> [EMAIL PROTECTED] (Philip P. Pappas, II) writes:
>
> > Thank you for your thoughtful comments. I make the statement that the "tim
e
> > method is the prefered method for setting a sundial if and only if the
> > sundial is properly designed, constructed and leveled (correcting for the
> > EOT and longitude of course).
>
> I would say that it is the preferred method *especially* if you
> suspect you have a poorly made dial. If you set it up by the time
> method, then at least you know it is accurate at one time for two days
> of the year. This is not guaranteed to, but is likely to reduce the
> errors on average.
>
> > > 4. This has just occurred to me and is probably not
> > >relevant but it has got my mind wondering. As we know, the earth is a
> > >flattened sphere. Gravity, from which we derive a vertical (and
> > >subsequent horizontal) reference comes from the centre of the earth's
> > >mass. This is presumably right in its centre, assuming that differences
> > >in local density do not move it by much. But as we move towards the
> > >flattened poles the angle to the centre of gravity will no longer be a
> > >true vertical. But even so, it is this centre of gravity which is the
> > >true reference point for the earth in its orbit around the sun.
> > > Then there is the centrifugal force due to its rotation. Will
> > >this effect a true vertical? At the equator - no, but imagine a point
> > >at 45 degrees latitude, where the centrifugal force must have some
> > >effect on any plumb line/spirit level. I guess that all of these
> > >effects are so tiny as to be irrelevant, but I would like to know how
> > >much they modify the results.
>
> These effects are one and the same. The Earth is flattened at the
> poles *because* centrifugal force pulls it out around the equator. At
> the Equator and at the poles the vertical passes through the center of
> the Earth, inbetween it doesn't, but that doesn't affect the accuracy
> of a properly designed dial.
>
> Just for fun, the radius of the Earth is 6,378 km and the difference
> between the the equatorial and the polar semiaxis is 21.4 km. This
> makes the maximum discrepancy in the angle about (2*21.4/6378) = 0.4
> degree.
>
> Art Carlson
I happened across a discussion of this just today in the 1999
Astronomical Almanac (page K 13).
Astronomical Coordinates
Many astrometric observations that are used in the
determination of the terrestrial coordinates of the point of
observation use the local vertical, which defines the zenith,
as a principal reference axis; the coordinates so obtained are
called "astrometrical coordinates." The local vertical is in
the direction of the vector sum of the acceleration due to the
gravitational field of the Earth and of the apparent
acceleration doe to the rotation of the Earth on its axis.
The vertical is normal to the equipotential (or level) surface
at the point, but is inclined to the normal to the geodetic
reference spheroid; the angle of inclination is known as the
"deflection of the vertical."
The astronomical coordinates of an observatory may differ
significantly (e.g. by as much as 1') from its geodetic
coordinates, which are required for the determination of the
geocentric coordinates of the observatory for use in
computing, for example, parallax corrections for solar system
observations. The size and direction of the deflection may be
estimated by studying the gravity field in the region
concerned. The deflection may affect both the latitude and
longitude, and hence local time. Astronomical coordinates
also vary with time because they are affected by polar motion.
Although this may be a significant deviation for an astronomical
observatory, I think for a sundial we may ignore the one minute
deflection.
Jim
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| Jim Cobb | 540 Arapeen Dr. #100 | [EMAIL PROTECTED] |
| Parametric | Salt Lake City, UT | (801)-588-4632 |
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It is proof of a base and low mind for one to wish to think with the
masses or majority, merely because the majority is the majority.
Truth does not change because it is, or is not, believed by a majority
of the people. -- Giordano Bruno
