Pioneer 10 Trajectory ?

One of the assumptions leading to the ‘observed’
anomalous acceleration of Pioneer 10 toward the Sun was the earthsite
motions of the sending and receiving stations
That is, the predicted Doppler shifted frequency of a radar
frequency sent to the spacecraft and returned to earth two light
times later were used to check successive Newtonian positions and
velocities of the spacecraft as it moved away from the Earth.
That is, the launch and subsequent velocities imparted to the
craft and calculations of the gravitational effects of Earth, Jupiter,
the Sun etc were combined since the launch in 1973 to produce craft
positions and velocities for each minute since the launch.
Marquardt has said that there were problems in determining the craft
trajectory when in this way when P10 was near Jupiter and the other
planets in the first years after launch which suggests that the
Doppler corrected Newtonian predictions were even more different then
from the observed frequencies than accounted for by the anomalous
acceleration toward the Sun.
If something is wrong with the assumption as to which earthsite
motions to use to obtain the Doppler shifted frequencies, the result
could be continual errors, eg accelerative or decelerative trends in
the discrepancy between the predicted and observed frequency.
That is, a comparison of the tracking data, ie the radar frequency,
constantly sent from or to and from the moving spacecraft, to the
observed frequency, assuming specific earthsite motions during
transmission and reception, showed unexplained discrepancies.
Presumably the positions and velocities of the craft were altered
to make them consistent with this tracking data. Then Newtonian
calculations of the new position and velocity of the craft were made
and the process repeated.
It appears that at some point in time, the readjustment of the
Newtonian calculated positions and velocities ceased and the ephemeris
positions were based only on Newtonian calculations from this time
forward.
Thus at any point in time, one can look at the tracking data
given minute by minute in the UTC or GMT time system and compare this
to the predicted frequency given the earth site motions at the
corresponding time in the CT time system.

That is one can adjust the position and or velocity of the craft to
make the observed frequency equal the predicted frequency,assuming
specific transmission and reception earth site motions, for any
specific reception time. The subsequent position and velocity of the
craft based on this and the gravitational effects of the sun etc would
determine the next position and velocity. A credible trajectory would
be one where there were no accelerative or decelerative trends and the
variation of the discrepancy between predicted and observed was small
and uniformly distributed.
For example: 1)Project the Madrid earthsite velocity wrt
sun,V=(v1(t),v2(t),v3(t)),a vector starting at Madrid at a specific
time( eg t=21:23 Oct 7 1987) onto the line between Madrid and the
craft position at this same time based on an the above estimation
procedure and conventional earth site motions assumptions.
However we will assume in obtaining the next position and
acceleration, the nearly instantaneous light delay
model.v1(t)=(x(t)-x(t-1))/60sec., etc.
(in this example the earthsite velocity is roughly V=30km/sec and the
projected velocity on the simulataneous Madrid-craft line is roughly
W= 25km per second, more exactly at this time,V=30.02755,W=25.42127).
Note the projection magnitude is the sum of the cross products of the
velocity components times the corresponding Madrid-craft vector
components divided by the Madrid-craft distance. The angle of
projection is arcos(0.879900957)= 28.36958169 deg.

2)Note that if we change the magnitude of the projected earthsite
velocity at Madrid by trial and error in the spreadsheet to 24.780755,
the predicted frequency minus the observed frequency is .008…
Hz.
This means that if the craft position is at a slightly larger angle
of projection,namely arcos(24.780755/30.02755)= 34.38440, or about six
degrees more, the motion of the earthsite to the craft would be
reduced enough so that when the craft velocity away from the earth
assumed to be the same is, subtracted, the net velocity of the earth
to the craft is smaller and enough smaller to make the predicted
frequency match the observed frequency to within .004Hz.
Of course we could also assume a slightly larger velocity of the
craft away from the earth and a smaller increase in the angle of
projection of the earthsite velocity onto the line between the
earthsite and the new craft position..
In this example the positions of the earth sites given by the
ephemeris are 55 seconds later than the times for the frequencies in
the tracking data. Thus the change in position of the Madrid earthsite
wrt the Sun from 21:23 to 21:24 divided by 60 seconds and associated
with the spreadsheet time, 21:24, represents the average velocity
during this minute in the CT time system but in the GMT time system
this is the average velocity from 21:22 to 21:23 and this produces the
Rx frequency in the tracking data recorded at 21:23 etc. So we compare
the spreadsheet predicted frequency for 21:24 with the observed
frequency for 21:23 etc.

(Ralph Sansbury) wrote in message . com...
One of the assumptions leading to the
anomalous acceleration of Pioneer 10 toward the Sun was the earthsite
motions of the sending and receiving stations

Revised method of obtaining P10 trajectory using different earthsite
motions during transmission and reception.



Light speed is assumed to extrapolate to the most distant stars and
galaxies but for distances beyond the GPSS satellites at 11,000 miles,
the evidence is not unambiguous(see appendix). Now the recently
observed anomalous acceleration of Pioneer 10 indicates that light
speed does not extrapolate beyond one minute. That is, the
predicted Doppler shifted frequency of a radar frequency sent to the
spacecraft and returned to earth two light times later were used to
adjust successive Newtonian calculated positions and velocities of
Pioneer 10 as it moved away from the Earth. When the earthsite motions
hours apart, used to compute the Doppler shifts were replaced by
earthsite motions 1 minute apart, the anomalous accelerative
discrepancy between the Newtonian positions and velocity and the
position and velocity adjustments, implied by the Doppler shifted
frequency received, this discrepancy can be removed.


1)Project the Madrid earthsite velocity wrt
sun,V=(v1(t),v2(t),v3(t)),a vector starting at Madrid at a specific
time( eg t=21:23 Oct 7 1987) onto the line between Madrid and the
craft position assuming the nearly instantantaneous light delay model,
at this same time.The coordinates of the craft positions however are
based on the above estimation procedure and earth site motions
assuming the conventional light delay model.
The velocity coordinates of the earth site are
v1(t)=(x(t)-x(t-1))/60sec., etc.
(in this example the earthsite velocity is roughly V=30km/sec and the
projected velocity on the line from the earth site to the ephemeris
craft position at this same time is roughly W= 25km per second, more
exactly at this time,V=30.02755,W=25.42127; for the craft
v=13.06,w=12.84). The projection magnitude is the sum of the
products of the velocity components times the corresponding
Madrid-craft vector components divided by the Madrid-craft distance.
The angle of projection is arcos(0.879900957)= 28.36958169 deg.

2) If we change the magnitude of the projected earthsite velocity at
the Madrid earthsite by trial and error in the spreadsheet to
24.780755, this leads to a predicted frequency minus the observed
frequency of .008Hz.
This means that if the craft position is at a slightly larger angle
of projection,namely arcos(24.780755/30.02755)= 34.38440deg, or about
six degrees more, the motion of the earthsite to the craft would be
reduced enough so that when the craft velocity away from the earth
assumed to be the same as in the old position, is subtracted, the net
velocity of the earth to the craft is smaller and enough smaller to
make the predicted frequency match the observed frequency to within
..004Hz.
We have ignored the effect of the implied craft position change on
the craft Madrid velocity but we can assume tentatively that the craft
velocity wrt the sun was slightly greater so as to compensate for this
effect. Of course we could also assume an even larger velocity of the
craft away from the earth and a smaller increase in the angle of
projection of the earthsite velocity onto the line between the
earthsite and the new craft position.
If this assumption produces a trajectory that requires even less
adjustment than our first assumption we can change this later.
In this example the positions of the earth sites given by the
ephemeris(telnet observer table) are 55 seconds later than the times
for the frequencies in the tracking data. Thus the change in position
of the Madrid earthsite wrt the Sun from 21:23 to 21:24 divided by 60
seconds and associated with the spreadsheet time, 21:24, represents
the average velocity during this minute in the CT time system but in
the GMT time system this is the average velocity from 21:22 to 21:23
which produces the received frequency in the tracking data recorded at
21:23 etc. So we compare the spreadsheet predicted frequency for 21:24
with the observed received frequency for 21:23 (or a linear
interpolation of the value for 21:23:05)etc.

(Ralph Sansbury) wrote in message . com...
One of the assumptions leading to the
anomalous acceleration of Pioneer 10 toward the Sun was the earthsite
motions of the sending and receiving stations

Revised method of obtaining P10 trajectory using different earthsite
motions during transmission and reception.



Light speed is assumed to extrapolate to the most distant stars and
galaxies but for distances beyond the GPSS satellites at 11,000 miles,
the evidence is not unambiguous(see appendix). Now the recently
observed anomalous acceleration of Pioneer 10 indicates that light
speed does not extrapolate beyond one minute. That is, the
predicted Doppler shifted frequency of a radar frequency sent to the
spacecraft and returned to earth two light times later were used to
adjust successive Newtonian calculated positions and velocities of
Pioneer 10 as it moved away from the Earth. When the earthsite motions
hours apart, used to compute the Doppler shifts were replaced by
earthsite motions 1 minute apart, the anomalous accelerative
discrepancy between the Newtonian positions and velocity and the
position and velocity adjustments, implied by the Doppler shifted
frequency received, this discrepancy can be removed.


1)Project the Madrid earthsite velocity wrt
sun,V=(v1(t),v2(t),v3(t)),a vector starting at Madrid at a specific
time( eg t=21:23 Oct 7 1987) onto the line between Madrid and the
craft position assuming the nearly instantantaneous light delay model,
at this same time.The coordinates of the craft positions however are
based on the above estimation procedure and earth site motions
assuming the conventional light delay model.
The velocity coordinates of the earth site are
v1(t)=(x(t)-x(t-1))/60sec., etc.
(in this example the earthsite velocity is roughly V=30km/sec and the
projected velocity on the line from the earth site to the ephemeris
craft position at this same time is roughly W= 25km per second, more
exactly at this time,V=30.02755,W=25.42127; for the craft
v=13.06,w=12.84). The projection magnitude is the sum of the
products of the velocity components times the corresponding
Madrid-craft vector components divided by the Madrid-craft distance.
The angle of projection is arcos(0.879900957)= 28.36958169 deg.

2) If we change the magnitude of the projected earthsite velocity at
the Madrid earthsite by trial and error in the spreadsheet to
24.780755, this leads to a predicted frequency minus the observed
frequency of .008Hz.
This means that if the craft position is at a slightly larger angle
of projection,namely arcos(24.780755/30.02755)= 34.38440deg, or about
six degrees more, the motion of the earthsite to the craft would be
reduced enough so that when the craft velocity away from the earth
assumed to be the same as in the old position, is subtracted, the net
velocity of the earth to the craft is smaller and enough smaller to
make the predicted frequency match the observed frequency to within
..004Hz.
We have ignored the effect of the implied craft position change on
the craft Madrid velocity but we can assume tentatively that the craft
velocity wrt the sun was slightly greater so as to compensate for this
effect. Of course we could also assume an even larger velocity of the
craft away from the earth and a smaller increase in the angle of
projection of the earthsite velocity onto the line between the
earthsite and the new craft position.
If this assumption produces a trajectory that requires even less
adjustment than our first assumption we can change this later.
In this example the positions of the earth sites given by the
ephemeris(telnet observer table) are 55 seconds later than the times
for the frequencies in the tracking data. Thus the change in position
of the Madrid earthsite wrt the Sun from 21:23 to 21:24 divided by 60
seconds and associated with the spreadsheet time, 21:24, represents
the average velocity during this minute in the CT time system but in
the GMT time system this is the average velocity from 21:22 to 21:23
which produces the received frequency in the tracking data recorded at
21:23 etc. So we compare the spreadsheet predicted frequency for 21:24
with the observed received frequency for 21:23 (or a linear
interpolation of the value for 21:23:05)etc.