Re: Pioneer Anomoly


"John C. Polasek" <jpolasek@xxxxxxxxxx> wrote in message
news:krnmb1hq717rutfupoctgc5j20teqi8tfm@xxxxxxxxxx
> On Fri, 24 Jun 2005 00:03:33 +0100, "George Dishman"
> <george@xxxxxxxxxxxxxxxxx> wrote:
>>"John C. Polasek" <jpolasek@xxxxxxxxxx> wrote in message
>>news:otbkb1t2ko0hf53jkis7chjrdvvodl0fq5@xxxxxxxxxx
....
>>> I have half read the paper again and I saw the statement that when P10
>>> got the signal it amplified it and re scaled it and retransmitted it.
>>> I find that hard to believe, when it seems so much cleaner to trigger
>>> a local oscillator and get a clean primary signal back to earth. I
>>> believe it makes a big difference.
>>> I am continuing to investigate.
>>
>>That's what they do, there is an on-board high
>>stability oscilator which can be phase-locked
>>to the uplink carrier. The PLL includes a fixed
>>ratio divider so that the downlink frequency is
>>exactly related to the uplink.
>
> George and Jonathan:
> If the downlink is phaselocked to the uplink (plus the divider) how
> are you expected to get doppler drift?

Suppose the craft is moving away from Earth. There
is a Doppler red shift on the uplink. The craft
multiplies that frequency by 240/221 and sends it
back. There is another Doppler red shift on the
downlink. If the Earth were at rest, the shift is
twice that on either link alone.

> That clock in space has to be a
> free agent. It doesn't even seem to be a valuable complication.

They use both methods, free running and transponding.
The stability of the free clock is not as good as
when it is locked to the ground based maser reference
system.

>>The text discusses the meaning of "phase coherent"
>>in the third paragraph of section 3.1, and there
>>is a more general description in section 2.4.
>
> I have a much more serious question and that is that I could not find
> in Andersons paper any record of the actual doppler shifts

The actual shift varies minute by minute. You
have worked out part of it below but try these
as well, they will put the problem into
perspective:

The craft is leaving the Solar system at about
12km/s. What shift does that produce?

The Earth orbits the Sun at about 30km/s. That
produces a sine wave frequency shift with a
period of one year. What amplitude?

The Earth rotates once per sidereal day. At
the latitude of the DSN stations, the speed
is about 350m/s. What is amplitude of the
resulting shift?

> and can't
> understand their residuals.

Using the Doppler, they compute the most
likely trajectory for the craft. The
residuals are the difference between the
difference between the measured value and
the predicted value at each measurement
time. The "most likely trajectory" is that
which produces the least total residuals.

> But let me point out an outrageous obstacle.
>
> The downlink is at 2.295Ghz and Ap is 8.74x10^-10m/ss.
> Doppler shift for velocity v is given by
> DS = F x v/c hz
> Doppler drift is given using dv/dt which in our case is Ap:
> DSdot = F x Ap/c hz/second
> DSdot = 6.7 x 10^-9 Hz/second
> Time for change of 1 Hz:
> T/hz = 1Hz/DSdot = 1.5 x 10^8 seconds = 4.7 years!!
> A change of 1Hz in nearly 5 years?
> I have probably made an error somewhere. Help me out.

Your only error is that the shift is doubled
because it applies on both the uplink and
downlink. The residuals shown in Figure 8
(page 36) amount to about 3Hz in 8 years.

Craig Markwardt independently repeated the
calculations developing his own software and
his results are here:

http://www.arxiv.org/abs/gr-qc/0208046

Figure 2 shows the residuals after also
assuming a constant acceleration A_p.

As you can see, the spread is of the order
of 4 mHz (yes, I do mean 0.0042 Hz !).

Going back to your original point, the
frequency of the on-board oscillator would
need to be accurate to 1 part in 10^15 even
after many years in space, and that's not
feasible. Without the transponder, the
results would be indistinguishable from a
slow drift in the oscillator due to aging.

George


.

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