Re: Winter Solstice at Newgrange, Ireland
Dear Warren, Many thanks for supplying Bill Gottesman's comments which I very much take to heart. Getting good sightings at sunrise and sunset in real life is seriously challenging and even when you are in luck, the shadows are weak and the effect of refraction is at its greatest and you have to worry about temperature, pressure and height above sea-level. Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Winter Solstice at Newgrange, Ireland
Dear Geoff, Yes, you are absolutely right. Silly me for not spotting a trivial simplification! It is, indeed, much neater to write: cos(az)=sin(dec)/cos(lat) This also readily shows that reversing the sign of the declination results in 180 degrees being added to (or subtracted from) the azimuth. It is slightly less obvious that dec+lat and dec-lat must be in the range -90 to +90 though. Also... ... its comforting to realise that the sun has been rising a little bit closer to the north for the last couple of mornings. There is a delightful paradox in this. What you say is certainly true but, nevertheless, the (clock) time of sunrise is still getting later, and the latest sunrise this year is not for another week. You will have to survive Christmas before you can start feeling comfortable!! By way of compensation, the evenings have been drawing out for the past 10 days. Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Dialling Puzzle for Christmas Eve
Dear All, The BBC has been trailing their broadcast of the Christmas Eve Carol Service from King's College here in Cambridge with this introduction... At 3 o'clock, just as the shadows begin to lengthen,... My first thought was that shadows begin to lengthen immediately after 12 noon but, on thinking about it, I can see several ways to arrange for shadows to begin lengthening at exactly 3 o'clock. Would anyone else like to make some suggestions? As it happens, with just over an hour to go, it is 100% overcast here so this puzzle is rather academic! Happy Christmas Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Dialling Puzzle for Christmas Eve
Frank, The west-declining vertical dial on the side of my house has a gnomon shadow which shortens until about 1440hrs and then lengthens. A hasty (and therefore unreliable) calculation suggests that a vertical dial declining about 38 degs west of south in the latitude of Cambridge might experience its shortest shadow around 1500hrs. Now it's nearly time to switch on the radio for the carol service. Best wishes, Geoff Thurston 51D18N 00D54W -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Frank King Sent: 24 December 2007 13:43 To: Sundial List Subject: Dialling Puzzle for Christmas Eve Dear All, The BBC has been trailing their broadcast of the Christmas Eve Carol Service from King's College here in Cambridge with this introduction... At 3 o'clock, just as the shadows begin to lengthen,... My first thought was that shadows begin to lengthen immediately after 12 noon but, on thinking about it, I can see several ways to arrange for shadows to begin lengthening at exactly 3 o'clock. Would anyone else like to make some suggestions? As it happens, with just over an hour to go, it is 100% overcast here so this puzzle is rather academic! Happy Christmas Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Azimuth of Sunrise - Sunset
Thank you all for the answer(s) to this little problem and for the bread-crumb trail to try to retrace the derivation. My original question was sparked by wondering about the maximum deviation from east-west at the solstice(s) so I could display my erudition and bore people with comments like: The sun rises in the East and sets in the West, right? Well, not really. Actually What I had meant about reading the answer directly from the sundial, assuming that you already know the time of sunrise, is that if you were to lay the straight edge of a protractor between the root of the gnomon and the time of sunrise on the dial face, you could read the deviation from east-west where the six o'clock line intersects the protractor scale. Of course, if my sunrise time were taken from the daily newspaper, I would have to adjust for longitude. At my latitude (38.88 north) the formula tells me that on the solstice, sunrise/sunset deviates from east-west by 30.74 degrees, which looks like it agrees with the protractor method (allowing for the fact that I can't actually lay it on the dial without removing the gnomon). Jack At 08:28 AM 12/24/2007, Frank King wrote: Dear Geoff, Yes, you are absolutely right. Silly me for not spotting a trivial simplification! It is, indeed, much neater to write: cos(az)=sin(dec)/cos(lat) This also readily shows that reversing the sign of the declination results in 180 degrees being added to (or subtracted from) the azimuth. It is slightly less obvious that dec+lat and dec-lat must be in the range -90 to +90 though. Also... ... its comforting to realise that the sun has been rising a little bit closer to the north for the last couple of mornings. There is a delightful paradox in this. What you say is certainly true but, nevertheless, the (clock) time of sunrise is still getting later, and the latest sunrise this year is not for another week. You will have to survive Christmas before you can start feeling comfortable!! By way of compensation, the evenings have been drawing out for the past 10 days. Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Azimuth of Sunrise/Sunset
I have not been able to follow this thread in detail during the holiday turmoil, but it seems appropriate to note that my program, The Electric Astrolabe (astrolabes.org/electric.htm) is very good at showing this sort of thing both visually and numerically. You can even find the differences between now and 3100 BC. Merry Christmas, Jim James E. Morrison [EMAIL PROTECTED] Astrolabe web site at astrolabes.org --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Dialling Puzzle for Christmas Eve
Dear Geoff, Yes, I agree with your hasty calculation (having taken far longer than you to do it!)... A hasty ... calculation suggests that a vertical dial declining about 38 degs west of south in the latitude of Cambridge might experience its shortest shadow around 1500hrs. This was one of my thoughts: you arrange the wall's declination so that the sub-style and the 3 o'clock shadow coincide. Not allowing for the equation of time (small today) or the longitude offset of Cambridge (small every day) I make it just a little over 38 degrees too. The wall doesn't have to be vertical of course. Indeed, provided only that it catches the sun at 3 o'clock, you can use any irregular surface with arbitrary orientation and just drive a pin into it, carefully arranging the orientation of the pin so that its altitude and azimuth match those of the sun at 3 o'clock today. Now it's nearly time to switch on the radio for the carol service. As always, I enjoyed almost all of it! Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Azimuth of Sunrise - Sunset
Hi Jack, Frank and al, Your question What is the path of the sun at sunrise or set? is a good one. The answer given by Frank is simple and subtle. Actually it is a Smart question, posed by W. M. Smart in his Textbook on Spherical Trigonometry. Prof Smart leaves it as a question to be solved by students as a homework exercise, Question 2, Chapter 2 If Phi is the angle which a star makes at rising with the horizon, prove that Cos Phi = Sin Lat x Cos Dec. I enjoy sunrise and sunset. These are the only times of the day when you can almost get away with staring at the sun. I summarized the derivation and application of the sunrise equations in a presentation at the NASS conference in Hartford in 1999. Have a look at Sunset Phenomenon: The Use of Spherical Trigonometry to Determine when, where and how the sun rises and sets This is available at my website www.walkingshadow.info as a small, 200 kb pdf file, # 14 on the list of sundial publications. It is a relatively small (200 kb) pdf file as I deleted all the sunset photos.The spherical trigonometry is all there except for the Prof Smart's proof. I will leave that as a homework exercise for students. It remains a great question for the final exam. Regards, Roger Bailey - Original Message - From: Jack Aubert To: 'Sundial List' Sent: Monday, December 24, 2007 7:21 AM Subject: Azimuth of Sunrise - Sunset Thank you all for the answer(s) to this little problem and for the bread-crumb trail to try to retrace the derivation. My original question was sparked by wondering about the maximum deviation from east-west at the solstice(s) so I could display my erudition and bore people with comments like: The sun rises in the East and sets in the West, right? Well, not really. Actually What I had meant about reading the answer directly from the sundial, assuming that you already know the time of sunrise, is that if you were to lay the straight edge of a protractor between the root of the gnomon and the time of sunrise on the dial face, you could read the deviation from east-west where the six o'clock line intersects the protractor scale. Of course, if my sunrise time were taken from the daily newspaper, I would have to adjust for longitude. At my latitude (38.88 north) the formula tells me that on the solstice, sunrise/sunset deviates from east-west by 30.74 degrees, which looks like it agrees with the protractor method (allowing for the fact that I can't actually lay it on the dial without removing the gnomon). Jack At 08:28 AM 12/24/2007, Frank King wrote: Dear Geoff, Yes, you are absolutely right. Silly me for not spotting a trivial simplification! It is, indeed, much neater to write: cos(az)=sin(dec)/cos(lat) This also readily shows that reversing the sign of the declination results in 180 degrees being added to (or subtracted from) the azimuth. It is slightly less obvious that dec+lat and dec-lat must be in the range -90 to +90 though. Also... ... its comforting to realise that the sun has been rising a little bit closer to the north for the last couple of mornings. There is a delightful paradox in this. What you say is certainly true but, nevertheless, the (clock) time of sunrise is still getting later, and the latest sunrise this year is not for another week. You will have to survive Christmas before you can start feeling comfortable!! By way of compensation, the evenings have been drawing out for the past 10 days. Best wishes Frank -- --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Azimuth of Sunrise - Sunset
How about a single (composite) photo of the sun rising AND setting on the Winter Solstice? http://apod.nasa.gov/apod/ap071222.html Bob --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Azimuth of Sunrise - Sunset
Dear Jack, I enjoyed your the motivation... My original question was sparked by wondering about the maximum deviation from east-west at the solstice(s) so I could display my erudition and bore people with comments like: The sun rises in the East and sets in the West, right? Well, not really. Actually If you are happy to visit the Arctic or Antarctic you can experience sunrise anywhere from due north through east to due south and you don't have to make your visit coincide with the solstices either. For a latitude phi in the Arctic, the sun will rise due north when the declination is 90-phi and will rise due south when the declination is phi-90. At latitude 70N the declinations are +20 and -20. These assertions need a little interpretation because, for example, when the sun rises due north it hasn't properly set: it just dips down to the horizon and, because of refraction, you see the whole solar disc anyway. Your other point is certainly valid for a horizontal sundial (that's important). Reinterpreted what you say can be generalised... If the time of sunrise is (say) 7 o'clock then if you look along the 7 o'clock hour-line on the dial from the label end towards the root of the gnomon then you are looking in the direction of the sun at the moment of sunrise. There is nothing special about a 7am sunrise and there is nothing special about the solstices except that they are the extreme cases. Your example is correct... At my latitude (38.88 north) the formula tells me that on the solstice, sunrise/sunset deviates from east-west by 30.74 degrees, which looks like it agrees with the protractor method... You don't give the time of sunrise but it is about 7:22am and if you were to draw in the special time line for that time on your horizontal sundial you could look along it in the direction of the root of the gnomon and you would be looking in the direction of sunrise at the winter solstice. The explanation is simple. When the sun is on the horizon it is in the same plane as the (horizontal) dial and the direction of the shadow cast by the gnomon in the special circumstances of sunrise (or sunset) is independent of the gnomon's orientation. Accordingly, the direction of the shadow is the same as it would be if the gnomon were vertical and so, obviously, gives the azimuth of sunrise. If this sounds unlikely try this experiment: Place a white sheet of paper on a table and hold a light (a simple flashlight will do if the room is slightly darkened) at the exact same level as the table. You point the light so the upper half shines on the paper. This is the sun at sunrise. Then hold a pencil so that the pointed end sticks into the paper and wave the other end around in any direction you like. The direction of the shadow will always be directly away from the light whatever the orientation of the pencil. As soon as your light rises above the table top then the shadow direction WILL change if you wiggle the pencil. Hey, this is cheap (and educational) Christmas Entertainment that all the family can enjoy! Hmmm. I'd better go and wrap up some presents. Best wishes Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Ho Ho Ho!
Another year and the sun is still shinning. Merry Christmas and a Happy New Year to all. Steve Irick Yorktown Va USA--- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Azimuth of Sunrise - Sunset
Robert Terwilliger wrote: How about a single (composite) photo of the sun rising AND setting on the Winter Solstice? http://apod.nasa.gov/apod/ap071222.html Bob Beautiful!! Be sure to click through to the photographer's pages. Some great astronomical and travel photos. The pages of crepuscular landscapes has some really striking work, including this APOD and what appear to be some extra sunset series from the same site. Dave --- https://lists.uni-koeln.de/mailman/listinfo/sundial
