Agreed...
>This should vary with the date, just as the height of the
> sun varies with the date.
Here's where we disagree.
> Both start at the true latitude (measured in
> degrees from the horizon) at the Vernal Equinox,
Actually, they would be 90-degree complements of eachother. At the north
pole, Polaris is directly overhead and the sun is on the horizon at noon on
the equinox.
> then appear higher and
> higher in the sky until the Summer Solstice, when the sun is directly
> overhead at the Tropic of Cancer, then descend until the true latitude is
> reached on the Autumnal Equinox (height of the sun/Polaris above
> the horizon
> equals the number of degrees from the equator to your location), then
> descend until they reach their lowest height at the Winter Solstice, when
> the sun is directly overhead at the Tropic of Capricorn. It's all because
> the earth is tilted about 23 1/2 degrees on its axis.
Right, and I agree 100% with your analysis of the sun. But polaris is
colinear with the poles of the earth, and since the the poles don't wobble
(in our lifetimes anyways) due to the gyroscopic action of a large spinning
mass, polaris is always at the same relative spot, regardless of time of day
or time of year. That why its called the pole star.
Because the earth rotates, polaris HAS to be at the same 'angle' which
happens to be the same as your lattitude. If it moved, well, it wouldn't be
polaris. Think of it this way. At the north pole, if Polaris wasn't always
straight up, but rather moved it would, effectively, be SOUTH. :)
More practically, a few degrees off the north pole, if Polaris moved up and
down in coordination with the seasons (like the sun effectively does), it
would frequently not be north at all.
If the star DID move like you describe over the course of the year, we'd
pick a star that WAS indeed colinear with the poles, and call IT polaris :)