Maybe this will help. Or not.
I'm not sure it really clarifies things much as it uses the usual example of something (a space craft) that moves directly away and directly back to earth. Whereas, with the satelittes, once in orbit, their relative speed is 0, although their angular velocities are wildly differing.
So maybe the relativistic affects only apply a) as the satallite achieves orbit; b) as its signals return to earth.
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
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Well its way beyond me, but this experiment seems to explain it to me clock times going East vs. West So I'm guessing the GPS satellites are travelling either E or W, to remain at a constant point above the ground point, and as the plane experiment shows, the clocks will be different. Beyond that, I'm not going to think about it anymore, it's blowing my mind. :-)
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One mistake that I (and others I think) made, is in thinking that GPS satalittes are goestationary. They're actually in Medium Earth Orbit (20200k) and orbit the earth every 11h 58m. They're also run at an inclination of 55 degrees, so that adds another relative motion.
To my mind, the most amazing bit about relativity is not the math (which I have to take as read), nor the apparent paradoxes it produces; it's how anyone ever came up with the notion in the first place.
Conceptually, it's right up there with the blind French mathematician, Bernard Morin who proved (topologically), that you can turn a hollow sphere inside out without breaking or creasing the surface.
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
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