Re: Pioneer 10 & 11 Spacecraft Deceleration Anomaly
- From: "Koobee Wublee" <kublai@xxxxxxx>
- Date: Tue, 12 Apr 2005 23:33:21 -0700
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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