The Pioneer Spacecraft have shown an anomalous acceleration towards the
Sun of ~8 x 10^-16 m/s^2.

Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.

Now, the Pioneers will have experienced time dilation in the correct
direction (blue-shift for us on earth) as they escape the gravitational
well of the Sun, as follows:

We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
and dt is ephemeris time (bookkeeper time) valid at a great distance.

The mass of the Sun is 1.989 x 10^30 kg, or 1.477 x 10^3 m (in
length-units, valid for the above equation). I'll use 1.5 x 10^3 m in
the following.

And the earth is 1 a.u., or 1.496 x 10^11 m, from the Sun. I'll use 1.5
x 10^11 m in the following.

So, time dilation on the earth relative to ephemeris time, is:

dt_e ~= (1 - 2.1.5 x 10^3 / 1.5 x 10^-11) ^ 1/2 dt
= (1 - 2.10^-8)^1/2 dt
~= (1 - 10^-8) dt

And time dilation on Pioneer, when at n a.u. from the Sun (i.e. n times
the earth's distance from the Sun) is:

dt_p ~= (1 - 2.1.5 x 10^3 / n.1.5 x 10^-11) ^1/2 dt
~= (1 - n.10^-8) dt

So, time will 'speed up' on Pioneer relative to the earth at a rate:

dt_e/dt_p = (1 - 10^-8) / (1 - n.10^-8), where n is in a.u.
(astronomical units).

So, the rate of change of relative time dilation between Pioneer and
earth, per a.u. is ~10^-8 / a.u. (differentiate and approximate), as
long as Pioneer is not too far away (certainly less than 10^4 a.u.).

Now, Pioneers move at about 1.2 x 10^4 m/s, which is about 1.2 x 10^4 /
1.5 x 10^11 a.u./s, or ~ 8 x 10^-8 a.u./s.

So, the apparent rate of relative time dilation of the Pioneers, as seen
by earth will be about:

10^-8 x 8 x 10^-8 /s

= 8 x 10^-16 / s.

This corresponds to an apparent acceleration of 8 x 10^-16 m/s/s of the
Pioneer craft as viewed from earth, which is in excellent agreement with
the measurements of just over 8 x 10^16 m/s/s, normally presented as ~8
x 10^-13 km/s/s.

Actually I think the last step of my logic is deeply dodgy, but the
nunmbers were in such good agreement that I felt compelled to ignore my
reservations

Enjoy
Roland

"Roland PJ" wrote in message
...
: The Pioneer Spacecraft have shown an anomalous acceleration towards the
: Sun of ~8 x 10^-16 m/s^2.
:
: Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
: 1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.
:
: Now, the Pioneers will have experienced time dilation in the correct
: direction (blue-shift for us on earth) as they escape the gravitational
: well of the Sun, as follows:
:
: We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
: dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
: and dt is ephemeris time (bookkeeper time) valid at a great distance.
:
: The mass of the Sun is 1.989 x 10^30 kg, or 1.477 x 10^3 m (in
: length-units, valid for the above equation). I'll use 1.5 x 10^3 m in
: the following.
:
: And the earth is 1 a.u., or 1.496 x 10^11 m, from the Sun. I'll use 1.5
: x 10^11 m in the following.
:
: So, time dilation on the earth relative to ephemeris time, is:
:
: dt_e ~= (1 - 2.1.5 x 10^3 / 1.5 x 10^-11) ^ 1/2 dt
: = (1 - 2.10^-8)^1/2 dt
: ~= (1 - 10^-8) dt
:
: And time dilation on Pioneer, when at n a.u. from the Sun (i.e. n times
: the earth's distance from the Sun) is:
:
: dt_p ~= (1 - 2.1.5 x 10^3 / n.1.5 x 10^-11) ^1/2 dt
: ~= (1 - n.10^-8) dt
:
: So, time will 'speed up' on Pioneer relative to the earth at a rate:
:
: dt_e/dt_p = (1 - 10^-8) / (1 - n.10^-8), where n is in a.u.
: (astronomical units).
:
: So, the rate of change of relative time dilation between Pioneer and
: earth, per a.u. is ~10^-8 / a.u. (differentiate and approximate), as
: long as Pioneer is not too far away (certainly less than 10^4 a.u.).
:
: Now, Pioneers move at about 1.2 x 10^4 m/s, which is about 1.2 x 10^4 /
: 1.5 x 10^11 a.u./s, or ~ 8 x 10^-8 a.u./s.
:
: So, the apparent rate of relative time dilation of the Pioneers, as seen
: by earth will be about:
:
: 10^-8 x 8 x 10^-8 /s
:
: = 8 x 10^-16 / s.
:
: This corresponds to an apparent acceleration of 8 x 10^-16 m/s/s of the
: Pioneer craft as viewed from earth, which is in excellent agreement with
: the measurements of just over 8 x 10^16 m/s/s, normally presented as ~8
: x 10^-13 km/s/s.
:
: Actually I think the last step of my logic is deeply dodgy, but the
: nunmbers were in such good agreement that I felt compelled to ignore my
: reservations
:


Actually the first step in your logic was so deeply dodgy that the rest
can be ignored with impunity as meaningless unprovable drivel.

Catch 22:
http://www.fourmilab.ch/etexts/einst...ures/img22.gif
http://www.fourmilab.ch/etexts/einst...ures/img76.gif


Heller wrote: "There was only one catch and that was Catch 22, which
specified that a concern for one's safety in the face of dangers that were
real and immediate was the process of a rational mind.
"Orr (a character in the novel) was crazy and could be grounded. All he had
to do was ask, and as soon as he did, he would no longer be crazy and would
have to fly more missions.

"Orr would be crazy to fly more missions and sane if he didn't, but if he
was sane he had to fly them. If he flew them he was crazy and didn't have
to; but if he didn't want to he was sane and had to."

In Einstein's case if you use c+v you can derive c = (c+v)/(1+v/c) from
the cuckoo malformations he blamed on Lorentz. That says you can't
use c+v.

What troll kooks like Schwartz, Poe, McCullough, Roberts, Draper, Lawrence,
Andersen, Nieminen, ewill, Olson, Tom & Jeery et. al. fail to realise is
the existence of isomorphism

http://en.wikipedia.org/wiki/Isomorphism

between Sagnac's real experiment and Einstein's hallucination experiment,
shown he
http://www.androcles01.pwp.blueyonde...oSpeedRack.gif

Einstein sends light along the rack and back again, the rack
moving at velocity v in his pipe dream.

Sagnac sends the light around the gear wheel for real.
If you analyse one you should get the same result as the other, but
you cannot use SR to derive SR, that is petitio principii, circularity.
http://en.wikipedia.org/wiki/Begging_the_question

c+v is essential to the derivation of the cuckoo malformations, the
part where Einstein screws up is:
'we establish by definition that the "time" required by
light to travel from A to B equals the "time" it requires
to travel from B to A' because I SAY SO. -- Rabbi Albert Einstein

What he is claiming is that his "definition" is true for all frames of
reference. The absurdity that the velocity of light is the same
in all frames of reference is a consequence of that claim.


http://www.androcles01.pwp.blueyonde...rt/tAB=tBA.gif

Here are some mathematical proofs:
http://en.wikipedia.org/wiki/Mathematical_proof

Not included are
Proof by "because I say so",
Proof by "everybody knows",
Proof by "it is written",
the three most popular forms used in sci.physics.relativity.

You'll often see this pathetic mob muttering "Lorentz Transformations"
but they haven't a clue how they are derived and faithfully follow their
indoctrination like lemmings.

Catch 22:
http://www.fourmilab.ch/etexts/einst...ures/img22.gif
http://www.fourmilab.ch/etexts/einst...ures/img76.gif

Prediction:
The troll kooks will ignore it, they are too stooopid to understand a
proof.

RULES OF REASONING IN PHILOSOPHY.

RULE I.
We are to admit no more causes of natural things than such as are both true
and sufficient to explain their appearances.

To this purpose the philosophers say that Nature does nothing in vain,
and more is in vain when less will serve; for Nature is pleased with
simplicity,
and affects not the pomp of superfluous causes.

-- Sir Isaac Newton

On Dec 24, 7:07 am, Roland PJ wrote:
The Pioneer Spacecraft have shown an anomalous acceleration towards the
Sun of ~8 x 10^-16 m/s^2.

Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.

Now, the Pioneers will have experienced time dilation in the correct
direction (blue-shift for us on earth) as they escape the gravitational
well of the Sun, as follows:

We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
and dt is ephemeris time (bookkeeper time) valid at a great distance.

....and your justification for this is what, exactly?

Remember what the Schwarzschild solution describes.

[...]

On Dec 24, 6:34 pm, "Androcles" wrote:

:
: Now, the Pioneers will have experienced time dilation in the correct
: direction (blue-shift for us on earth) as they escape the gravitational
: well of the Sun, as follows:
:

Actually the first step in your logic was so deeply dodgy that the rest
can be ignored with impunity as meaningless unprovable drivel.

No, this is is completely undisputed. Any mass will cause time
dilation according to General Relativity. The Sun is not exempt.

You are talking about Special Relativity, which is not appropriate to
my argument.

But thanks for the digression

Roland

On Dec 24, 6:51 pm, Eric Gisse wrote:
On Dec 24, 7:07 am, Roland PJ wrote:

The Pioneer Spacecraft have shown an anomalous acceleration towards the
Sun of ~8 x 10^-16 m/s^2.

Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.

Now, the Pioneers will have experienced time dilation in the correct
direction (blue-shift for us on earth) as they escape the gravitational
well of the Sun, as follows:

We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
and dt is ephemeris time (bookkeeper time) valid at a great distance.

...and your justification for this is what, exactly?

Remember what the Schwarzschild solution describes.

Modeling the Sun as a stationary point mass, and computing the time
dilation effects of the Sun within the Pioneers' paths ( 100 a.u.). A
point mass iss certainly accurate enough when we get as far away as
the earth, no?

Note that any mass will cause time dilation according to GR. With
black holes the time dilation is massive near the event horizon, but
common and garden bodies like the Sun (and even a tennis ball) will
cause similar (although much smaller) time dilation effects.

Roland

No, with extremely high confidence. The people who work on this are
experts in GR and would not miss a basic aspect of GR.


Tom Roberts

On Dec 24, 7:58 am, Roland PJ wrote:
On Dec 24, 6:51 pm, Eric Gisse wrote:



On Dec 24, 7:07 am, Roland PJ wrote:

The Pioneer Spacecraft have shown an anomalous acceleration towards the
Sun of ~8 x 10^-16 m/s^2.

Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.

Now, the Pioneers will have experienced time dilation in the correct
direction (blue-shift for us on earth) as they escape the gravitational
well of the Sun, as follows:

We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
and dt is ephemeris time (bookkeeper time) valid at a great distance.

...and your justification for this is what, exactly?

Remember what the Schwarzschild solution describes.

Modeling the Sun as a stationary point mass, and computing the time
dilation effects of the Sun within the Pioneers' paths ( 100 a.u.). A
point mass iss certainly accurate enough when we get as far away as
the earth, no?

Note that any mass will cause time dilation according to GR. With
black holes the time dilation is massive near the event horizon, but
common and garden bodies like the Sun (and even a tennis ball) will
cause similar (although much smaller) time dilation effects.

1) The Schwarzschild solution _still_ does not apply.

2) Time dilation cannot be confused with acceleration, no matter how
badly you butcher the analysis.


Roland

On Dec 24, 8:06 pm, Eric Gisse wrote:
On Dec 24, 7:58 am, Roland PJ wrote:



On Dec 24, 6:51 pm, Eric Gisse wrote:

On Dec 24, 7:07 am, Roland PJ wrote:

The Pioneer Spacecraft have shown an anomalous acceleration towards the
Sun of ~8 x 10^-16 m/s^2.

Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.

Now, the Pioneers will have experienced time dilation in the correct
direction (blue-shift for us on earth) as they escape the gravitational
well of the Sun, as follows:

We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
and dt is ephemeris time (bookkeeper time) valid at a great distance.

...and your justification for this is what, exactly?

Remember what the Schwarzschild solution describes.

Modeling the Sun as a stationary point mass, and computing the time
dilation effects of the Sun within the Pioneers' paths ( 100 a.u.). A
point mass iss certainly accurate enough when we get as far away as
the earth, no?

Note that any mass will cause time dilation according to GR. With
black holes the time dilation is massive near the event horizon, but
common and garden bodies like the Sun (and even a tennis ball) will
cause similar (although much smaller) time dilation effects.

1) The Schwarzschild solution _still_ does not apply.

Why not? The Schwarzschild solution applies to all point (or
spherically symmetric) masses. Why doesn't it apply to the Sun?

2) Time dilation cannot be confused with acceleration, no matter how
badly you butcher the analysis.

Yes it can. The Doppler shift of signals from the Pioneer (which is
the basis of the inferred acceleration) is directly related to the
time dilation, and the apparent motion of a constant-velocity body
(viewed from earth) will appear to decelerate, as a direct result of
the time dilation due to distance from the Sun (the dominant mass in
the solar system).

You can make up arguments to suit your agenda (what is it?), but you
should show your workings (i.e. maths), or show where my analysis is
flawed. Otherwise you're just blowing smoke.

Roland

On Dec 24, 9:20 am, Roland PJ wrote:
On Dec 24, 8:06 pm, Eric Gisse wrote:



On Dec 24, 7:58 am, Roland PJ wrote:

On Dec 24, 6:51 pm, Eric Gisse wrote:

On Dec 24, 7:07 am, Roland PJ wrote:

The Pioneer Spacecraft have shown an anomalous acceleration towards the
Sun of ~8 x 10^-16 m/s^2.

Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.

Now, the Pioneers will have experienced time dilation in the correct
direction (blue-shift for us on earth) as they escape the gravitational
well of the Sun, as follows:

We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
and dt is ephemeris time (bookkeeper time) valid at a great distance.

...and your justification for this is what, exactly?

Remember what the Schwarzschild solution describes.

Modeling the Sun as a stationary point mass, and computing the time
dilation effects of the Sun within the Pioneers' paths ( 100 a.u.). A
point mass iss certainly accurate enough when we get as far away as
the earth, no?

Note that any mass will cause time dilation according to GR. With
black holes the time dilation is massive near the event horizon, but
common and garden bodies like the Sun (and even a tennis ball) will
cause similar (although much smaller) time dilation effects.

1) The Schwarzschild solution _still_ does not apply.

Why not? The Schwarzschild solution applies to all point (or
spherically symmetric) masses. Why doesn't it apply to the Sun?

Is the solar system spherically symmetric?


2) Time dilation cannot be confused with acceleration, no matter how
badly you butcher the analysis.

Yes it can. The Doppler shift of signals from the Pioneer (which is
the basis of the inferred acceleration) is directly related to the
time dilation, and the apparent motion of a constant-velocity body
(viewed from earth) will appear to decelerate, as a direct result of
the time dilation due to distance from the Sun (the dominant mass in
the solar system).

Uh, no.

Doppler shift is ONLY a function of velocity - not acceleration.
Knowing the doppler shift of the signals allows a determination of
velocity as a function of time, and from that, acceleration.


You can make up arguments to suit your agenda (what is it?), but you
should show your workings (i.e. maths), or show where my analysis is
flawed. Otherwise you're just blowing smoke.

Roland

Your analysis is flawed because it has already been considered,
because the Schwarzschild metric is NOT a valid model for the solar
system, and because you didn't even do it right.

To get the total change, you have to integrate along the path. Which
you didn't bother doing.

I can also tell you are wrong without even going through the analysis
by looking at your conclusions - you have concluded that _doppler
shift_ can make something appear to be accelerating. This is
completely and utterly wrong.

Oh, one more reason why you are wrong. The deceleration is, as far as
can be determined, constant. Would you like to make the claim that the
gravitational effects are the same regardless of how close the craft
is to the sun?

On Dec 24, 8:07 am, Roland PJ wrote:
The Pioneer Spacecraft have shown an anomalous acceleration towards the
Sun of ~8 x 10^-16 m/s^2.

Pioneer 10 and Pioneer 11 were traveling at about 1.22 x 10^4 m/s and
1.16 x 10^4 m/s away from the Sun at the end of their lifetimes.

Now, the Pioneers will have experienced time dilation in the correct
direction (blue-shift for us on earth) as they escape the gravitational
well of the Sun, as follows:

We will use Swarzschild time dilation, dt_shell = (1-2M/r)^1/2 dt, where
dt_shell is shell time (i.e. use on earth, or Pioneer's electronics),
and dt is ephemeris time (bookkeeper time) valid at a great distance.

The mass of the Sun is 1.989 x 10^30 kg, or 1.477 x 10^3 m (in
length-units, valid for the above equation). I'll use 1.5 x 10^3 m in
the following.

And the earth is 1 a.u., or 1.496 x 10^11 m, from the Sun. I'll use 1.5
x 10^11 m in the following.

So, time dilation on the earth relative to ephemeris time, is:

dt_e ~= (1 - 2.1.5 x 10^3 / 1.5 x 10^-11) ^ 1/2 dt
= (1 - 2.10^-8)^1/2 dt
~= (1 - 10^-8) dt

And time dilation on Pioneer, when at n a.u. from the Sun (i.e. n times
the earth's distance from the Sun) is:

dt_p ~= (1 - 2.1.5 x 10^3 / n.1.5 x 10^-11) ^1/2 dt
~= (1 - n.10^-8) dt

So, time will 'speed up' on Pioneer relative to the earth at a rate:

dt_e/dt_p = (1 - 10^-8) / (1 - n.10^-8), where n is in a.u.
(astronomical units).

So, the rate of change of relative time dilation between Pioneer and
earth, per a.u. is ~10^-8 / a.u. (differentiate and approximate), as
long as Pioneer is not too far away (certainly less than 10^4 a.u.).

Now, Pioneers move at about 1.2 x 10^4 m/s, which is about 1.2 x 10^4 /
1.5 x 10^11 a.u./s, or ~ 8 x 10^-8 a.u./s.

So, the apparent rate of relative time dilation of the Pioneers, as seen
by earth will be about:

10^-8 x 8 x 10^-8 /s

= 8 x 10^-16 / s.

This corresponds to an apparent acceleration of 8 x 10^-16 m/s/s of the
Pioneer craft as viewed from earth, which is in excellent agreement with
the measurements of just over 8 x 10^16 m/s/s, normally presented as ~8
x 10^-13 km/s/s.

Actually I think the last step of my logic is deeply dodgy, but the
nunmbers were in such good agreement that I felt compelled to ignore my
reservations

LOL, "compelled". the thing about the anomally
is it's ratio (acceleration), somewhere around
1/1700. Usually SR and GR effects are proportional
to v^2/c^2 (or 2 phi/c^2), this effect is more
like 3Vescape/c or something like that,(my papers
are filed), that's actually a pretty large
effect to be handled by "known" relativity.
Anyway, do your theory calculation and present a
formula. Then at the end plug in your values.
Regards
Ken S. Tucker

Roland