"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