Ranging and Pioneer

wrote:
George Dishman wrote:
"Spud" wrote in message
oups.com...

gr-qc/0102103 is worth a look

I believe that analysis may be incomplete.

I would say simplified

Given that I probably need more explanation
than the target readership, that's probably
reasonable.

What I believe has been overlooked in gr-qc/0102103
is there will be an "expansion of space", notably
of the distance between the Earth and the craft in
accordance with the usual cosmological scale factor
a(t) during the time the signals are in flight.

As above

Possibly, I'm speculating there.

I'm not up to handling GR but taking a macroscopic
view, I think the end result of the above should be
close to 2*H*v which is much larger than the range
value given in the above paper but still about four
orders smaller than the observed anomaly. It would
be interesting to know if that 'educated guess'
works out.

gr-qc/0402024

Thanks for the link.

Bottom of page 2:

"The acceleration a_P is introduced by formula (15)
in [1], i.e.

[v_obs(t) - v_model(t)] = -v_0 * (2 * a_P * t / c)

snip definition of v_model - see paper (5)

where ν_0 is the reference frequency, the factor 2 is
because of two way data, v_model is the modeled
velocity of the spacecraft due to the gravitational
and other forces, and ν_obs is frequency of the
re-transmitted signal observed by DSN antennae."

So far, so good.

"After time 2t has been detected a small blue shift
on the top of the red shift caused by the motion of
the spacecraft outwards the Sun. Form (5),
an unexplained blue shift

v = v_0(1 + 2 * a_P * t / c) (6)

is detected, where 2t is the time of the light signal
in two directions."

That is incorrect, it should read:

"After time t has been detected a small blue shift
on the top of the red shift caused by the motion of
the spacecraft outwards the Sun. From (5),
an unexplained blue shift

v = v_0(1 + 2 * a_P * t / c) (6)

is detected, where t is the time at which the
measurement was made in seconds since
1 Jan 1987."

In other words it ranges from 0 to 8 years instead
of roughly from 12 to 16 hours. The factor of 2 is
for the two legs of the journey as stated so
should be omitted in the definition. I haven't seen
whether that affects what follows yet, it may just
be restricted to the description.

Near the bottom of page 4 there is:

dv/dt = -a - 2Hv

where a is the "Newtonian acceleration .. toward
the Sun". Since the anomaly is the difference
between the measured and the predicted values
it follows directly that a_P = 2Hv which is what
I expected.

I need to read the paper more carefully to see how
he gets the relation H = a_P/c which appears at
the top of that page in eqn (9) when a_P/c is used
to replace H in the previous line.

George