Craig Markwardt wrote:

"GSS" <gurcharn_sandhu@yahoo.com> writes:

... At certain point of time, the
object A (DSN type Earth station) and the object B (Pioneer type
spacecraft) could both be moving with a common velocity of about 30
km/s along AB in BCRF. The round-trip signal propagation time Tr could
be measured with a precision atomic clock located in the ground
station. Here all the *observers* are co-located at the ground station
and hence at rest wrt the object A and *not* wrt the BCRF. In fact we
can make a general statement here that all space missions are always
referred to the BCRF and *none* of the observers is ever at rest in
BCRF. Therefore, all round-trip signal propagation time measurements
made with precision atomic clocks *at rest* in the ground station are
always *valid* irrespective of the fact the ground station is in motion
wrt the Celestial Reference Frame considered.

And of course all proper space ranging/tracking analysis accounts for
the round trip light travel time, including the motions of both the
remote bodies and the earth station(s) during the trip, so your
"effect" would not be relevant. Your original toy model posited a
*common* motion of V ~ 200 km/s. That is not the case for any
spacecraft tracking experiment that you are just now bringing up.
*Now* that you discuss 30 km/s instead of 200 km/s, let's see what
your equation (9) predicts [*] .... about 16 usec. Suddenly it
becomes a lot less interesting in comparison to the actual Shapiro
delay.

Sorry, Craig you have again skirted the main issue here. I wanted you
to agree with me that "all space missions are always referred to the
BCRF and *none* of the observers is ever at rest in BCRF." ...

... Similarly
when we refer the objects to Galactic reference frame the observers
need not be at rest in that Galactic frame.

Quoting from arXiv:gr-qc/0208046 v1
Independent Confirmation of the Pioneer 10 Anomalous Acceleration

"The epoch of transmission from the Earth is t1, the epoch of
interaction of the signal with the Pioneer 10 spacecraft is t2, and the
epoch of reception back at the Earth is t3.

The 3-vectors r1, r2, and r3 represent the positions of the
corresponding antenna at the corresponding epoch, and v1, v2, and v3
represent the velocities. The vector difference, r12, is defined as r2
- r1. These vector quantities are measured in the solar system
barycenter frame. The original station times in the ATDF records are
referred to Coordinated Universal Time (UTC)."

Thus even in your own papers you have never insisted that the DSN
atomic clocks *must* be at rest in BCRF.

That is true. However it was *you* that set up completely separate
problem of the effect of common motion in the galaxy (V ~ 200 km/s).

In the paper that you refer to -- and indeed all proper spacecraft
tracking analysis -- the correct coordinate transformations between
frames are done, and an accounting of the round trip light travel time
including body motions during the signal travel time are accounted
for. Thus, the very thing that you were bemoaning was not occurring
(scientists treating motion of the bodies during signal signal
transmission), is in fact occurring!

Here again you are skirting the main issue. I wanted to draw your
attention to your own words, "These vector quantities are measured in
the solar system barycenter frame" when all the observers and the
instrumentation are *not at rest* in the Barycentric frame. Similarly
there should be no objection to measure the position vectors in the
Galactic reference frame while all observers and the atomic clocks are
*not at rest* in that frame.

Craig Markwardt wrote:

"GSS" <gurcharn_sandhu@yahoo.com> writes:

Craig Markwardt wrote:

"GSS" <gurcharn_sandhu@yahoo.com> writes:

.....

Of course for a known value of the common velocity V of A and B, we can
compute the time delay (Tr-2D/c) as,

From relation (5) we get,
Tr =(2D/c).[1+(V/c)^2] ... (8)
Or (Tr-2D/c)= (2D/c).(V/c)^2 ... (9)

....

In the very beginning I had made it clear,
"Let me first illustrate the main principle by which the common
velocity V of two objects A and B separated by distance D=AB in a
Celestial Reference Frame (where V is assumed to be along AB) can be
determined just by measuring the total uplink and downlink or
round-trip signal propagation time Tr. [We may consider A to be an
Earth Station, B a Pioneer type spacecraft]"

The 'Celestial Reference Frame' considered above could be the
Barycentric Celestial Reference Frame (BCRF) in which the positions of
all spacecraft are invariably referred.

.....

Yes, the time delay (Tr-2D/c) will vary as the cosine of the angle
between the line AB and the velocity vector of the Solar system motion
in the Galactic reference frame. To demonstrate that, the line AB will
have to be oriented in *all* possible directions in the space. ...

That is an erroneous statement. It is not necessary to sample *all
possible* directions to distinguish between your "effect" (cosine
dependence) and the Shapiro effect (with logarithms, etc). The
Shapiro effect is very greatly enhanced along lines of sight that pass
close to the sun, while your "effect" is not.

... But that
has never been done in practice because firstly it was never considered
necessary and secondly there are enormous problems associated with such
measurements. Because this time delay was pre-conceived as a
'gravitational' delay, this has always been measured only around
superior conjunction of two planets where the variation of 2D/c factor
on the RHS of equation (9) becomes a dominant factor (apart from the
refraction effects).

That is also incorrect. Many spacecraft have been sent on many
trajectories throughout the solar system, both in the plane and out of
the plane (examples: Voyagers, Pioneers, Ulysses, Galileo). When also
adding to the mix planetary (and asteroid) ranging, it is of course
absurd to argue that they all have superior conjunction along exactly
the same line in celestial coordinates. They do not. In fact, the
observed Shapiro delay strongly depends on the Earth-Sun-Body angle,
irrespective of the solar system motion vector through the galaxy.

Kindly quote at least one reference from a space mission where D and Tr
have been measured independently, that is without resorting to Tr=2D/c.

Most often D is either increasing or decreasing and never constant for
a long period. Even if in some odd case it was possible to measure Tr
and D independently, the variation in D during the signal round trip
time Tr is so great that it will not be feasible to choose the 'proper'
value of D for use in the time delay relation Tr-2D/c.

In fact when the line AB is significantly away from the superior
conjunction, the distance D itself is 'evaluated' by equating Tr with
2D/c and this Tr is assumed as 'normal'. Thereafter as the line AB
passes through the superior conjunction, the *excess* of Tr is noted
and taken as 'Shapiro delay'. Quoting from one of the study reports on
Shapiro time delay measurements with Mariner spacecraft,
"As the line of sight between Earth and Mars drew closer and closer to
the sun, a measurable excess time delay began to occur. When the line
of sight came nearest to the Sun (called superior conjunction), the
maximum excess time delay occurred -- about 200 microseconds as
predicted by Shapiro's equations."

Ignoring the above comments, which are already fatal to your supposed
effect, let's consider a body which is several different positions
relative to the sun (let's say 1, 5, 10 and 20 degrees, on either side
of the sun). The corresponding Shapiro delay is (using
4GM/c^3*ln(1-cos(th))),

Angle [deg] -20 -10 -5 -1 +1 +5 +10 +20
Shapiro [us] 55 82 110 173 173 110 82 55

with a "cusp" at conjunction.

Now let's compare that to the "cosine effect". Since that is
dependent on the earth-sun-galactic motion angle, let's consider two
cases, one where the earth-sun line is parallel to the galactic
motion, and one where it is perpendicular. To be generous, let's pick
speeds of 30 km/s and distances of 2 AU, although since the equation
is not exactly sensical, the values are a bit arbitrary. In reality,
at conjunction, most motion will be perpendicular to the line of
sight, so your "effect" would be even smaller. Your equation (9),
after accounting for the cosine effect, yields,

Angle [deg] -20 -10 -5 -1 +1 +5 +10 +20
Parallel [us] 18.79 19.69 19.92 19.99 19.99 19.92 19.69 18.79
Perp. [us] -6.84 -3.47 -1.74 -0.35 +0.35 +1.74 +3.47 +6.84

with no "cusp" in either case.

In short, your "effect" is far too small, produces far too little
variation at conjunction, and is of the wrong functional form, to be
mistaken for a Shapiro-like delay. Thus your claimed "effect" is
falsified.

No, in the above illustration you did not formulate the problem
correctly.

For this purpose let us consider the motion of Earth-Mars system before
and after a superior conjunction E0-M0. For the purpose of illustration
let us assume that the solar system is moving in the Galactic reference
frame along direction E0-M0 with a velocity of V0=100 km/s. Let M1, M2,
M3 and M4 be sequential positions of Mars at 10 degree angular
intervals 'beta'. Let E1, E2, E3 and E4 be the corresponding positions
of Earth. From the orbital radii and speeds of Mars and Earth, we can
easily compute the Earth-Mars separation distance D for each location.
Similarly we can also compute the inclination angle 'theta' of En-Mn
line wrt E0-M0. We can also compute corresponding parameters for
opposite positions of Mars and Earth marked as M1', M2' etc.

. M0
. M1' | M1
. |
. |
. |
. |
.................S..............
. |
. |
. |
. E1 | E1'
. E0
.

Salient computed parameters are tabulated below.

Table 1
Position Beta D Theta 2D/c
(degree) (10^9 m) (degree) (second)

M4' -40 360.44 -53.75 2402.9
M3' -30 367.65 -40.35 2451.0
M2' -20 372.84 -26.92 2485.6
M1' -10 375.96 -13.46 2506.0
M0 0 377.00 0 2513.3
M1 10 375.96 13.46 2506.0
M2 20 372.84 26.92 2485.6
M3 30 367.65 40.35 2451.0
M4 40 360.44 53.75 2402.9

Since in the Galactic frame the solar system is moving along E0-M0 with
velocity V0, the component of this velocity along inclined directions
E1-M1 etc will be given by V=V0.Cos(theta). Therefore, equation (9) for
computing Galactic motion induced time delay T_d will get modified to,

T_d=(Tr-2D/c)=(2D/c).(V0/c)^2.Cos^2(theta) ... (10)

With the assumed value of V0=100 km/s, the above table can be extended
to compute T_d for all positions. Finally, treating the M4 (and M4')
positions as 'normal' in the sense that we take Tr=2D/c, subtract T_d
value for M4 position from the T_d values of all other positions to get
the modified delay T_sh. This modified or normalized time delay is what
is being perceived as Shapiro gravitational time delay.

Table 2
Position Theta 2D/c T_d T_sh
(degree) (second) (us) (us)

M4' -53.75 2402.9 93.3 0
M3' -40.35 2451.0 158.2 64.9
M2' -26.92 2485.6 219.6 126.3
M1' -13.46 2506.0 263.4 170.1
M0 0 2513.3 279.3 186.0
M1 13.46 2506.0 263.4 170.1
M2 26.92 2485.6 219.6 126.3
M3 40.35 2451.0 158.2 64.9
M4 53.75 2402.9 93.3 0

This shows that the time delay values computed above are comparable to
the experimental values of Shapiro delay obtained from Mariner mission.

The major problem associated with the measurement of such time delays
(Tr-2D/c) with planetary objects (like earth and Venus) is the
variation of D during the signal propagation times of a few hundred
seconds when the accuracy in D required for measuring a few microsecond
time delay must be of the order of a few meters.

(a) What makes you think that the variations in D during signal travel
time are not accounted for in the analysis? They are.
(b) One microsecond accuracy corresponds to approx c(dt) = 300 meters
not a "few meters." What makes you think that ranging techniques are
not accurate to the ~km level? They can be.
Thus, your claimed "major problems" are negligible.

Assuming an average rate change of D of about 3 km/s for the system
considered above, the expected change in D, during the signal round
trip time Tr of the order of 2400 seconds, will be about 7000 km. But a
mere 60 km variation in D will cause a variation in 2D/c of about 200
microseconds. I hope you can now appreciate the "major problems"
involved in actually measuring such time delays when D is not constant.
That is why in my illustrative example I had assumed a constant D for
the sake of simplicity.