Dan-George Uza <cerculdest...@gmail.com> wrote:
> While I am familiar to the stereographic projection used for the climates
> of astrolabes, I have no idea how to go about on creating an oblique
> azimuthal for generating the horizon line in a planisfere such as
> Chandler's. Polar equal azimuthal for the starmap seems fairly easy to do.
I happen to collect planispheres from around the world, and have
studied the subtle differences among them. David Chandler's unique
innovation is his use of a second projection to show the horizon-
hugging swath of sky opposite the celestial pole with much less
distortion.
However, Chandler's representation of the horizon on all his products
is technically flawed -- yet close enough to a truthful representation
so as not to impair usage: the subtle flaw being that the horizon line
exhibits a "corner" on both the east and west sides. A faithful
depiction would have a smooth horizon all around.
I'm certain that Chandler is aware of this inaccuracy; it may have
lessened the tooling cost to create a punch for a cardboard or plastic
horizon mask. Nevertheless, most other commercial planispheres
correctly feature a smooth horizon.
The distance (d, in degrees) from the celestial pole (the "pivot") to
the horizon on an accurate planisphere, in terms of the hour angle and
local latitude, should be as follows:
d = 90 + arctangent[ cosine HA / tangent Lat ]
If you are trying to replicate the horizon on the back side side of
Chandler's planispheres (that is, the horizon for the swath of sky opposite
the celestial pole), just change the plus sign in the above formula to
a negative sign.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Mark Gingrich gri...@rahul.net San Leandro, California
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