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Ranging and Pioneer
Sorry for the delay in my response to this which got overlooked due to
other distractions. Thus spake " Oh No wrote: Thus spake " Oh No wrote: Thus spake " .... I don't think Anderson actually says how frequent cycle slips were, just that some were examined by an analyst. They did exclude the data. The samples are generally once per minute and few are missing in the small sample of days I have examined. That may give you an upper limit of a few per hour at most, possibly much lower, that you could compare with your predicted rate. Of course where there is a drift the rate should be increasing. I am not clear that a rate for cycle slip is calculable for Pioneer, as it should only be detected when we are able to perform direct measurements of position, and hence find a conflict between ranging and Doppler. I am hoping that in attempting to answer your points things will become clearer to me. In the instance of Mars I calculate a maximum shift equivalent to a velocity 0.34m/s, which I believe should be detectable in principle at optical frequencies, although is actually two orders of magnitude smaller than the resolution of HIRES, the most accurate echelle spectrometer. This equates to a proportional shift of 0.34/c, or 10^-9. That does not translate directly into a rate for cycle slip, because the disparity between Doppler and ranging should only be detectable at the frequency corresponding to measurement accuracy. Thus, if we can measure Mars to an accuracy of 12m (Anderson's figure), then intermediate positions calculated from high frequency Doppler (if we could resolve them with sufficient accuracy) would have to be corrected every 12/c secs. I am not quite sure where the 15000 increase is, or what the equation a_H = 2 Hv refers to. snip derivations ... giving an apparent acceleration of 5.50e-14 m/s^2. Compare that with the anomaly of 8.74e-10 m/s^2. Did that clarify my comment and show how the speed of the craft comes into the equation? Can you now explain why your result is so much higher for Pioneer As I think I said elsewhere, this is not the calculation I am doing. In quantum coordinates the time coordinate shows an acceleration in time which leads to prediction of a shift equivalent to uniform acceleration, independent of the motion of the spacecraft. Radar uses measured time in classical coordinates, so should not show any such acceleration. yet that doesn't translate to extra-galactic redshift measurements? Ah, but it does. Actually my arguments, and results, are much clearer for extra galactic red shift measurements. Translating them into results for Pioneer I find much harder. The basic result is that for measurements on a distant stellar object cosmological redshift goes as the square of the expansion parameter. This leads to the result that recession velocities are half of those calculated in the standard model, and it directly follows that the universe is twice as old and requires a quarter of the mass density for closure as in the corresponding standard model. I have calculated the m-z relation and done a comparison with supernova data from Astier and Riess, and find that, for a no Lambda model, the predicted curve is almost indistinguishable from that of the standard concordance up to redshifts in the region of z=1.5. After renormalising Omega so that Omega=1 is critical density, for the 115 points in the SNLS (Astier) data set I find Omega=1.85 with chi^2=113.4, compared to a standard fit of Omega=0.264 with chi^2=113.6. There is a slightly larger difference for the Riess data set which includes SN of higher redshifts. For 154 dof (3 outliers removed from the gold set) the standard model has Omega=0.295 with chi^2=151.3, while I find for the no Lambda model, Omega=1.90 with chi^2=150.0. These fits are really too close to call, and I await SNAP (maybe 15yrs hence) for any real advance based on SN detections at z1.5. However I also take it as a positive indication that I have greater consistency in the predicted values of Omega from the two data sets, as evidenced by a slightly increased difference in chi^2 values when data sets are combined. For 225 dof including 154 supernovae from the Riess gold set and 71 SNLS supernovae, corrected for the choice of Hubbleâ~@~Ys constant, the best fit standard flat space Lambda model has Omega=0.284, chi^2=212.5. The best fit teleconnection no L model has Omega=1.89, chi^2=210.8. I have it that quantum coordinates introduce an acceleration in time which can be shown by a coordinate transformation equivalent to an acceleration Hc. What puzzles me here is that your anomalous acceleration is independent of the craft speed. If the craft were sitting at a fixed location with neither radial nor tangential velocity (e.g. station keeping with a solar sail), this implies you would still get a downlink frequency shift which increased linearly with time for a constant uplink frequency and it would also be independent of distance (as is observed) hence should apply to short range measurements over some spread of distance resolution. ... Of the phenomenological time models considered by Anderson et al, do any of their equations (60) through (65) match? ... Equation 60 is the probably the best match, though I am not sure how different it is from 61 or 62. I need to refresh my memory on the details. I used cosmic time, but in the quantum domain an "accelerating" time coordinate is used, proportional to the expansion parameter. This will affect Doppler, but not ranging which is based on cosmic time. Interesting, that might offer you another test as an inconsistency with other means of measuring the solar plasma. From page 10 of gr-qc/0104064: "Thus, the ranging data are independent of the Doppler data, which represents a frequency shift of the radio carrier wave without modulation. For example, solar plasma introduces a group delay in the ranging data but a phase advance in the Doppler data. Ranging data can also be used to distinguish an actual range change from a fictitious range change seen in Doppler data that is caused by a frequency error [39]. The Doppler frequency integrated over time (the accumulated phase) should equal the range change except for the difference introduced by charged particles." Yes. I think really though that a new mission is required, preferably one which allows both Doppler and ranging measurements in the outer solar system. Regards -- Charles Francis substitute charles for NotI to email |
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