Re: Pioneer 10 & 11 Spacecraft Deceleration Anomaly

>From Turyshev, Nieto, and Anderson's paper you quoted, the basis of
Pioneer's anomaly is the observed rate of change of the Doppler frequency.
An assumed acceleration towards the sun is calculated based on this
observation. What I had done is to address directly at the observation. I
was able to show the observed anomaly is not due to any anomaly in
acceleration. Besides, in that paper, there is no mentioning of rotational
acceleration nor translational acceleration. Where did you get these from?
How did you calculate these two accelerations from the observed rate of
change in Doppler frequency?

----- Original Message -----
From: Richard Saam
Newsgroups: sci.physics.relativity
Sent: Thursday, April 14, 2005 02:41 PM
Subject: Re: Pioneer 10 & 11 Spacecraft Deceleration Anomaly

Your derivation does not explain linked translational and rotational
deceleration
with translational and rotational velocities 3 orders of magnitude from each
other

----- Original Message -----
From: "Koobee Wublee" <kublai@xxxxxxx>
Newsgroups: sci.physics.relativity
Sent: Tuesday, April 12, 2005 11:33 PM
Subject: Re: Pioneer 10 & 11 Spacecraft Deceleration Anomaly

The assumption that these deep-space probes are slowing more so than
expected is because that the received Doppler frequency from these probes is
not as much as expected. So, here I offer another explanation with math
backing it up without any other unexpected force acting to slow these probes
down. Since the anomaly is Doppler in nature, I am going to explore this
subject more so than conventional physics. And since math is not very well
received by the readers of this newsgroup, I will skip a few steps showing
detail derivations.

Let's start with the equation governing relavitistic Doppler effect.

f' / f = sqrt(1 - B) / sqrt(1 + B)

Derived from

** E' = (E + B * p) / sqrt(1 - B^2)

Where

** f' = observed frequency arrived on earth
** f = frequency of the photon on the probe
** v = B c = speed of the probes
** c = speed of light
** p = the photon's momentum on the probe
** E = the photon's energy on the probe
** E' = the photon's observed frequency arrived on earth
** * = dot product of two vectors

My position has been that the speed of light cannot be the same every where.
It is a function described by the following equation.

c = c0 (1 - U + ....)

Where

** U = G M / c0^2 / r
** c0 = speed of light at where r' = infinity
** G = gravitational constant
** M = mass of the sun
** r = distance of the probe from the sun

r is one of the observer's parameters. For another observer, G and M would
be different, and so is r. The resulting U would be universally the same
everywhere.

So, the Doppler equation with the speed of light not universally the same
everywhere is

f' / f = (c / c') sqrt(1 - B) / sqrt(1 + B)

If (1 >> B), we have

f' / f = (c / c') (1 - B)

This Doppler equation is derived from

E' / c' = (E / c + B * p) / sqrt(1 - B^2)

If interested, I can post the derivation of it.

Taking the derivative of f' with respect to dt, we have

df'/dt = (f / c') (dc/dt) (1 - B) - (f c / c') (dB/dt), or

df'/dt = f B (dc/dr) - (f c / c') (dB/dt), or

Since we assume (dc/dr = 0, all thanks to the ingenius assumpation made by
Einstein more than 100 years ago), we have

dB/dt = - (df'/dt) / f

Or

dv/dt = - (df'/dt) c / f

After taking the sun's gravitational effect into account, the above equation
describes approximately the anomaly of acceleration towards the sun with
(df'/dt > 0).

However, dB/dt can be zero (no anomaly of acceleration) that still causes
the observed Doppler anomaly. So, we have

df'/dt = f B (dc/dr) = (f v / c) (G M / c / r^2) = G M f v / c^2 / r^2

Where

** c = c0 = c', approximately, using only c for simplicity

Since (df'/dt) is observed over a period of time, we must take the average
of it by integration from t1 to t2 and divided by (t2 - t1). In doing so,
we get

df'/dt = G M f v / c^2 / r0 / r1

Where

** r0 = distance where this anamaly started to be noted
** r1 = final distance of signing off

>From the data I have gathered, (all in MKS units)

** G = 0.667E-10
** M = 2E30 kg
** c = 3e8 m/sec
** f = 2.295 GHz
** v = 12.24E3 m/sec
** r1 = 70 AU = 1.05E13 m
** r0 = 4.4 AU = 6.6E11 m

r0 was tweaked to get the following. At low r0, the dot product (B * p) is
not necessarily in the same direction. To my opinion, r0 = 4.4 AU is a
reasonable number. Maybe Mr. Anderson can comment on this. So, we get

df'/dt = 6E-9 Hz/sec

As observed by Mr. Anderson, et al.

----- Original Message -----
From: Richard Saam
Newsgroups: sci.physics.relativity
Sent: Monday, April 11, 2005 08:06 AM
Subject: Pioneer 10 & 11 Spacecraft Deceleration Anomaly

Slava G. Turyshev, Michael Martin Nieto, and John D. Anderson
have reduced the Pioneer deceleration anomaly
to a set of basic physics parameters:

Study of the Pioneer Anomaly:
A Problem Set Slava G. Turyshev, Michael Martin Nieto, and John D. Anderson
(Dated: February 24, 2005)
http://xxx.lanl.gov/abs/physics/0502123





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