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Derivation of the formula for longitude of ascending node for a satellite

I've been looking into the document IS-GPS-200H to understand how to calculate satellite location in the ECEF coordinate. I am having problem understanding the formula to derive $\Omega$, the ...
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Sensitivity of calculated orbital elements to observational errors

These days, we have some very precise ways of making measurements, but I'm sure it wasn't so in Kepler's day. So I am wondering how astronomers of that time could make such accurate determinations of ...
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Are ascending node of sun, the point of intersection of prime meridian and equator and center of earth all collinear?

I did a bit of googling but couldn't find the exact answer, so are the following 3 points collinear or not ? 1_center of earth 2_ascending(or descending) node of sun 3_point of intersection of ...