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I don't understand what you think is nonsense about this claim. Can you elaborate?

The timing numbers I quoted are purely based on the orbital motion of a (hypothetical) satellite, and have nothing to do with radio signals. Kepler's third law states that a body's orbital period varies in proportion to the 1.5th power of its semi-major axis. A 1cm altitude difference for a satellite in LEO corresponds to a change of about 1.5 parts per billion, which translates to a 2.2 ppb change in orbital period. As I said, this amounts to a cumulative difference of a couple hundred microseconds per day.

And it's actually much easier to precisely measure frequency differences than amplitude differences, if you have sufficiently accurate clocks. If you have a 150.000000MHz reference signal and a 150.000001MHz doppler-shifted signal, you can simply multiply them together to get a 1Hz beat frequency. Using this technique, you can measure phase differences that are considerably less than a single cycle of the original signal.

A major limiting factor, of course, is the stability and precision of your reference clocks. Apparently, the Jason-2 satellite that (until recently) was responsible for a lot of these measurements had a high-precision quartz oscillator that was stable to roughly one part per trillion: https://www.ncbi.nlm.nih.gov/pubmed/30004875

Measuring the absolute position and velocity of a satellite is comparatively a lot more difficult. But with sufficiently precise Doppler relative-velocity measurements from multiple points, you can solve for both the orbital parameters and the slowly-varying perturbations with a high degree of accuracy.

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