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Ranging and Pioneer
Oh No wrote:
Sorry for the delay in my response to this which got overlooked due to other distractions. OK, I just glad you hadn't dismissed me as a crank ;-) Thus spake " Oh No wrote: .... 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. This is getting really confusing. I would ask how performing a range measurement could affect the Doppler measurement but since they share the carrier there is an obvious link. What I don't see is why cycle slips would occur if a range measurement was in progress but not if only the Doppler was being used on pysical grounds, though it is clear why the range modulation sweep rate might exceed the ability of the PLLs to follow in lock at a practical level. I am hoping that in attempting to answer your points things will become clearer to me. Yes, I hope I can act as a test for your explanation. 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. I haven't a clue what you mean so I'm going to take a Devil's Advocate stance and throw up something for you to knock down. Assuming a carrier of 2.291GHz, the two-way Doppler at 12.5km/s would be about 191048.836 Hz. An error of 0.34m/s would produce a further shift of 5.196Hz giving 191054.032 Hz. Are you say that the signal would consist of short sections at 191048.836 Hz separated by phase discontinuities such that the mean phase rate was 191054.032 Hz ? Even so, why would that cause cycle slips? Surely it would just give a sawtooth modulation on the PLL control voltage? And then how is the rate of slips influenced by the theoretical resolution of a range measurement which was not actually being performed at the time? Sorry, I guess I have completely misunderstood your explanation but hopefully you will see where I am going wrong and point me in the right direction. 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. Well the ranging system as I said was theoretically capable of better than cm resolution, it just wasn't working. For other spacecraft it did but why that would create cycle slips in the frequency measuring system is unclear to me. 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. Well it is still a measurement against a local clock so I would expect it would but let's drop that, if your calculation is purely a time acceleration I need to study Anderson's phenomenological time models before commenting. 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. OK, it is really the Pioneer effect I am focussing on so since I have been studying for some time so I'll snip your comments on red shift. 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. I have a few ideas on that myself, probably not practical though :-( George |
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