Dear Jack, An interesting puzzle...
> I have been half-heartedly attempting ... to figure > out where the sun rises and sets at the Solstices. I have derived the following formula (which I am sure must be very well known) for giving the azimuth of the sun at sunrise at an arbitrary latitude phi and solar declination dec... tan(az) = [sqrt(cos(phi+dec)*cos(phi-dec))] / sin(dec) If you plug in your latitude and set the value of dec to the declination at your chosen solstice (+/- 23.46 deg) you will get the azimuth at sunrise as a bearing measured clockwise round from true north. You will see that the formula doesn't need to know the hour-angle (time) of sunrise. If you want the azimuth at sunset, then use the negative square root. Note also that if either of phi+dec or phi-dec is outside the range -1 to +1 then there is no solution. This is because you are in the arctic or antarctic. > One should, I think, be able to read this directly > off the face of a sundial, given the time of > sunrise/sunset on the solstice. Hmmm. Well you could read up about seasonal markers on analemmatic sundials that this list discussed a few months ago. Alternatively, you could equip yourself with a sundial that showed azimuth as well as other values. > I found a web site with a java applet that will > perform that calculation, given your latitude, > longitude, time zone, etc. Hmmm. You don't need to know the time zone. > I found another that claimed that the answer is > simply (1/cosine * latitude) -- which did not > agree with the result from the java applet. > I think the applet is probably correct. I am not sure I can reverse-engineer what this formula is trying to say! Somewhere you need to plug in the declination at the solstices, if for no other reason than that this value changes over the centuries. > Is there a straightforward formula that gives > the azimuth of sunrise at the solstice as a > function of one's latitude? Yes, see above, but don't trust it! Using someone else's formula is rather like using someone else's toothbrush. Best wishes Frank King Cambridge, U.K. --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
