WHAT'S MY QIBLA? -------------- John Pazmino NYSkies Astronomy Inc firstname.lastname@example.org 2007 December 8
Introduction ---------- The question comes to me from time to time, 'what is the qibla for New York?'. From somewhere I recall it is 59 degrees east of north. I knew also that the qibla is the direction toward Mecca along a great circle from the City and that Muslims face this direction for praying. In July 2007 the question came again, with a twist. 'How is the qibla determined?' Knowing that it involves the 'straight line' from New York to Mecca, I figured it would be a simple task for spherical trigonometry and some formulae exercised on a calculette. To a large degree this is true. But in poking around, I found there is more to the qibla question than that.
Spelling ------ Before going further, I must note that in this here article the spelling of various Arabic words is, uh, scattered. Arabic has sounds and accents that do not map well into the Latin alphabet in a consistent manner. The effect is much like the attempts of European settlers to write down words from the native Americans. More than that, among Arabs writing in the Latin alphabet, like on websites or magazines, the spelling of a given word can differ widely. The situation is like, but more severe than, the variant spelling of the Arabic names of stars. For the word 'qibla' I found 'qibllah', 'quiblla', 'kiblih', 'quabbla', to recall only a few of the ways this word turned up in the litterature I examined. Hence than that, because I have no expertise in Arabic as a language and I took material from many separate sources, the speeling of Arabic words here is not even within a particular scheme of translitteration. Please expect the spellings to be at variance with what you may be used to elsewhere. Perhaps some reader versed in reanslitterated Arabic can furnish a consistent suite of spellings for the next revision of this article?
What is qibla? ------------ From history and culture, Muslims kneel and face Mecca when they pray. Mecca, in present-day Saudi Arabia, is the birthplace of Islam. More specificly, they face the Kaabah, or central ark, in the courtyard of the main mosque of Mecca. This ark, of wood and stone, rebuilt over the centuries, is today roughly a cube about 12 meters on a side. From what I read about the Kaabah, the interior is a n emtpy chamber with no artificial lighting and decorated with Arabic scirptures. Only the keepers of the ark are allowed inside. On the outer wall at eye level is a silver display window framing a dark stone. This is likely a meteorite that was found in or near Mecca in the preIslamic era. While it is not itself a sanctified object, it enjoys a special honor for Muslims. When Islam was still young and its followers lived in or near Mecca, it was easy to face the Kaabah or, at least, the mosque itself from anywhere within its sight. The practice showed the unity of Muslims and not a glorification of the Kaabah or the meteorite. During praying, Muslims deploy in circles centered on the Kaabah. As people farther away took up the faith, they were more likely to live beyond sight of Mecca. A way was needed to tell where Mecca was, so the prayer could face in the proper direction. For short distances away, within a couple hundred kilometers, a straight line on a flat map, like a modern road map, was valid. The flat map was small enough to be a good approximation to the curved Earth surface, such as that of a US state or European province. Beuond that, things got tricky.
Qibla in English -------------- 'Qibla' is now a word in English meaning ' orientation','focus', 'heading', 'bearings'. It's used both in the literal sense of getting about on travels and in general life. One of the earliest mentions I heard was in the mid 1970s at a cafeteria. You stopped at various counters to assemble your meal. One fellow, in a group of coworkers, was turning round left and right in place looking for a certain counter. A buddy shouted,'Yo, Pete, you lost your qibla?'. Similar sense is applied to a person choosing or shifting among careers, investments, lifestyles, relationships. 'Mecca' is also an English word, almost always spwlling 'Mecca' or 'Mekka'. It means a focal place where large crowds are attracted from time to time for some common purpose. It could be a park or square, a stadium or pavilion, or a whole town. The purpose has to be a special one, occurring at longish intervals, annually typicly. Examples are a carnival, festival, convention. It can't be an ongoing function like that of a train depot or maarket place.
Why face Mecca? ------------- There is no compelling reason to do so, except as a deep tradition to show the overall unity of Muslims thruout the world. A Muslim should make a good faith effort to face Mecca to pray using what ever resources he has to hand. With Islam represented in just about all countries by the early 21st century, there is usually an Islamic authority close by who informs about the local qibla. On travels or in strange territory, it may be tough to figure out where Mecca is. There are also situation where the Muslim can not turn toward Mecca, like being in an airline seat or minding a control console. In such cases, the Muslim enjoys a waiver. There are situations where the Muslim is in rapid change of heading that would force him to continuously change his orienttion to keep Mecca in front. The modern example is an Muslim astronaur in Earth orbit. In such cases, he should try to face mecca at the start of his praying, then stay put until he finishes, letting Mecca slew away from his local forward position. The underlying principle is that the praying is given to the creator, not to a earthly thing like the Kaabah. Hence, the creator, who is every where and every when, will receive the devotions of the Muslim regardless of orientation. Facing Mecca to pray is only a cultural tradition that shold be followed when pracitcal but which can be waivd for special circumstances.
Qibla accuracy ------------ Because it is impossible to face exactly toward Mecca, but only to within a degree or so, excessive accuracy in the computation of qubla is empty accuracy. For just about all purposes, a qibla cited to the nearest whole degree is perfectly valid. The qibla for New York City is variosly stated in the range of 58 to 59 degrees. This is quite adequate for a proper facing toward Mecca from any where within a few tens of kilometers around Manhattan. Ideally, a mosque's axis should align with the qibla. In many situations the mosque is built into an existing structure where such alignment is impossible. As a means of orienting the congregation, a marker is placed on the wall behind the prayer master. The congregation faces that marker and, thus, faces Mecca. In New York, the first allnew mosque, not fitted into older structure, is the Islamic Cultural Center on 96th St and 3rd Av on Manhattan. The Center is oriented to Mecca, explaining its skewed placement on the block relative to the street grid. All previous mosques were built into existing buildings with no alignment to Mecca.
Which qibla? ---------- The one, alnost universal, facing of Muslims in praying is toward Mecca. However, there are niche groups of Nuslims who face other special towns. I came across Cairo, Jerusalem, Constantinopolis, and Alexandria (in Egypt) as a focal point for praying. The concept of qibla is the same for all, so I'll stay with that for Mecca.
Moslem science ------------ Because of the need to facilitate remote Muslims to face Mecca, early Islamic leaders used science to figure out the qibla for various places on Earth. For starts, they, as did other educated people, knew the Earth is substantially a sphere. The school-boy story about sailors fearing to fall off the 'edge of a flat world' is, and always was, nonsense. The deck hands, recruited from riff-raff hanging out on the docks, may have held such dread from the prevalent shallow education among the general public. The ones who commanded the ships, ran the businesses, funded the trips, and otherwise made the world go round, were in full knowledge of a round Earth. As a matter of fact, in the late mediaeval times, when Europe started to revive from the Dark Ages, they drew heavily on Islamic scholars for skills and arts of navigation. Columbus himself, as example, either spoke Arabic or had an aide who did, so he could discuss astronomy and navigation with Islamic colleagues. Some papers attributed to him have Arabic notations, but it is still not certain whether Columbus or an associaite wrote them.
Europe's gratitude ---------------- The gratitude of Europe to Islamic science of the late mediaeval years and into the renaissance is forever immortalized in the names of craters on the Moon. They were placed there by European astronomers in the 1600s to thank Arabian figures who contributed to the progress -- some claim sheer survival! -- of western culture thru the Middle Ages. This gratitude continued to the late 20th century when the Moon's averted hemisphere was charted by spacecraft. A similar thank-you for Arabic science now extends to craters on certain other planets and their satellites. Islamic astronomers also, as just one example, sussed out the size of the Earth as about 40,000 kilometer circumference. Columbus, for what ever reason, disputed this value and stayed with an earlier one of only 25,000 kilometers. In his day this trip, allowing for the land mass of Europe and Asia, would be across an ocean narrow enough for the ships of the late 1400s to survive out of reach of land. If the world was bigger, the Arabian size, that ocean would be far and away too wide for a 1400s ship to last. The journey would be a one-way ticket to Davy Jones locker. No one seriously entertained the possibilty of a new intervening land that interrupted this huge ocean. Various Islamic explorers described large regions of land, most likely Brazil, beyond the Canary and Azore islands. Some Arabian mural maps in Spain have 'Plus ultra' noted in the waters west of Europe! It just so happened that when Columbus expected to arrive near China, after traverseing his short ocean, he did hit islands like those in southeast Asia. These were the 'Indies' whence today we have the East Indies, the real ones in Asia, and the West Indies, the ones in the Caribbean Sea. It wasn't until his later trips that he realized he found a whole other continent separting the ocena into two, the Atlantic and the Pacific. That's why the East Indies are far WEST of the United States, while the West Indies are a bit EAST [and south] of it.
Great circle ---------- On a plane the shortest distance between two points is along a straight line between the points. The direction from the one to the other is the azimuth of that line. The azimuth from the other to the one is the ampliment, adding to the first azimuth for 360 degrees. On a sphere this concept transforms into a great circle between the two points. If you put a plane thru the center of the sphere and turn it to touch the two points on the surface, it intersects the surface in a 'straight line'. This is the great circle connecting the two points. The azimuths at the two ends are NOT ampliments! You must calculate each separately. Thus, it is essential to note from which point the azimuth is cited. If one point is at a pole of the globe, the great circles from it to all other points are meridians. The azimuth of any one is 180 degree! From the remote point to the pole, it's 0 degree. Mecca is no where near a pole of the Earth, so the calculation of qibla, or, what is really the same thing, of the great circle route requires formulae of spherical geometry. In fact, because the lat-lon grid is somewhat arbitrarily defined, we can translate it so Mecca is at the pole. This is done in map projections where the point in the center of the map is the pole of the coordinate grid defining that projection.
Great circle for New York ----------------------- In this worked example I use a nominal geographic location for the City of 40.7 degree N lat and 73.9 deg W lon. New York City covers an area about 50 kilometers across, about 30 minutes of arc. Because we are so far from Mecca, some 10,300 kilometers, the qibla for this location is valid for about 100 kilometers around. I inspected qibla tables, worked out to the hundredth of a degree for Manhattan (unspecified place), then Hoboken, Yonkers, St George, Jamaica, Mineola, and other nearby towns. It is humanly impossible to distinguish in a praying posture between these qiblas! In the maths below, phi is latitude; lambda, longitude; zeta, azimuth. The formulae are written as BASIC code, in a linear style. No attempt is made to replicate the actual maths symbols in this plain- text article. The maths are those of a spherical triangle with corners M for Mecca; C, the City; P, north pole. The qibla is angle PCM, in the normal sense of azimuth in astronomy or navigation. the distance between Mecca and New York is side CM. Due to the erstaz way caculette handle trigonometry, you MUST mind the sense of the calculated angles and be ready to throw them into their complement, supplement, ampliment. A sketch, clumsily drawn here, helps keep things right way round. The curved sides CM and PM remind that the triangle is drawn on the Earth, NOT on a plane.
P-------- | \ | \ | \ | \ | - - - \ | / \ | | / \ | |/ \ | C \ | \| M
The formula for the angle at C, PCM, in angular measure, is
PCM = atn(sin CPM / ((sin CP / tan PM) - (cos CP * cos CPM)))
CP is the colatitude of New York, (90) - (+40.7) = 49.3 PM is the colatitude of Mecca = (90) - (+21.4) = 68.6 CPM is the delta(lon) between New York and Mecca, minding that the two are on opposite sides of the zero meridian. It is given a positive signum, regardless of which way you do the substraction. P = (-73.9) - (+39.8) = -113.7 -> +113.7. The formula becomes
PCM = atn(sin 113.7 / ((sin 49.3 / tan 68.6) - (cos 49.3 * cos 113.7)))
PCM = atn(0.9157 / ((0.7581 / 2.5512) - (0.6521 * -0.4019)))
OCM = atn(1.637)
PCM = 58.59
Thus, the azimuth FROM C (New York) TO M (Mecca), PCM is 58.59 degree. In THIS PECULIAR CASE, no adjustment for ampliment, complement, supplement is needed. The angle ALREADY, as seen in the sketch the right way round for the specification of azimuth. That is, azimuth is measured clockwise from north, thru east, back to north. This angle, 58ish degree, is the very qibla of Mecca for New York. It is routinely rounded to 58, 58-1/2, or 59 degrees, all with utterly equal validity.
Mecca to New York --------------- If, for some reason, you wanted the qibla of New York as seen from Mecca, you have to swop the colatitudes in the above formula. Note that the answer is NOT the amplument of 58.58, like it would be on a flat map.
PMC = atn(sin CPM / ((sin PM / tan CP) - (cos PM * cos CPM)))
OMC = atn(0.9157 / ((0.9311 / 1.1626) - (0.3649 * -0.4019)))
PMC = 0.9664
PMC = 44.02 -> 315.98
Notice that in THIS PECULIAR CASE the angle has to throw to its ampliment. That's because the calcked angle is the one INSIDE the triangle and falls to the LEFT, WEST, of the meridian of Mecca, side PM. Since azimuth is counted eastward from north, we must go round OUTSIDE the triangle, subtracting the 44ish degree from 360, to get the correct qibla.
Shape of Earth ------------ For just about all domestic and most specialized purposes, it is well to treat the Earth as a perfect sphere. All celestial navigation and all spherical astronomy are founded on a spherical Earth. The geometry of a sphere is simple and yields results that are a whisker's distance from the vastly more complex maths of the real Earth shape. Earth in a second order approximation is an oblate shperoid with the equator bulged out slightly. The equatorial diameter of Earth is about 25 kilometers more than the polar, a generally negligible amount against the 6,400 kilometer overall diameter. In calculating qibla by the great circle method, the spherical Earth is assumed unless otherwise deliberately stipulated. For New York's qibla the difference between the qibla from the spherical and ellipsoidal glibe is only aabout a tenth of a degree.
Qibla by the Sun -------------- It's one thing to work out the qibla and hand out the answer, but where is this azimuth in the landscape? A prayer has to face towad a local feature, beyond which, along the great circle, is Mecca. There ae two main ways to instruct the prayer about his qibla, the Sun method and qibla compass. Imagine that you are a few kilometers from the Kaabah and can not see it directly. If at the Kaabah there was a tall mast with a lamp on top, you could find the Kaabah beyond the forground skyline and face toward it. If you were farther away, a taller mast could be built. Beyond 50 or so kilometer, the limits of building masts, or even substantial skyscrapers, visible from that far away are too great. The late World Trade Center, among the tallest structures ever built, was visible from the Carskills, Taconics, and inner Poconos. But no human edifice could mark the Kaabah for a prayer even a couple hundred kilometers from it. There is a very, very!, tall 'lamp' that can mark the location of Mecca. It's the Sun! With Mecca being at 21.4 degree north latitude, the Sun crosses the latitude of Mecca twice a year on its way to and from the summer solstice. On these two particular days, there is an hour when the Sun stands in the very zenith directly above the Kaabah. The zenithal stations of the Sun over Mecca occurs on May 28 09:18 UT and July 15 09:27 UT. You must convert UT to the local mean time of your location, including the offset from the standard timezone meridian. Mind, too, the offset during your daylight savings time. In the United States daylight savings time prevails on both dates. You must be wisely about the practice in other countries where you fix the qibla by the zenithal station method. If you on these dates and hours look toward the Sun, and note where it stands above your local skyline, you are looking toward Mecca. You got the qibla for Mecca once and for all. A photograph of the landscape with the Sun in it wil guide you for all the days therafter. It's a bit of luck that you have two shots at ths each year in case of bad weather. Fortunately, there is a wiggle room of two days and about 8 minutes. A cloud over Sun at the very moment that passes away in a couple minutes will not upset your qibla sighting. Nor will rain that clears up on the next day. This trick works so long as you actually can see the Sun. The Sun illuminates half of the Earth, out to quite 10,000 kilometers from the subsolar point at Mecca. The other half of Earth, bwyond 10,000 kilometers, can not see the Sun. It is down at the two critical moments. New York, at 10,300 kilometers from Mecca, misses the Sun on the two qibla moments because they occur before local sunrise.
Qibla by the antiSun ------------------ For those in the night side of Earth on the two qibla moments, there is the antiSun method. Wait until the Sun stands directly over the diametricly opposite point on the globe from Mecca. This is the antipode of Mecca, same latitude in southern hemisphere and 180 degree away in longitude. This point is in the South Pacific Ocean near no major island. On these two other qibla moments, look straight at your shadow. It points into the horizon toward Mecca. A photograph of the landscape with that shadow fixes your qibla. The antisolar zenithal crossing or, perhaps simpler to visualize, the solar nadir crossing of Mecca happen on November 29 21:09 UT and January 14 21:30 UT. In New York, these translate to:
November 29 16:13 LMT, Sun alt 2.6, Sun azm 238.6, qibla 58.6 January 14 16:34 LMT, Sun alt 2.9, Sun azm 238.8, aibls 58.8
By utter chance, and ONLY that, the two pairs of dates are close to the dates of the Manhatan Stonehange sunset in summer and Manhattan Stonehenge sunrise in winter!
An other solar method ------------------- The zenithal, or nadir, crossing method works as long as the weather is favorable on the two dates. If you miss the Sun due to clouds in a given year, you must wait a whole year for the next chance. To avoid such lengthly deadtime, an other solar method was devised. In most places, the Sun at some hour of a good part of the year stands in the azimuth toward Mecca, but not actually over the very Kaabah. It's the direction that you're figuring out, so the Sun may be anywhere along the great circle from you to Mecca. There are periods of the year when the Sun never attains to the proper azimuth, but there the span when it does give you many shots at getting a good qibla fix. For New York the Sun can touch the qibla azimuth of 59 degrees (rounded), only just after sunrise between June 11th and July 1st. That is, on the 20 days centered on the summer solstice. Then after during the day the Sun migrates right of the qibla. This narrow window of qibla azimuth for the Sun results from the City's close proximity to the 'equator' of the world, whose pole is at Mecca. We're only 300 kilometers beyond that equator in the opposite hemisphere. Never the less, it does give a chance over a 20 day span to get a qibla fix instad of just the two days (even with a two day leeway) from the zenith/nadir method.
Qibla by stars ------------ Various bright stars stand in the azimuth of qibla at some time in their diurnal and annual motion. They offer many more days, to beat adverse weather, for finding your qibla. Once determined, by noting where the star stands over the local landscape, the qibla is fixed then after. The star method is not widely promoted beecause it requires a familiarity with the constellations, an art rare among the general public. However, as examples here are the days and hours for Capella and Vega for New York. Times are EST, not EDST.
---------------------------------------------------------------- star | 18h | 19h | 20h | 21h | 22h | 23h | 00h | 01h --------+------+------+------+------+------+------+------+------ Capella |Dec 26|Dec 11|Nov 26|Nov 11|Oct 27|Oct 11|Sep 27|Sep 11 Vega | -- | -- |May*28|May 13|Apr 28|Apr 13|Mar 29|Mar 14 -----------------------------------------------------------------
I calcked the times for hours when a person would plausibly step outside and look for Vega or Capwlla. You may fix your qibla by this table within two days of the listed date and within 8 minutes of the listed hour. For intermediate dates and hours, you may linearly interpolate between the tabulated values. The result will be within the tolerance for a valid qibla fix. These values will drift secularly due to precession, but are good for a single lifetime. Note that either one or the other is at the qibla, they being more or less opposite each other across the north celestial pole. May 28 has a '*' to indicate that Vega is then is evening twilight at 20h EST. Vega is among the brightest stars in the sky. so it may be visible thru twilight. A '--' means the hour is in daylight before or near sunset; Vega would be quite invisible then.
Celeestial navigation ------------------- The use of the Sun's or star's location in the sky to find a direction is a variation of celestial navigation. In celestial navigation we use their position to calculate our location on the Earth. It uses the direction to the Sun/star as an intermediate step in that process. In brief, we first compute the altitude and azimuth of the Sun/star for the local hour of observation and for an assumed location. This location comes from general navigation skills and is the 'dead reckoning' position. At the given hour we examine the target with the sextant, an instrument for taking altitude sightings. If the reading is greater than the computed altitude, we are closer to the target, on the spherical surface of Earth, than we assumed. If lesser, farther. On a map we mark our dead reckoning place and draw a line from it into the azimuth of the target. If the assumed altitude is too small, we pace off along the azimuth line the deficit minutes of arc -- which are the same as mautical miles (about 1,800 meters) -- TOWARD the target. The derviced point is where we really are. If the assumed altitude is too big, we pace off the sufficit minutes of arc AWAY from the target along the azimuth line. The final place we land at is where we actually are. We pick at least two stars so we get an intercept of lines on the chart as a check against each other. To get a better intercept, we choose stars about 90 degree apart in azimuth. The altitude sighting of stars is done in evening or morning twilight. We need both the star and the horison to see thru the sextant. This period of time, where both the brighter stars, used in navigation, and the horizon are visible is nautical twilight.
Qibla compass ----------- A handy device for Muslims who travel is a qibla compass. This may be either a physical device or a computer program on a handheld. In the physical form it is a regular camping/hiking magnetic compass set into a well marked in what at first look like degrees of azimuth. The aero point is a stylized minnaret, altho it may look more like a stylized arrow. In the models I saw, the well is divided with 400 -- not 360! -- parts. They are NOT degrees of azimuth. I could not learn why this is so, but in the end it really doesn't matter. On the smaller model, for the pocket, there are 40 divisions, each corresponding to 10 on the large models. From the local Islamic community or a booklet with the device you get an index number fo the qibla. Place the comapss on the ground where you are kneeling on to pray. Turn the entire gadget so the north end of the compass needle points at the index number. The zero point (arrow or minnaret) now aims to Mecca. The index number is in substance the ampliment of the qibla, plus the magnetic deviation from true north. For New York on a 400-part compass, the index number is 320. This can be derived by
(geographic qibla) - (magnetic deviation) = (magnetic qibla) (59) - (-13) = 72
(mag qibla) - (360) = (amplument of mag qibla) (72) - (360) = 288
(ampl mag qibla) * (400/360 ratio) = (index number) (288) * (10/9) = 320
One thing I was surprised at is the large deviation of magnetic north, 13 degrees west of geographic north! It turns out that the magnetic pole wanders rapidly up there in north Canada. The net motion as seen from New York is westward, away from the geographic north, by about a degree per decade. This is important in navigation by magnetic compass. You better update old navigation charts and tables. The index number, of the ones I looked up on various Moslem websites, all seem to assume the 400-part compass. It may be well to specificly ask if the offered index number is for a 400 or a 360 part compass, just to be safe. If the number is for the opposite dialing from that of your compass, ratio it by 9/10 (400 index to 360 dial) or 10/9 (360 index to 400 dial). An other wrinkle is that the index number may be cited for a 40- part (or 36-part) compass. In this case, suffix a zero (multiply by 10). Or divied by 10 if you got the 40-part compass and are offered a 400-part index number. This can be misleading for a low index number. It could be in units or in truncated tens. '25' may be 25 or 250. Ask which it is!
Here's China ---------- It seems that more and more articles of everyday life are imported from China. Most of the goods are passably good and are a fair value for the price. You don't feel too bad if the shoulder bag seams burst on you; you only paid $5 for the bag. When looking for qibla compasses to inspect, I found many are made in China! And they are cheap, in the $7-$25 range. This is often LESS than what the magnetic compass by itself costs as an American product! What's more, the construction seems adquate for gentle handling, like packing in carryon luggage. The factory just glues the magnetic compass into its well, sometimes in some symmetrical way. The well is molded with the 40/400 or 36/360 divisions around it in both 'arabic' and real Arabic numerals. That's it, really. There is no blessing, benediction, holy water sprinkle, or other ritual to be done. It's ready for use straight from the box. The only down side could be the instruction book. It may be in pigeon English, or pigeon Arabic!, and could have grammar, spelling, printing mistakes. You can discard the book and use the index numbers from a local Islamic source.
Possible worry ------------ With the concern in 2007 about lead paint on toys and poisoned pet food from China, it's best to exert consumer smarts when shopping for a qibla compass. This is specially the case if the compass is given to a child entering the culture. The device could be expropriated as a handy teething ring! It can also happen that lax workmanship leaves flashing or burrs on the compass that can break off and be swallowed. Ask at the local health or consumer agency about the safety of a compass under considertion.
Computer compass -------------- A handy computer program for a handheld is a qibla compass. Even if you're not a Muslim, it can be a useful general purpose compass for all outdoor activiry by day. After setting your home location and switching daylight time on/off, the screen shows a compass rose, a qibla mark, and a Sun symbol. It self sets from the handheld's clock. I heard of a qibla program that includes the Moon for use after sunset or before sunrise but I could not find it to try out. Hold the computer screen horizontal and turn it so the Sun symbol aims at the Sun in the sky. You may hold a pencil upright on the symbol and turn the computer so its shadow fall over the center of the compass rose. The compass is now aligned to the geographic directions and the qibla mark points to Mecca. It really works. Ignoring the qibla mark leaves a good computer compass for hiking, camping, and the like. In the specific program I have, the Sun is displayed for ANY hour of the day, even at night. Checking with astronomy programss, the Sun's direction is correct, only it's out of sight below the horizon.
Craig's reverse-azimuth map ------------------------- You can NOT use an azimuth map centered on Mecca, like for airline routes, to find your qibla. The azimuth labels are those FROM Mecca to rest-of-world. As we saw for New York, as example, the qibla from Mecca to ROW is NOT simply the ampliment of that from ROW to Mecca. For a rough qibla fix there is the reverse-azimuth map, also called the 'Mecca map'. This is a world map, centered on Mecca, invented by Craig in 1910. The longitude meridians are parallel verticals. The latitude circles are twisted out of their 90-degree intercept with the meridians. I'm being kind to say that the shapes and sizes of the countries are wildly distorted. The map, when extended to cover the whole globe reesembles a bowtie with a large knot! Radial curves from Mecca, in the center, are lines of constant azimuth TO Mecca. They are labeled NOT with the azimuth seen at Mecca, but with that seen from points along the curves. That is, the azimuths are 'reversed'. The world is contorted to make all points with a given qibla sit on the corresponding radial line. Finding your location in this geography can be a bit of a hunt.
Other 'Mecca' maps ---------------- Hammer in 1910 improved Craig's map by building in both reverse azimuth and distance from Mecca. When covering the globe, the thing looks like a cookie with an excentric C-shape hole! A line from any point to Mecca in the center gives both its qibla and distance from Mexxa. As you may expect, the countries are wildly contorted out of shape and size. It turns out that there can be TWO places on Earth with the SAME qibla AND same distance from Mecca. Hence, the Hammer map, and the next one from Tobler, have regions where countires OVERLAP! They share common points of azimuth and separation from Mecca. Need less to say, finding your location within these zones can be tricky. Tobler in 2002 invented a qibla map that is at least simple to use, while being as crazy in form as the others. He plots qibla against distance as a simple graph. Distance is the x-axis; qibla, y- axis. Mecca is the whole top edge of the map with qibla ranging from 0 (left side) to 360 (right side). Distance from Mecca is zero at the top to 20,000Km (half the Earth circumference) at the bottom. The antipode of Mecca, in the Pacific Ocean, is along the bottom edge. What happens within the graph is an other story. There are zones of overlap where two distinct places share the same qibla and distance from Mecca. While the overall shape is rectangular, there is in the middle an elongated hole. The map looks like the cover plate for a light switch! Or the top of a box of popup tissue! A steroegraohic map centered on Mecca with the normal lat-lon grid is yet an other aid for finding qibla. A stereographic map preseves angles and all great cirles are true crcles or straight lines. A radial line from Mecca cuts your site's longitude meridian at the correct angle for qibla. You do have to measure this angle by geometric construction and an angle gauge. For a portion of this map covering a single country, this may be feasible because the lat-lon lines can be farther apart and easier to read.
Early maps -------- The routine way to issue qibla information in the Islamic lands was by tables and math books. These are preserved from the earliest era of Islam. Until 1989 we had no actual maps from early Islam. In that year a brass qibla map was discovered in Iran. It isThe engraved on a disc about 24cm diameter and is fitted with a ruler pivoted at the center over Mecca. A second specimen was found in 1995. From books already in hand about this device, the 1989 sepcimen lacks a detachable sundial and embedded magnetic compass. The 1995 one is complete. The compass orients the map so the qibla on it aims to Mecca. The sundial seems to be just for finding the hour of the day, perhaps for times of praying. They date from around 1700 and are remarkably similar to the central part of the Hammer map! With the sundial and compass, It's the earlier-day version of the computer compass I described above! They cover the region around Mecca, most of Europe and some of Africa. This was more or less the full diffusion of Islam in the 17th century, Countries, coasts, rivers are not laid out, just towns as labeled dots. By placing the ruler over your town, the qibla is read from the rim. Distance is taken from the scale on the ruler. Scholars examining these instruments conclude that they are accurate and correct, save for flaws in geography. Geography in the western world in the 17th century was also a much fragmented art.
Flat-earth method --------------- While collecting material for this article I came across a really, like really, bizarre feature of American Moslem practice. It seems that some minor groups in the United States do not use the great circle method to find qibla. They go by -- I am NOT making this up!! - - a flat-earth model. No, these folk are not sputniks of the flat- earth belief, but they would make a capital poster child for it. In this scheme of qibla, the world is a flat plane on the Mercator projection. The Mercator map has the property, useful in the dawn days of European sailing, that a stright line between two points has a constant compass bearing along it. A sailor leaving one end would merely have to keep this bearing and he will get to the opposite end. This line is a 'rhumb line'. The idea works only on paper -- litterally -- because there are so many obstructions, not the least of which is intervening land along the rhumb line. However, when ocean sailing was a new pursuit in Europe in the late MIddle Ages, the Mercator method was about the best chance of getting from place to place on the high seas. The rhumb line is not the shortest distance between the end points. It is not even a 'straight line'. It is a spiral that eventually joins the two poles of the world. On the Mercator map they appear straight because the map is on purpose distorted at the poles to make the longitude meridians stay parallel and to spread out the latitude circles. This causes the famous 'Greenland effect', where Greenland, a modest island near the north pole, looks as big as South America. From the pragmatic view of the 1400s navigator, the shortest distance was not all that critical. The trip acorss the sea would take a couple months at least, anyway. Having to be at sea an extra couple weeks because he followed a rhumb line, not a great circle, didn't matter that much. The result of using the rhumb line in the US for qibla is just ludicrous. It aims the prayer into an azimuth for New York of about 110 degrees rather than the correct 59 degrees! The argument is that on the flat map the direction from New York to Mecca IS kind of east- southeast. It's NOT way up to the northeast on the great circle.
This doesn't work --------------- The rationale offered in the litterature I read is plain nonsense. It is trivial to show that the rhunb line doesn't work. For starts, the Mercator map used is always sliced open from its real cylinder shape at or near the International Date Line. On this map the line between New York and Mecca does steer an east-southeast course. The slicing of the map near the IDL is merely for convenience. It keeps the parts of the workd important in western history connected near the middle of the map. The Atlantic Ocean, critical in western history, is in one piece. Voyages are easier to follow across it between Europe and the Americas. However, pura mente BECAUSE the Mercator map is a cylinder, it may be unrolled along ANY meridian. Suppose we cut it along the 0th degree meridian. This splits Europe and Africa into the two sides of the map, but keeps the Pacific Ocean together. This map could be useful in Hawaii, Japan, Australia. Now the 'straight line' from New York to Mecca is a little south of west! It runs across the whole United States, Pacific Ocean, the Far East, India, the Middle East. Isn't THIS the 'correct' rhumb line? In fact, as a cylinder, the Mercator projection has TWO rhunb lines connecting any two points on it! One spirals clockwise toward the poles; the other, counterclockwise. By applying the reasoning of the flat-earth Muslims, each is just as valid as the other. At their praying session. some of the congregation should be allowed to face east-southeast and the rest to face west-southwest! An other way to demolish the flat-earth argument is to rotate the lat-lon grid so Mecca is at one pole. Can any one fail to see that the direction to Mecca is along a meridian from any place on the globe? Meridians are great circles, not rhumb lines.
Why a flat-earth? --------------- I heard assorted, equally silly, motivations for setting aside the traditional and proper methods of finding qibla. Here I note only two extreme explanations. The first is that American Muslims want to distance themselfs from the overseas Muslims. They seek to avoid being gathered up with the fundmentalists and radical elements of Islam and be treated as a distinct American group. Facing Mecca is one highly visible trait of Muslims, one that is commonly mocked by those beyond the Moslem culture. Hence, by modifying this feature, American Muslims hope to segregate themselfs. 'See, we don't katow-katow to those people. we have our own way to face Mecca. We be the nice guys.' The other extreme is that the flat-earth feature is part of the radical agenda to dismantle knowledge, understanding, learning in America. By teaching a nonsensical theme, they can say, 'Look, western science is wrong. It shows we face northeast to Mecca. We really have to face east-southeast!'. This platform is on a par with the biblicists in other sectors of American society. They hope to impose bogus biology and cosmology, replacing science and objective study of these subjects. I can't assess what the true story is, but you will hear them and many others across the social and political spectrum in the years to come. So far, the falt-earth Muslims are a fringe sector among the tens of millions of traditional Muslims in the United States.
Conclusion -------- The practice of facing Mecca when out of its sight and in strange territory was a prime factor in the development of science, notably astronomy and mathematics, in the early Islamic period. This work was deeply appreciated by western peoples, who then were struggling out of the Dark Ages. Today, finding qibla is a trivial matter of pressing buttons on a computer or lining up a magnetic compass. yet it still reminds us of the time and energy it took to get the maths and science in place over a millennium ago.