

The speed of the craft,now 12km/sec according to Pioneer
home page was about 36.67km/sec as it passed Jupiter while
29km per sec relative to the sun when it was on earth
orbiting the sun.
If the spacecraft was in orbit around the sun at a distance
r from
the sun it would have an orbital velocity of v from
GM/r^2=v^2/r
So its orbital velocity at a distance r can be compared to its
actual
velocity v*_r compared to v_r.
The hypothesis is proposed that the mass of objects is
proportional
to the total number of protons and neutrons in the object and to
the transverse speed
of the object wrt its attractive center eg the center of the
earth for objects on the
earth or in orbit around the earth, and the sun, for planets and
other
objects like the spacecraft beyond the earth's orbit.
The Pioneer 10 spacecraft is moving almost completely
radially away
from the sun such that the sine of the angle between its
trajectory and a radial line
to the sun is very small eg .001.
The spacecraft is also free to rotate.
According to this hypothesis there would be change in the
attraction
of the spacecraft to the sun proportional to the difference
between
(GM/r)^1/2 and v*_r. If r=10^12 then
((6.67)(10^-11)(1.99)(10^30)/(10^12))^1/2=3.66(10^3.5)=11.57km/se
c
about and the speed of the craft was probably more.


The attractive mass of an object on the earth directed to
the
center of the earth is assumed to be due to electrostatic dipole
inside protons and neutrons of length 10^-18 meters so that
(6.67)(10^-11) times [(1.67)(10^-27)]^2 = (9)(10^9)(es)^2 if
s=(.9)(10-18) is the gravitational force between two protons
one
meter apart represented as the force between two electrostatic
dipoles one meter part and colinearly and attractively oriented.
And so the gravitational force between the sun and the earth
could be written as the force between radially oriented dipoles:
GmM/R^2 = 9(10^9)mM[6.02)(10^26)]^2 times kK times s*S*
times
(2.56) times 10-38 divided by R^2 where the dipoles are es* and
eS* and e=1.6(10^-19)Coul.;this implies kKs*S*=
(.0079)10^(-61-11+38) =
10^-36 approximatelySince the Sun is .75H+.25He so that 1.75kg
of
Sun contains 6.02 times 10^26 molecules each of which contains
on
average 1.75 protons+neutrons so 1kg of the gaseous Sun
contains 6.02 times 10^26 protons+neutrons in a volume that is
larger of course than that of 1 kg of a solid planet; but 1kg of
any planet or the Sun contains the same number of
protons+neutrons. There are about 2(10^30) kg in the Sun. Hence
the Sun contains 6.02 times 10^26 times M or 12 times 10^56 and
the Earth contains 6.02 times 10^26 times m or 3.59 times 10^51
unit dipoles in the Earth. The total dipoles a
1.2(10^57)k(s)RS* and 3.59(10^51)K(S)Rs*.
Hence . Now RkS* and RKs* are the magnitudes of the dipoles
associated with the Sun and planet respectively where R varies
from around 1.5(10^11)meters 10^10 to 10^13 meters. But we also
know that the Earth's dipoles cannot be much larger than atomic
nuclei about 10^-15meters =RKs* that Ks*=10^-26 which implies
kS*=10^-10 and also RkS*= 10^(-10+11) so the dipoles on the
Sun are 10 meters in length or
the amount of charge in each dipole is more than e=^-19 etc.
We assume, following the Wilson Bartlett relation between
angular momentum and gravity,
that dipoles in protons and neutrons on planets that produce
their attraction to the sun is
due to the orbital speed of the planets and so a part of the
planet, like the spacecraft, when moving apart from the planet
at
a different speed
will have its dipoles change and so its attractive mass will
change.
see http://www.bestweb.net/~sansbury

On Sun, 23 Nov 2003 18:01:41 -0500, "ralph sansbury"
wrote:

The Anomalous Acceleration of Pioneer 10 toward the sun of
about 10^-8cm/sec^2
at various distances r from the sun can be associated with
the fact that the velocity of the spacecraft is greater than the
orbital velocity the
spacecraft would have in a circular orbit at the same distance.
A rationale for this coincidence is given below.

The speed of the craft,now 12km/sec according to Pioneer
home page was about 36.67km/sec as it passed Jupiter while
29km per sec relative to the sun when it was on earth
orbiting the sun.
If the spacecraft was in orbit around the sun at a distance
r from
the sun it would have an orbital velocity of v from
GM/r^2=v^2/r
So its orbital velocity at a distance r can be compared to its
actual
velocity v*_r compared to v_r.
The hypothesis is proposed that the mass of objects is
proportional
to the total number of protons and neutrons in the object and to
the transverse speed
of the object wrt its attractive center eg the center of the
earth for objects on the
earth or in orbit around the earth, and the sun, for planets and
other
objects like the spacecraft beyond the earth's orbit.
The Pioneer 10 spacecraft is moving almost completely
radially away
from the sun such that the sine of the angle between its
trajectory and a radial line
to the sun is very small eg .001.
The spacecraft is also free to rotate.
According to this hypothesis there would be change in the
attraction
of the spacecraft to the sun proportional to the difference
between
(GM/r)^1/2 and v*_r. If r=10^12 then
((6.67)(10^-11)(1.99)(10^30)/(10^12))^1/2=3.66(10^3.5)=11.57km/se
c
about and the speed of the craft was probably more.


The attractive mass of an object on the earth directed to
the
center of the earth is assumed to be due to electrostatic dipole
inside protons and neutrons of length 10^-18 meters so that
(6.67)(10^-11) times [(1.67)(10^-27)]^2 = (9)(10^9)(es)^2 if
s=(.9)(10-18) is the gravitational force between two protons
one
meter apart represented as the force between two electrostatic
dipoles one meter part and colinearly and attractively oriented.
And so the gravitational force between the sun and the earth
could be written as the force between radially oriented dipoles:
GmM/R^2 = 9(10^9)mM[6.02)(10^26)]^2 times kK times s*S*
times
(2.56) times 10-38 divided by R^2 where the dipoles are es* and
eS* and e=1.6(10^-19)Coul.;this implies kKs*S*=
(.0079)10^(-61-11+38) =
10^-36 approximatelySince the Sun is .75H+.25He so that 1.75kg
of
Sun contains 6.02 times 10^26 molecules each of which contains
on
average 1.75 protons+neutrons so 1kg of the gaseous Sun
contains 6.02 times 10^26 protons+neutrons in a volume that is
larger of course than that of 1 kg of a solid planet; but 1kg of
any planet or the Sun contains the same number of
protons+neutrons. There are about 2(10^30) kg in the Sun. Hence
the Sun contains 6.02 times 10^26 times M or 12 times 10^56 and
the Earth contains 6.02 times 10^26 times m or 3.59 times 10^51
unit dipoles in the Earth. The total dipoles a
1.2(10^57)k(s)RS* and 3.59(10^51)K(S)Rs*.
Hence . Now RkS* and RKs* are the magnitudes of the dipoles
associated with the Sun and planet respectively where R varies
from around 1.5(10^11)meters 10^10 to 10^13 meters. But we also
know that the Earth's dipoles cannot be much larger than atomic
nuclei about 10^-15meters =RKs* that Ks*=10^-26 which implies
kS*=10^-10 and also RkS*= 10^(-10+11) so the dipoles on the
Sun are 10 meters in length or
the amount of charge in each dipole is more than e=^-19 etc.
We assume, following the Wilson Bartlett relation between
angular momentum and gravity,
that dipoles in protons and neutrons on planets that produce
their attraction to the sun is
due to the orbital speed of the planets and so a part of the
planet, like the spacecraft, when moving apart from the planet
at
a different speed
will have its dipoles change and so its attractive mass will
change.
see http://www.bestweb.net/~sansbury







Apparently, the accepted explanation for the anomalous acceleration of
Pioneers 10 and 11 is that they're experiencing a larger gas and dust
density in the Kyper belt than was expected.

In message , Igor
writes
On Sun, 23 Nov 2003 18:01:41 -0500, "ralph sansbury"
wrote:

The Anomalous Acceleration of Pioneer 10 toward the sun of
about 10^-8cm/sec^2
at various distances r from the sun can be associated with
the fact that the velocity of the spacecraft is greater than the
orbital velocity the
spacecraft would have in a circular orbit at the same distance.
A rationale for this coincidence is given below.

Apparently, the accepted explanation for the anomalous acceleration of
Pioneers 10 and 11 is that they're experiencing a larger gas and dust
density in the Kyper belt than was expected.


Interesting. Do you have a reference for that? I'd be surprised, because
the acceleration has been almost constant since about 15AU (inside the
orbit of Uranus) and if anything there is _less_ dust than expected in
the Kuiper belt..
Personally, I think it's looking more and more likely that Ned Wright is
correct and they hadn't modelled thermal emission from the RTGs
correctly. I haven't seen any evidence of an anomaly on Cassini.
--
Rabbit arithmetic - 1 plus 1 equals 10
Remove spam and invalid from address to reply.

On Mon, 24 Nov 2003 00:03:07 +0000, Jonathan Silverlight
wrote:

In message , Igor
writes
On Sun, 23 Nov 2003 18:01:41 -0500, "ralph sansbury"
wrote:

The Anomalous Acceleration of Pioneer 10 toward the sun of
about 10^-8cm/sec^2
at various distances r from the sun can be associated with
the fact that the velocity of the spacecraft is greater than the
orbital velocity the
spacecraft would have in a circular orbit at the same distance.
A rationale for this coincidence is given below.

Apparently, the accepted explanation for the anomalous acceleration of
Pioneers 10 and 11 is that they're experiencing a larger gas and dust
density in the Kyper belt than was expected.


Interesting. Do you have a reference for that? I'd be surprised, because
the acceleration has been almost constant since about 15AU (inside the
orbit of Uranus) and if anything there is _less_ dust than expected in
the Kuiper belt..
Personally, I think it's looking more and more likely that Ned Wright is
correct and they hadn't modelled thermal emission from the RTGs
correctly. I haven't seen any evidence of an anomaly on Cassini.

Check out this link:

http://www.newtonphysics.on.ca/Anoma...eleration.html

In message , Igor
writes
On Mon, 24 Nov 2003 00:03:07 +0000, Jonathan Silverlight
wrote:

In message , Igor
writes

Apparently, the accepted explanation for the anomalous acceleration of
Pioneers 10 and 11 is that they're experiencing a larger gas and dust
density in the Kyper belt than was expected.


Interesting. Do you have a reference for that? I'd be surprised, because
the acceleration has been almost constant since about 15AU (inside the
orbit of Uranus) and if anything there is _less_ dust than expected in
the Kuiper belt..
Personally, I think it's looking more and more likely that Ned Wright is
correct and they hadn't modelled thermal emission from the RTGs
correctly. I haven't seen any evidence of an anomaly on Cassini.

Check out this link:

http://www.newtonphysics.on.ca/Anoma...eleration.html

Very interesting! It's somehow satisfying that the explanation is
conventional, not due to some boring property of the spacecraft, and
gives new information.
Presumably the reason Cassini hasn't seen an acceleration is that it's
more than 20 x as massive.
One thing does occur to me. Paul Marmet rather fancifully suggests that
the Pioneers will gather dust as they move. It seems to me that the dust
particles will actually be moving at very high speed relative to the
spacecraft and will vaporise. More to the point, that means they will
impart their kinetic energy to the spacecraft, which scales as V^2, not
V.
--
Rabbit arithmetic - 1 plus 1 equals 10
Remove spam and invalid from address to reply.

In article ,
Igor writes:
Check out this link:
http://www.newtonphysics.on.ca/Anoma...eleration.html

It's an interesting idea. While I didn't check the calculations in
detail, the method looks correct, and it certainly appears to produce
an upper limit for the density of the Kuiper Belt of 1.4E-19 g cm^-3.

What I wonder is how reasonable that density is. It seems awfully
high to me. At a "normal" gas to dust ratio of 100, that's about 8E6
hydrogen atoms per cubic centimeter. I suppose one could argue that
the gas is depleted, or maybe this density is reasonable. Anybody
able to comment?

One clear mistake in the web page is the assertion that the IRAS data
show the Kuiper Belt. Dust in the KB is far too cold to have been
seen by IRAS. The IRAS data sample the Zodiacal cloud roughly 1 AU
from the Sun. (Of course the data average over a range of
distances.) That's why the data are depicted as blue in the figu
they represent the 12 micron observations.

COBE produced much better data on the Zodiacal cloud, leading to
detailed models. However, not even the COBE data detect dust at the
KB distance from the Sun. The expected temperature is roughly 75 K
at 30 AU.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)

Jonathan Silverlight writes:

In message , Igor
writes
Check out this link:

http://www.newtonphysics.on.ca/Anoma...eleration.html

Very interesting! It's somehow satisfying that the explanation is
conventional, not due to some boring property of the spacecraft, and
gives new information.
Presumably the reason Cassini hasn't seen an acceleration is that it's
more than 20 x as massive.
One thing does occur to me. Paul Marmet rather fancifully suggests that
the Pioneers will gather dust as they move. It seems to me that the dust
particles will actually be moving at very high speed relative to the
spacecraft and will vaporise. More to the point, that means they will
impart their kinetic energy to the spacecraft, which scales as V^2, not

Marmet's explanation is unconvincing. It depends entirely on the
density of dust in the outer solar system, which according to Marmet:

This amount of dust in the outer region of the solar system appears
quite reasonable remembering that the daily amount of dust falling
on Earth is reported as many tons of dust grains per day.

which is a completely fallacious argument. The number of "tons" of
dust falling on the earth has nothing to do with the dust conditions
in the outer solar system, because (a) one must normalize the captured
"tons" by the cross sectional area of the earth; and (b) the
conditions are different in the outer solar system. In particular,
the dust density drops of precipitously beyond Jupiter.

It is straightforward to show that the net acceleration due to dust
is:
a_dust = -2 (A/M) n V^2 m
where A/M is the area to mass ratio of the body, n is the dust
density, V is the body velocity, and m is the mean dust mass. This
conservatively assumes elastic scattering. It is likely that the dust
will be captured, in which case a_dust will be half the value quoted
above.

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.

Craig

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

--
--------------------------------------------------------------------------
Craig B. Markwardt, Ph.D. EMAIL:
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
--------------------------------------------------------------------------

In message , Craig Markwardt
writes

Jonathan Silverlight writes:

In message , Igor
writes
Check out this link:

http://www.newtonphysics.on.ca/Anoma...eleration.html

Very interesting! It's somehow satisfying that the explanation is
conventional, not due to some boring property of the spacecraft, and
gives new information.
Presumably the reason Cassini hasn't seen an acceleration is that it's
more than 20 x as massive.
One thing does occur to me. Paul Marmet rather fancifully suggests that
the Pioneers will gather dust as they move. It seems to me that the dust
particles will actually be moving at very high speed relative to the
spacecraft and will vaporise. More to the point, that means they will
impart their kinetic energy to the spacecraft, which scales as V^2, not

Marmet's explanation is unconvincing. It depends entirely on the
density of dust in the outer solar system, which according to Marmet:

This amount of dust in the outer region of the solar system appears
quite reasonable remembering that the daily amount of dust falling
on Earth is reported as many tons of dust grains per day.

which is a completely fallacious argument. The number of "tons" of
dust falling on the earth has nothing to do with the dust conditions
in the outer solar system, because (a) one must normalize the captured
"tons" by the cross sectional area of the earth; and (b) the
conditions are different in the outer solar system. In particular,
the dust density drops of precipitously beyond Jupiter.

It is straightforward to show that the net acceleration due to dust
is:
a_dust = -2 (A/M) n V^2 m
where A/M is the area to mass ratio of the body, n is the dust
density, V is the body velocity, and m is the mean dust mass. This
conservatively assumes elastic scattering. It is likely that the dust
will be captured, in which case a_dust will be half the value quoted
above.

I don't understand how the dust can be captured. Isn't it likely to be
hitting with a relative velocity of the order of Pioneer's own speed (12
km/sec)?
But is the question still open, or is anisotropic thermal emission still
the best candidate to explain the Pioneer effect? Marmet doesn't mention
the conventional explanations.
--
Rabbit arithmetic - 1 plus 1 equals 10
Remove spam and invalid from address to reply.

Jonathan Silverlight writes:

I don't understand how the dust can be captured. Isn't it likely to be
hitting with a relative velocity of the order of Pioneer's own speed (12
km/sec)?

To be honest, I'm not sure. That's why I assumed the worst case of
elastic collisions, which maximize the momentum transfer to the
spacecraft. Since the dust particles are fluffy bodies, it is likely
that they will not elastically scatter, and so the momentum transfer
will be less.

But is the question still open, or is anisotropic thermal emission still
the best candidate to explain the Pioneer effect? Marmet doesn't mention
the conventional explanations.

I've looked into this a little more. From my analysis, there is some
evidence for a change in the acceleration over time. This is almost
enough to be consistent with the decrease in the amount of power
consumption in the Pioneer 10 equipment compartment. I think it is
quite possible there could be anisotropic emission from this
compartment, or via some other, similar means, which accounts for the
acceleration.

Craig

--
--------------------------------------------------------------------------
Craig B. Markwardt, Ph.D. EMAIL:
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
--------------------------------------------------------------------------

Craig Markwardt replied to Jonathan Silverlight:

But is the question still open, or is anisotropic thermal
emission still the best candidate to explain the Pioneer
effect? Marmet doesn't mention the conventional explanations.

I've looked into this a little more. From my analysis, there is
some evidence for a change in the acceleration over time. This
is almost enough to be consistent with the decrease in the amount
of power consumption in the Pioneer 10 equipment compartment.
I think it is quite possible there could be anisotropic emission
from this compartment, or via some other, similar means, which
accounts for the acceleration.

Craig,

I posted this on February 22, 2002, here in sci.astro, in reply
to Bruce Sterling Woodcock:

Presently some 2000W of RTG heat must be dissipated,
so it would seem that would be enough. But the problem is the
RTGs are located at the ends of the booms, and they only see
the antenna "edge on", subtending an angle of about 1.5% of 4
steradians. That means at most 30W of power could be impacting
it. Moreover, every RTG is not a spherical black body, but
rather has fins that are "edge on" to the antenna, which means
only 2.5% of the surface area of the RTG is actually facing the
antenna. The RTG mechanism doesn't provide enough power to
explain the anomalous acceleration.

Looking at photographs of the spacecraft leads me to wonder
whether the analysis you quote is correct. First off, you said
"an angle of about 1.5% of 4 steradians". That was probably
intended to be "4 pi steradians", meaning the total sphere.
By eyeball estimate, I'd say that the antenna and other parts
of the spacecraft sunward of the RTGs subtend a solid angle of
about 5% of a sphere, rather than 1.5%. I estimate that 20%
of the RTGs are visible to the sunward parts of the spacecraft,
rather than 2.5%. Those are pretty big differences. Perhaps
my estimates are that far off, or perhaps someone fouled up
the analysis. Take a look at some photos of Pioneer, and see
if you don't agree that the figures you give seem way too low.

Maybe it still isn't enough to cause the anomaly. But it looks
like a very good possibility.

Bruce replied, in part:

The RTG's have fins on them that are "edge-on" to the antenna.
The actual surface area that faces the antenna is much smaller
because of it.

And I replied to Bruce:

Yes, I can see that. It is why I estimate that only 20% of
the RTG surface area is visible to the back side of the antenna
dish and other parts of the spacecraft sunward of the RTGs,
rather than the approximately 45% that would be visible if they
were plain cylinders.

Any comments?

-- Jeff, in Minneapolis

Subtract 1 from my e-mail address above for my real address.
..