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    Re: Plumb-line horizon vs. geocentric horizon
    From: Frank Reed CT
    Date: 2005 Feb 9, 20:21 EST
    Jeff, you wrote:
    "Due to the oblateness of Earth, the plumb line differs from the actual center point of Earth by a navigationally significant amount, up to 12 minutes of arc.
    But this fact does not effect the practice of celestial navigation because the lat-lon grid itself and the Almanac's GP data are based on the plumb line."
    Right. 12'sin(2Lat). So at the equator or at the poles, a plumb-line points straight at the Earth's center.
    Something to consider: what would happen if the Earth were made of some perfectly rigid material? Let's suppose that it still rotates once every 24 hours, but since it's rigid, it's a perfect sphere, not driven oblate by the rotation. In this case, a plumb line would still be deflected away from the Earth's axis in the same way (same as on the real Earth), much the same way that a plumb-line hanging near the edge of a turning carousel would be deflected away from the central point by centrifugal "force". Without the physical oblateness, the deflection on the Earth would not be as great but it would still be present. The Earth's surface of constant gravitational potential, effectively the surface of the geoid, is determined by the gravitational pull of the mass distribution and ALSO the centrifugal acceleration from the Earth's rotation [technically, from the standpoint of Newtonian gravitation, these are fundamentally different, but from the standpoint of Einsteinian gravitation --general relativity, these are two sides of the same coin].
    But I wanted to emphasize the simple visual aspect of this (for fun). When you look "straight down", following visual clues and your inner-ear's best guess, you're not looking straight towards the Earth's center. You miss because the plumb line is tilted slightly away from the Earth's axis. To find that direction that heads straight to the Earth's center, place an object a quarter of an inch across on the floor. From a typical standing height, that object will be 12 minutes of arc in angular size. So when you look that far towards the north of the plumb-line, your line of sight passes through the Earth's center (assuming you're in mid-latitudes in the northern hemisphere). Another way of thinking about it: if you were to extend the plumb-line through the Earth, it would miss the exact center of the Earth by 12 nautical miles.
    42.0N 87.7W, or 41.4N 72.1W.
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