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    Re: What is the radius of the Prime Vertical?
    From: Frank Reed
    Date: 2019 Mar 14, 17:17 -0700

    Dave, you wrote:
    "The only thing I would add to the plane definition is that the plane also includes the centre of the Earth.  Including the observer and the observer's zenith in the definition does imply this, but mentioning the Earth's centre would give additional help when imagining it."

    Maybe, but it might get you in trouble rather quickly. The meridian works that way: ignoring deflection of the vertical (due to local mass anomalies), the plane of the meridian passes through the Earth's center, but the plane of the prime vertical does not --not quite. The zenith is determined by "apparent gravity" and that does not point directly toward the Earth's center. In mid-latitudes, it's inclined about 12 minutes of arc (12... if I remember correctly). So when you look "straight down", you're not looking at the center of the Earth. You're looking in a direction that is inclined slightly toward the equator. Of course, for a first-order approximation, you could ignore that. But 12' is a substantial difference in the world of celestial navigation.

    By the way, I like the celestial sphere. We "do" celestial navigation on the pure, perfect celestial sphere and then "drag it down" via the mundane local vertical field of the Earth's "impure" gravitational field.

    Frank Reed

       
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