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Re: Plumb-line horizon vs. geocentric horizon
From: Frank Reed CT
Date: 2005 Feb 9, 20:21 EST
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.
-FER
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars
