Hi David, The equation you quoted is correct. Cos t = Tan Dec / tan Lat. It is easier to calculate than it looks with a simple scientific calculator. As simple program or spreadsheet could easily add the add the equation of time and longitude to provide a table of clock times for each day of the year, or four year leap year cycle.
Not that this would help your group much as they seem to be making up their rules as they go along. I would think they would either use what was available at the time of Mohamed or go along with changes in like technologies as they became common. Why reject written information and accept clock time. It sounds like Galileo's dilemma, trying to prove the the solar centric model clocks with only naked eye observations. It is still a challenge. Regards, Roger Bailey Walking Shadow Designs N 48.6 W 123.4 <[EMAIL PROTECTED]>: > > First of all, my thanks to those people who took the time to reply to > my "cry for help" on this - and my apologies for a slight delay in > responding, but I had to 'clarify' a few things with the Muslim group. > > The following are (I think!) the criteria that they wish to fulfill: > > (1) They are not interested in the East/West DIRECTIONS, but in the > TIMES at which the sun is exactly at those directions - even if > it is obscured, or actually below their horizon at that time. > > (2) With regard to 'accuracy', they want the nearest minute (to be > confirmed by direct observation and/or comparison with clocks). > > (3) I had originally assumed that they would be more interested in > the 'apparent' (local sun) time, but they insist that it must > be their mean CLOCK time - which introduces added problems of > Longitude, Daylight-Saving, as well as the 'Equation of Time'. > > (4) They do not want some form of 'look-up chart', (especially if > it has been produced via a computer) - but instead prefer some > physical 'mechanism', which they can actually observe working. > (I get the impression that an accurate 'orrery' type of thing > would be their ideal, but doubt whether that can be produced). > > (5) This group of 'asylum seekers' do not know how these times had > been determined in the past (having lost contact with their > religious leaders) - or it could be that they are confused in > relation to their requirement, or are maybe even some form of > 'off-shoot sect' who want to start their own set of rules for > prayer observance times (I did not go into that any further)! > > > I spoke to a helpful man at "Armagh Planetarium" here in Northern > Ireland, who gave me the following 'formula' for times when the > sun is directly East and West (Hour-angle from South direction). > > cosine (Hour-angle) = cotangent (Latitude) x tangent (Declination). > > I am not a 'Maths' expert, but this looks reasonable. With a zero > Declination (at Equinoxes), the Hour-angle would be 90 degrees - so > the time will be 6 hours before/after noon, regardless of Latitude). > > Could anyone confirm if this formula is OK - but I assume that the > times also need 'corrected' for Longitude, plus Equation of Time? > > > Would there be any possibility of constructing a simple mechanical > device which could use that formula? Obviously, the Latitude will > be fixed - and, presumably, the sun's Declination could be varied > by means of some scale (like on Analemmatic or Capuchin sundials). > It will require correction for Longitude and Equation of Time, too. > > Carl Sabanski had kindly pointed me to his "Dialling Buddy" device, > which seems promising - but it would need to be made in a fairly > large size (in order to have daily and 'nearest minute' accuracy), > as well as having to deal with the points raised in item (3) above. > > As Carl had said, the time-keeping accuracy of its mechanical clock > system would also be a 'limiting factor' in using any such device. > > > At first sight, the suggestion from Tony Moss looked like it had > possibilities too - but although '24-hour' clocks are available, > the Hour-hand still goes round TWICE per day, and we need ONCE. > > I suppose some device could be made using a 1-rev-per-day motor, > though there would have to be a way to input the sun's varying > Declination - plus also allowing for the Equation of Time as well, > not forgetting adjustments for Daylight-Saving Time and Longitude. > > > To be honest, I rather wish that I had not become involved in this > project (more trouble than it is worth!) - but maybe some member > of this list will see it as a 'challenge', since (as confirmed by > Roger Bailey) this is an interesting and non-trivial requirement. > > Just to confirm, the direction of Mecca (as such) is not of any > specific interest to this group - only the East/West sun times, > but these must be established in their local mean time (which can > be confirmed by observing a shadow at the clock time indicated, in > order to give 'confidence' in the device when it is not sunny). > > > Once again, thanks for all your previous (and any future) comments, > but please do not waste a lot of time on this - as I have already > told the Muslim group that it will not be an easy task to fulfil > their criteria, especially if 'modern technology' is not allowed. > > > Sincerely, > > David Lawrence. > > > -- > - > -
