Re: The Shadow of a Pole and Azimuth

Sorcerer wrote:

"W. Watson" <wolf_tracks@xxxxxxxxxxx> wrote in message news:0ZoMg.16827$Qf.3077@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| Suppose I take perfectly round pole about 2' long and 1/2" wide out onto a
| very smooth surface, and let it cast a shadow from the Sun onto the surface.
| Now I take out a perfectly straight metal ruler and lay it along the shadow
| of the pole, and draw a line along one edge. Suppose I do this when the Sun
| crosses the local meridian and about 2 hours later. Will the angular
| distance agree with the computed azmithual angle as computed accurately from
| an ephemeris?
|
| I suspect not because the dark (umbra) shadow is elongated and wider near
| the base of the pole, and narrows to the top of the shadow; thereby
| producing an incorrect azimuthal line. Even with one rod, I suspect the
| drawn line will be a few degrees off the true azimuth line. It may be
| possible that the line from each time is off by a dissimilar amount, so the
| difference is also incorrect. Perhaps my observation about the shadow is wrong.
|
| I've done this a few times, and get about a two degree difference when using
| the computed azimuth at, say, 2 pm or so. That is, one might expect the line
| at the meridian to be accurate on N-S, but when working back from the 2 pm
| measurement, the angle to the N-S is off by 2 degrees.
|
| Any comments?


What you've created is a sundial, and what you've discovered is
a combination of the sidereal day, you own latitude, the tilt of
the Earth and the eccentricity of the Earth's orbit.

Let's take those one at a time, but imagine they are extreme.
1) The sidereal day.
Imagine the Earth rotated on its own axis once a year, always
keeping the same face to the sun, just as the moon keeps the same
face toward the Earth. Your shadow would always be due south
or due north, no matter what time your clock said.
In reality a sidereal day can be measured by your method, but
with two poles instead of one of because stars don't make
much of a shadow. Pick a star you'll recognise again, then align
the two poles so that you can sight along them and form a
straight line. Note down the exact time when star and poles
are aligned. Now repeat the following night, again noting the time.
Do NOT move the poles. You will find there is roughly a 4
minute discrepancy, because 24 hours * 60 minutes = 1440,
and 1440/4 = 360 degrees and the Earth has a 365 day year.
In other words it rotates on its own axis 366 times a year,
but appears to lose a day by going around the sun.

2) Tilt and latitude.
If you were at the north pole on 21 June, the sun circles
the horizon, right? The further north you are, the longer
summer days are and the shorter winter days are. Take
an Alaskan cruise and see for yourself, but this is the
wrong time of year, we are fast approach equinox.

3) Eccentricity of the Earth's orbit.
Again let's exaggerate and imagine that we graze the
surface of the sun at perihelion and go out as far as
(say) Mars at aphelion, still taking a year for the orbit.
As worked out by Kepler, we travel much faster
going around the sun when close to it than we do
when we are furthest away.
http://home.cvc.org/science/kepler.htm
The earth doesn't speed up its rate of rotation, though, and
so when close to the sun the sun will be overhead for longer
than it will when further away, and this will not agree with
your wrist watch. In other words we'd be keeping the same
face toward the sun when closest to it.
You can see the same effect from lunations:
http://antwrp.gsfc.nasa.gov/apod/ap051113.html


The guys who built this were building a calendar/clock, doing
what you are doing.
http://witcombe.sbc.edu/earthmysteries/EMStonehenge.jpg
I can see from the shadows that the photograph was taken
in mid-afternoon, and on 21 July the sun rises over the heel
stone (bottom right), which of course is why they put it there
3,500 years ago. They needed big stones so that nobody
would move them and they needed them tall for better
accuracy. Remember those guys knew how to smelt copper
and tin to make bronze for axes and clothing clasps, they were
pretty smart. Your average Joe Sixpack today wouldn't have
a clue.

Androcles



Thanks for the information packed response. Yep, smart is right. There were some clever people way back in our history.

As I mentioned in my response above to another poster, my eventual interest in doing this is to establish true N-S quickly and easily. I think this is working pretty well. I plan to set up markers (direction arrows) at places like our science museum entrance and fields where we sometimes have sky shows. It just helps our astro participants line up their scopes reasonably without having to use some other method. Of course, the bonus to this is that it's done during the day, which is a big help if you're driving stakes in the ground or errecting some marker.


Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
(121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
Obz Site: 39° 15' 7" N, 121° 2' 32" W, 2700 feet
--

"I have made a ceaseless effort not to ridicule, not to bewail,
not to scorn human actions, but to understand them."
-—Baruch Spinoza

Web Page: <home.earthlink.net/~mtnviews>
.

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