Uncle Al wrote in message ...

If the calculations are Newtonian then the answers to high precision
are precisely trivially wrong, perpetual empirical idiot sansbury.

http://arxiv.org/abs/gr-qc/0205059
Pioneer anomaly



Uncle Al has said that my calculations must be wrong. But Markwardt
and
Dishman calculations agree with mine in order of magnitude. The
problem is
Markwardt and Dishman have no explanation as to why these calculations
are NINE orders of magnitude different than what they should be if the
Pioneer anomaly is as claimed.
The reason is that the Pioneer anomaly is much larger than claimed
and too large to be explained by a modification of the law of
gravity.The required modification would make planets fall into the
sun.
A more acceptable explanation is that the speed of light delay
assumptions are wrong and lead to a wrong trajectory for Pioneer 10
and that the assumption that the speed of light delay does not
extrapolate beyond a second leads to the correct trajectory.

Here again is my original post. Please reply to if
you know something about radio astronomy and the problems discussed
here.


The Pioneer 10 anomalous acceleration is five orders of magnitude
larger than reported by Anderson et al. as revealed by archived data
for a one hour and a half time interval in 1987 when compared to the
NASA positions and velocities of the craft.
see http://mysite.verizon.net/r9ns/rangerate2.xls

These positions and velocities are based on Newtonian calculations
of
craft velocity changes due to the known craft's mass to the
attraction
of the sun and to previous velocities and positions of the craft
implied
by previous radiometric data and data on earth site motions during
transmission and reception.
The procedure is to use the last best estimate of craft position
and
velocity determined in this way and then to predict the position and
velocity a minute later using 1)this velocity and position and mass
and
2)the assumed earth site transmitter motion at the earlier time
implied
by the two way light speed delay and the receiver earth site motion
and
to compare this with the received Doppler shifted frequency and to
correct the position and velocity to make the predicted received
frequency equal the observed received frequency.
Dishman and Markwardt, mistakenly claimed that 1)the approximate
agreement of the results of this procedure with the NASA ephemeris,
and
2)the lack of agreement of these results with the assumption of some
other light speed delay assumption proved the validity of the
conventional light speed delay assumption, But this is a classic
petitio principi where the conclusion, here the craft trajectory,
is
assumed in the premise.
The "approximate" agreement of the results of this procedure and
the
actual received frequencies is actually a thousand times greater
than
the implied margin of error even allowing for the fact that the
later
NASA ephemeris calculations do not take the cumulative effect of the
anomalous acceleration into account.
It must be then that the successive positions of the craft are
different from the results of the above procedure. Let us obtain the
direction and speed of the craft assuming tentatively that the
received
frequencies here were produced by transmissions from the same earth
station a few seconds earlier while the earthsite velocity,V1, wrt
the
sun was nearly the same.
This would be the case if light speed delay did not extrapolate
beyond one second approximately, no matter how much the distance of
the
source from the receiver exceeded d=2.998(10^8)meters where
c=d/1second. That there is no clear evidence against this hypothesis,
contrary or popular opinion, is shown below.
Thus, if the craft was stationary and the total earth movement was
toward the craft, the Doppler shifted frequency received would be
(T)(1+2v1/c) where T = the transmitted frequency(here
2.291944138GHz),v1= K1V1, the earthsite velocity wrt the craft at the
reception time, t1, and c = the speed of light and K1 is the cosine
of
the angle between the craft to earthsite line and the earthsite
velocity wrt the sun at this time.
But the craft in this data is at these times moving away from the
sun
at about 13.059km/sec according to 1)the conventional model and 2)its
initial launch velocity etc. and the projection of this on the
earthsite
to craft line is, through a nearly zero angle, 13.059. Subtracting
13.059 from K1V1 etc., gives us a first tentative estimate of the
combined velocity of the earthsite to the craft without assuming the
conventional exact position of the craft.
(T)(1+2(K1V1-13.059)/c)=R1,
so ((R1-T)c+2T(13.059))/2V1T=K1
The arccos of K1 is the angle between the velocity of the earth
site
wrt the sun and the line to the craft from the receiver site at this
time. Suppose the site at this time is represented as the origin of
a
3 dimensional coordinate system where the horizontal y axis into the
page is the latitude and the vertical z axis is the longitude and the
horizontal x axis on the page is directed to the zenith point in the
sky. Suppose also that the latitude at this time is along the same
line
as the earth's orbital velocity and the spin and orbital velocity are
in
the same direction. The angle from K1 could define a line in the xy
plane or the yz plane or any plane in between but only one of these
would give the maximal intensity of the received signal.

This value of K1 so determined and the value given by the
conventional model for the craft sun distance, r1=6,295 116 208 gives
us
an estimate of the craft position. We can change,13.059, K and r as
needed to produce a succession of craft positions consistent with the
observed received frequencies and Newtonian calculations of
successive
velocities and positions of the craft. The craft acceleration at a
distance r toward the sun is a1 = kM/r^2=6.67(10^-11)(2)(10^30)/r1,
so
that the velocity that must be subtracted from each 'previous'
velocity
to obtain the next velocity and position and r value is,
(a1)(t2-t1)/2
for the assumed r1.
If the craft minute by minute trajectory obtained in this way over
any randomly chosen hour or so time interval like this one, is more
accurate without requiring anomalous acceleration or constant
adjustments after the intial adjustements, then the conventional
model
and light speed delay assumptions are disproven and the proposed
light
speed delay model is indicated.

The following data from Oct 7 1987 is from
http://mysite.verizon.net/r9ns/rangerate2.xls
:

Time DnCnFr R freq Hz V km/s r
K
21:27 810154 2292133984 30.03149 6295116208 0.848293063
21:28 810166 2292133972 30.03246 6295116975 0.848239147
...
22:43 811249 2292132889 30.09136 6295174532 0.844225255
22:44 811266 2292132872 30.09194 629517529
0.844172955


We note that the received frequencies,R, are decreasing but that
they
are all greater than the transmitted frequency which suggests that
the
earthsite motion wrt the sun(which includes the approx 353m/s earth
rotation at Madrid, has a component toward the craft but that the
motion toward the craft as the earth orbits and spins, is decreasing-
even though the total motion,V, of the craft wrt the sun is
increasing.