Patrick Powers wrote ...
The basic formula is actually f=(s^2)/(L), where f is
the focal length, s is the radius of the (infinitely thin!)
hole and L is the wavelength of the light.
I would express this a bit differently, since a pinhole does not form an
image in the sense that a lens
Dear John,
Let me try it this way. Take the Earth's orbit as it is and change the tilt
from 23 degrees to 10 degrees, but still pointing in the same direction.
Does this change affect where the Earth is at any particular moment? No.
Does this change affect the positions on the orbit that
John Shepherd wrote:
Now back to the original question: Why is the difference between the
time between the Vernal equinox and the Summer Solstice different
from the Summer Solstice and the Autumnal Equinox?
This effect is approximately due to the tilt of the
John Shepherd wrote:
1. The equation of time gives the difference between the sun time and
standard time. Your difference is cumulative or integral of the daily
difference. The orbital effect has a maximum difference of about 8
minutes (this does not include the inclination effect). Averaging
Since a caustic is a very different animal from an image, is there any
chance of getting around the 2 minute limit on sundial accuracy due to the
sun's angular diameter? Does the caustic of an extended object form a line,
or is it also smeared out? (I suspect there's no free lunch here, but I
Dear Bill, dear John,
I realize that a shadow smeared over 2 minutes can be read to a fraction of
that period (especially if it is symmetircal, as in John's dials), and that
using images can give you a sundial with extreme accuracy. (What is the
limit? Except with an azimuthal dial, I expect
You likely have a sheet of glass already clamped in place nearby -- the
window. Couldn't you calculate a vertical dial for the right orientation,
print it on a transparency, tape the transparancy to the window glass, and
mark out the lines with a laser pointer or perhaps with a projector that
Mystery solved. There are two different ways of carrying out the fold in
the first part of your step F. Of course, I first did the one that doesn't
work.
--Art
-Ursprungliche Nachricht-
...
Actually, I wasn't able to follow your instructions, Edley. I get line 6
to be parallel to
Neat stuff.
You can have it a bit easier, though, even if not quite so general. Take a
rectangular piece of paper and lay it in front of you with one the the short
sides near you. Fold it in half from left to right (the long way) and
unfold it again. Now bring the lower left corner onto the
Fernando wrote:
Without intending to be so meticulous as we think Germans are,
I'd like to do something similar (but much, much simpler), like
observing if seeds sowed in the new moon do any better than
seeds sowed in the waning moon, etc.
I'm afraid you will
The
classical experiment using a mirror to detect minute rotations is not by
Michelson and Morley, who used an interferometer, but by Cavendish, who measured
the universal gravitaional constant in the lab. But the technique has been
used often.
--Art
Carlson
-Ursprüngliche
Dear fellow dialists,
I am forwarding this inquiry I received privatly from Yaaqov Loewinger. It
seems right up our alley.
Regards,
Art Carlson
-Ursprüngliche Nachricht-
From [EMAIL PROTECTED] Fri Mar 2 10:21 MET 2001
Date: Fri, 02 Mar 2001 10:33:16 +0200
From: Y. Loewinger [EMAIL
Concerning Bill Gottesman's proposal of a method to measure the solar
diameter:
Well, it's basically a very good idea, but there are a number of traps
to watch for. First, the slits need to be parallel. They also need
to be aligned closely to North-South (or rather, perpendicular to the
sun's
Mac Oglesby [EMAIL PROTECTED] writes:
It does leave one surprised that apertures are quite commonly
installed at an angle to the plane receiving the shadow.
Is this irrational or are they just optimizing to some other feature?
I mean, what's really so great about circular spots? What you
[EMAIL PROTECTED] writes:
Oy vey! Maybe this will restart the Shadow Sharpener thread going
again! Sounds like quite a project-good luck. I would like to
suggest that if you use a pin-hole, that the aperture be parallel to
the dial face. This may seem obvious, but it wasn't obvious to me
Daniel Roth [EMAIL PROTECTED] writes:
This message is sent for two reasons: 1st to remind how
subscribing and unsubscribing works and 2nd to bring into
discussion again the allowed length of a message including
attachments.
...
The length of a message is limited to 25 kB. Many subscribers
Chris Lusby Taylor [EMAIL PROTECTED] writes:
Frans W. MAES wrote:
I know one more case of
an interesting bifilar dial. Using a pole style and a specially shaped
curve in the equatorial plane, one may obtain a polar dial with
straight, parallel E-W date lines, perpendicular to the hour
Dave Bell [EMAIL PROTECTED] writes:
I'd call it a fairly expensive joke!
Note that a real dial should, roughly speaking, have the hours from 0600
to 1800 in a semicircle, running from East through North to West (in the
northern hemisphere). This is a clock face, with only room for 12 hours
Richard Mallett [EMAIL PROTECTED] writes:
As for determining the length of the tropical year ... with a
gnomon between successive solar solstices, I don't believe this is a good
method. One can determine the exact date/time of an equinox much more
accurately than that of a solstice
... A photo of a dial similar to the one made for Patrick Moore can
be seen on the internet at
http://www.lindisun.demon.co.uk/smallest.htm
I have a question for Tony Moss about the dial pictured. Unless there
is another scale on the back we can't see or the dial plate can be
turned
Gordon Uber [EMAIL PROTECTED] writes:
The length of the tropical year was determined with a gnomen between
successive solar solstices. The length of the sidereal year was determined
from successive heliacal risings.
From Time in History by G. J. Whitrow.
I have long wondered how to
Allan Pratt [EMAIL PROTECTED] writes:
According to a source I read, Hipparchus, a 2nd C BC astronomer
calculated the length of the year to within six minutes of accuracy.
Considering that at best he had a sundial and a water clock, how did he
do this?
I hope a historian will answer this,
SÈrgio Garcia Doret [EMAIL PROTECTED] writes:
1 - Assume the hours equals exactly 1/24th of the earth revolution time and
suppose a disguster lover choose to retire into a cave, where daylight is
entirelly shut off for a period of six months to the minute. ...
What adjustment does his watch
Patrick Kessler [EMAIL PROTECTED] writes:
Can anyone recommend an essay on steriographic projection? In particular I
am searching for a proof that circles on the sphere are mapped onto the
equatorial plane as circles.
http://www.geom.umn.edu/docs/doyle/mpls/handouts/node33.html
outline[s]
I wrote:
Nevertheless, I have a feeling that it may not be possible to improve
on a simple pinhole.
Let me reconsider that.
Consider an aperture a distance L from a surface, so that the image of
the sun through an infinitesimal pinhole would have the diameter D =
L*(0.5 degree).
With a
It is easy to read a sundial with an accuracy a bit better than the
solar diameter, even if the shadow is from a simple edge. The worthy
goal of a shadow sharpener is to significantly improve on that
accuracy. Since we still want to make the reading with a human eye,
the best system will be
One of the things that got me going on sundials was an article in the
magazine of the German Alpine Club on telling directions from the
moon. I found the procedure impossibly complicated and spent much
time trying to understand celestial mechanics in order to think of
alternatives. At long
Willy Leenders [EMAIL PROTECTED] writes:
The equation of time has two causes. The first is that the orbit of
the earth around the sun is an ellipse and not a circle. The second
is that the plane of the earth's equator is inclined tot the plane
of the earth's orbit. Please can anyone explain
[EMAIL PROTECTED] (John Carmichael) writes:
It's an interesting thought to use the moon's shadow at sunrise and sunset
on the equinox to locate your east-west points. Although this can be done
with the sun, you would have errors using the moon, unless there is an
eclipse on the equinox
Looking up Foucault's pendulum experiment in Meyers Grosses
Taschenlexicon, I read the claim that Vincenzo Viviani in 1661 was the
first to do the experiment, 189 years before Foucault! Browsing
through the Web for more details, I was only able to find two further
references: In
Fernando Cabral [EMAIL PROTECTED] writes:
I've heard the French Assembly has approved
a Resolution 495 which determines (so I heard)
that every public organization in France has to replace
Microsoft Windows by Linux.
Even if it's not true it's a great rumor, so I have been working to
spread
Daniel Lee Wenger [EMAIL PROTECTED] writes:
The reading of standard time via a sundial may be accomplisted by
mearly reading the declination of the sun and using an analemma,
determining standard time. At no point is the current date needed to
do this.
Way, way back I explained why I was
John Davis [EMAIL PROTECTED] writes:
I have a question/challenge to all you sundial designers: what is the most
accurate design for a Standard Time dial?
...
As a starter, the Singleton dial recently discussed here would seem to be
a reasonable candidate. It's main limitation, common to
fer j. de vries [EMAIL PROTECTED] writes:
Back to the bifilar dial : A bifilar dial can be constructed in such
a way that the hourlines ( for local suntime ) are equi-angular
spaced. Than it is also possible to correct for EoT and/or
longitude by rotating the hourscale. So we have at least
[EMAIL PROTECTED] (John Carmichael) writes:
... Why not follow John Singleton's notion (p. 51, BSS Journal
for Feb 2000) and use your normal taut wire pole style?
Have I missed something in the discussion?
Maybe we all have. I think John Singleton's azimuthal will not work (except
at
John Carmichael listed the pros and cons of azimuthal dials and
concluded that it is NOT an appropriate design for me to build.
Of his pro arguments:
1. It looks different, original and pretty (especially if you like the
Batman logo!)
2. It can be made to tell Standard Time
3. It requires a
Gordon Uber [EMAIL PROTECTED] writes:
Let's face it: The Babylonians got it right when they developed the base-60
system. It was applied to the sixth of a circle (one sixtieth of this
being a degree) and the hour, of which we still use the first and second
minutes. Third minutes
Peter Tandy [EMAIL PROTECTED] writes:
... Of course, for some specialised work,
metric measurements are no better and no worse; atronomers for instance do
better with the numbers they need to measure huge distances, when in a
metric form, and physicists with the numbers they need to measure
Andrew James [EMAIL PROTECTED] writes:
My idea is this: is it possible to combine the two points made? Arrange,
say, two sets each of four posts with three 0.4 mm gaps between, one set
having slightly wider posts but with the same gap, so as to make three light
rays the outer two of which
I just wrote:
...You will find that you can make a beam anywhere within a few tens
of a degree. (To be precise, 0.5 deg at sunrise and sunset, closer
to 0.3 deg near noon.)
I got that backwards. The sun subtends a larger azimuth when it is
higher in the sky, so the beam can be formed to
Arthur Carlson [EMAIL PROTECTED] writes:
[EMAIL PROTECTED] (John Carmichael) writes:
Let's say ...
... Will this technique produce the same shape hour lines at any
time of the year?
Yes. The hour lines will always have the same shape. This is even
true if the gnomon
[EMAIL PROTECTED] (John Carmichael) writes:
Let's say you want to build a large sundial using the ground as the dial
face. The ground is somewhat irregular and not quite horizontal. You
decide to draw the hour lines, not by calculation, but by using the
technique of building the gnomon
[EMAIL PROTECTED] (John Carmichael) writes:
Thanks for taking the time to explain the Dali dial to us gnomonistically
challenged dialists. I think I'm beginning to understand it, but will have
to think about it some more. What threw me off was that I was thinking that
a Dali dial would be
[EMAIL PROTECTED] (John Carmichael) writes:
I'm trying to understand your letter. Your design sounds very intrigueing.
In fact, I've often thought of carving a map of the state of Arizona onto
the dial face, with Tucson at the center of the dial. All the hour lines
would radiate out from
A normal sundial has the gnomon coaxial with the Earth. This is
done to keep the errors with respect to clock time to a minimum during
the course of the year. If we have the ambition to make our sundial
read clock time to better than +/- 15 minutes, then we have to correct
for the Equation of
I can think of three ways to incorporate the Equation of Time into a
twisted band dial:
(1) A correction can be made in the hardware by simply turning the
band around its axis. Since it is hung up on a polar support, this is
easier to accomplish than with some other designs like horizontal
Jim_Cobb [EMAIL PROTECTED] writes:
I've thought of another tip for spotting worthless horizontal sundials
(such as is sold in garden shops, etc)--if the shadow of the gnomon
crosses the hour lines it's no good. This test requires only
horizontal positioning, not polar alignment, and a lot
Tony Moss wrote:
In my impecunious searches of WWII 'surplus' stores back in the
1950s I came across a Portable Heliograph Set' in a pouch. It
was simply a mirror about four inches across with a sighting hole
in the middle. A length of cord attached it to a short rod with
a bead on top.
Bob Haselby and Tony Moss dialoged:
This sounds like a signal mirror ... It uses double internal
reflection in the hole to give a virtual image of the sun
Any chance of a diagram or somesuch to show how this works Bob?
It could work like this: Set up two sheets of glass and a mirror so they
Any rule for calculating the celebration of Easter depends on whether you
are interested in the Western or Orthodox holiday. Furthermore, any
calculations for the future will become wrong if the rules are changed. See,
for example,
http://www.smart.net/~mmontes/pr.wcc.19970324.html
--Art
For the benefit of Tony Moss, a search on
http://bible.gospelcom.net/cgi-bin/bible in KJV for every thing
beautiful yielded:
He hath made every thing beautiful in his time: also he hath set the world
in their heart, so that no man can find out the work that God maketh from
the beginning to the
Bill Walton wrote:
To get the desired accuracy the pin-holes' themselves must be very
accurately aligned (not true if the free pin-hole technique is used and
the hole moved back and forth until the shadow of the gnomon is centered,
and on the hour mark, at the same time)
They would not have
Roger Bailey wrote:
I tried your Shadow Sharpener test today and was amazed at the result.
Me, too! It was easy, just using the shadows falling on my desk. My pinhole
was made by sticking a paper clip through a Post-It, which I stuck to the
edge of a clip board on my window sill. The gnomon
John Carmichael wrote:
The design which worked the best was a 1/8 inch spherical bead, suspended
by
thin brass crosswires, in the exact center of a 1/4 inch round hole. (The
style was about 24 inches from the analemma).
A very curious thing happens with this type of style. The bead alone,
John Carmichael wrote:
Does this mean that there is no upper limit for the size of a
sundial? *
Seems obvious to me. The limitation in most configurations is the fuzziness
of the shadow, which also implies that size doesn't improve precision.
If this is true, then one second
Speaking of barleycorns reminds me that one can have a lot of fun with
units. My favorite combination has components
atmosphere = 101,325 newton/m^2
yard = 0.9144 m
barn = 1 x 10^(-28) m^2
Combining these we get the
barn yard atmosphere = 9.265158 x
Martin [EMAIL PROTECTED] wrote:
Regarding Franks mention of simple folks cry of give us back our 11
days Well I would be pretty riled too if the rent was due 11 days
early as I'm sure evil land lords would have used the change in the
calender as a good excuse to ring money from
John Carmichael writes:
Hey, did anyone see the CNN story last night about the watch company
,Swatch that is now selling timepieces which tell Internet Time? I
can't remember exactly, but they said one minute of normal time=about 1 1/2
minutes Internet Time, and that the idea behind it is to
Jim_Cobb [EMAIL PROTECTED] writes:
I noticed that this time disagrees with the time given in the almanac,
so I thought I should provide more information so as not to impugn the
reputation of the excellent xephem program. The 16:08:17 UT time is
what xephem computes as the time of the full
[EMAIL PROTECTED] (Mr. D. Hunt) writes:
In relation to the recent question/replies, regarding detecting/correcting
'errors' in the setting of sundials - is there any feasible way of varying
the layout of an Analemmatic dial, to cope with it being on a GRADIENT ?
My own thinking is that
John Carmichael writes:
We could make this question even more complimented if we consider the speed
of light. When we see the sun's center on the horizon we are seeing light
that left the sun about 8 minutes earlier. The sun really has already set.
(of course this has no practical effect
[EMAIL PROTECTED] (Philip P. Pappas, II) writes:
Thank you for your thoughtful comments. I make the statement that the time
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
An analemmic dial would be insensitive to refraction effects, wouldn't
it?
Art Carlson
Dear Bob,
Fun problem.
1. If I were setting the thing up, I would turn the existing disk so
that the local longitude pointed up, not that of Greenwich. That way
the observer can see at a glance where in the world he is, as well
as the approximate time anyplace else in the world. There is a
Roger Bailey [EMAIL PROTECTED] writes:
I was experimenting with the shareware program Astronomy Lab. One
calculation that this program plots is the Moon Angular Speed in degrees
per day. This is the lunar equation of time we have been looking for. In
minutes rather than degrees, the
Fernando Cabral [EMAIL PROTECTED] writes:
Now I am planning to build a house for a small farm I have. I've
been thinking on how to take the best advantage of the solar
power. This includes where to have a garder with a nice sundial and
where to place the solar panels for water heating as
Dear John,
Your explanations sound like about the right level for a users'
manual. Maybe because I'm a scientist, I think it is important to at
least mention the major sources of error. In my opinion, the biggest
problem is determining the exact phase of the moon by looking at it.
(Of course,
John Carmichael writes:
I have a section which tells how to tell time by using moonlight and a
sundial. I provide a table of corrections from which the time can be
estimated if one knows the age (the phase) of the moon.
One question though: Is it nessary to correct moontime with the
Paul Murphy [EMAIL PROTECTED] writes:
September 11-24 , 1752
Unfortunately, Warren, even this depends where you were at that time! Had
you been in a place where the Gregorian Calendar had been accepted in 1582,
quite a lot might have happened. On the other hand had you been in Russia,
you
Tad Dunne [EMAIL PROTECTED] writes:
I'm working on an Excel spreadsheet and need a formula or function that
will give,
for an input A and B, the sum of all the powers of A for integers from
1 to B.
Example: 1.05 + 1.05 squared + 1.05 cubed ...
S = A + A^2 + A^3 + ... + A^(B-1) + A^B
Tom Mchugh [EMAIL PROTECTED] writes:
One thing which doesn't seem to have surfaced in the discussion
yet, is the imponderable effect of plate tectonics upon the accuracy
of any type of sundial over a period of 10,000 years, which effect
would cause both a latitude and longitude change in the
fer j. de vries [EMAIL PROTECTED] writes:
On this list many is said about the equation of time, the precession and
so on in relation to the milennium clock.
And in the quoted mail is said the clock should be accurate to the
minute in 10,000 years.
Is this possible at all?
Think of the
Luke Coletti [EMAIL PROTECTED] writes:
Arthur,
Please investigate for us
Touche. I think some of these questions will move to the back
burner. To significantly improve my understanding of celestial
mechanics, I need to do some systematic reading.
This thread started with the
Luke Coletti [EMAIL PROTECTED] writes:
Below are some data that may help you, the calculation date is
Jan 1 Noon UT, EoT values are in the form TA-TM. The discussion to date
has been more about the variation of our orbit and Earth's alignment
within, however all these events need to
Luke Coletti [EMAIL PROTECTED] writes:
You still appear to be asserting that in calculating the
Longitude of Perihelion (over a 10,000 year period), only Precession
need be considered and the shifting of Perihelion due to
perturbation and other smaller combined effects can be
I wrote:
... I think
the processes which change the eccentricity and obliquity of the
Earth's orbit work on a much slower time scale than the precession of
the equinoxes, so that we can still use the same Equation of Time
13,000 years from now. Does anybody know for sure about this?
Sonderegger [EMAIL PROTECTED] writes:
I think in the northern hemisphere summer is always in July, because the
beginning of spring is here always when then sun crosses declination of 0
degree from south to north (= crossing the ecliptic). The places of the
stars on then sky will change in
Thanks for the graph, Luke. If I take +/- 20 sec as the accuracy of a
very good sundial, then I see that I have to start correcting for
refraction around 10 deg altitude, i.e., the first hour after sunrise
and the last hour before sunset. Since Pete Swanstrom's earliest
observation is at 7:10
Anton Reynecke [EMAIL PROTECTED] writes:
When I was a young boy it amazed me that it was actually possible, but
now realise it is just a form of sundial.
It is situated in Pretoria and can only be seen in action less than an
hour every year (annum), and is is a special feature of the
[EMAIL PROTECTED] writes:
Could someone help me solve for declination of the sun or latitude
from the equation for altitude:
sin(Alt)=sin(dec)*sin(lat) + cos(dec)*cos(lat)*cos(local hour angle)
I would like to know how this is solved as much as just knowing the
answer.
You want to
language interface phase you.
Art
--
To study, to finish, to publish. -- Benjamin Franklin
Dr. Arthur Carlson
Max Planck Institute for Plasma Physics
Garching, Germany
[EMAIL PROTECTED]
http://www.rzg.mpg.de/~awc/home.html
, or 1/6 part of anything. I'm sure 5
fingers was a bad choice since it led to this muddle of the bases 8,
10 and 12.
Art
--
To study, to finish, to publish. -- Benjamin Franklin
Dr. Arthur Carlson
Max Planck Institute for Plasma Physics
Garching, Germany
[EMAIL PROTECTED]
http://www.rzg.mpg.de
wants to get married a day farther into the summer. How about getting
married in a valley, and counting the time the sun rises/sets over the
mountain tops?
Art
--
To study, to finish, to publish. -- Benjamin Franklin
Dr. Arthur Carlson
Max Planck Institute for Plasma Physics
Garching, Germany
[EMAIL
you both are profiting equally from it. In this spirit, I would
suggest that you plight your troth near the equinox, but don't
calculate the time too pedanticly.
With best wishes,
Art Carlson
--
To study, to finish, to publish. -- Benjamin Franklin
Dr. Arthur Carlson
Max Planck Institute
the year will change in 4 digits. Pure
numerology. Like watching your odometer turn over. And that happens
when 1999 changes to 2000.
Hope to see you then,
Art
--
To study, to finish, to publish. -- Benjamin Franklin
Dr. Arthur Carlson
Max Planck Institute for Plasma Physics
Garching, Germany
85 matches
Mail list logo
