Qibla Direction
Creator: Dr.Mohibullah N.Durrani
Date: 2007-07-25
Description: The calculation for the Mathematical Direction for Kabah from any point on the surface of the world.
Format: text
Identifier: http://www.islamworld.net/qibla.html
Language: en
Subject: prayer
Title: Qibla Direction
Created on: Wed Jul 25 21:31:56 -0400 2007
Updated on: Wed Jul 25 21:31:56 -0400 2007
Version: 1
Abstract: ... Degrees East. Then, the spherical triangle would have: Angle "A" = 90 Degrees (the difference in the Longitudes of "B" and "C") Side "b" = 10 Degrees (90 - Latitude of Point "C" = 90 - 80 = 10 Deg) Side "c" = 10 Degrees (90 - Latitude of Point "B" = 90 - 80 = 10 Deg) __ __ -1 | SIN A | C = TAN | ----------------------------------- | |__ sin b cot c - cos b COS A __| __ __ -1 | SIN 90 | C = TAN | --------------------------------------- | |__ sin 10 cot 10 - cos 10 COS 90 __| __ __ -1 | 1.000 | C = TAN | --------------------------------------- | |__ sin 10 cot 10 - cos 10 COS 90 __| C = 45.44 Degrees Note: Even though B and C are on the SAME LATITUDE, B is approximately North-East (45 Deg E of N) of C !!! D. EXAMPLES *********** All the examples in this section do NOT include the variation of the Magnetic North Pole from the (True) North Pole. The values given in Section B includes, in addition, the Qibla direction as read from a magnetic compass, and hence from the Magnetic North Pole. Examples: 1. Points around the North Pole (NP), all on the same Latitude, NEAR THE NP. 2. Points around the North Pole, on constant Latitudes, upto Equator. 3. Points on the same Latitude as Kabah. 4. Points all around Kabah (0 Deg to 360 Deg). 5. Points on the same Longitude as Kabah. 6. Points at approximately the center of U.S.A., France, Australia, Japan. EXAMPLE D-1: Points around the North Pole (NP), all on the same Latitude, ========================================================================= NEAR THE NP. ============ This is an INTERESTING EXAMPLE. It seems contrary to "intuition". Many CONCEPTS OF SPHERICAL TRIGONOMETRY can be understood by this "extreme" case of pints on a constant Latitude circle around and NEAR THE NORTH POLE. Consider a Circle around the North Pole with a small radius of only ten (10) feet. Choose "N" as the center of the circle. We choose four points around the circumference, "A" at 0 Deg, "B" at 90 Deg, "C" at 180 Deg, and "D" at 270 Deg. Choose the positive direction of the "X" axis from the center of the circle, "N", through the Point "A" on the circumference. Choose the positive direction of the "Y" axis from the center, "N", through the Point "B" on the circumference. On this small scale for our circle, ALL POINTS "A", "B", "C", "D", and "N" ARE DIRECTLY VISIBLE FROM EACH OF THE OTHER POINTS. Join DA and drop a perpendicular from N to DA to intersect DA at "E". Exprapolate NE to meet the circumference of the circle at "F". Y ^ | | B (90 Deg) ------+------ / | \ / | \ ( | ) C | | N | A (0 Deg) (180 Deg)+-----------+-----------+---------------> X | | \ / | ( | \E/ ) \ | / \ / \ | / / F ------+------ D (270 Deg) Since the center of this circle is the North Pole, "N", each INWARD-DRAWN RADIUS, from any point on the circumference would be the NORTH DIRECTION for that particular point on the circumference. Similarly, EN is the North direction for point E. These North directions are NOT parallel to each other. The North directions converge to the center of the circle, which we had chosen as the North Pole. The North (N) direction is defined as the direction pointing to the North Pole. The AZIMUTH (angular direction, in degrees, of any one point from any other point) is the angular rotation FROM NORTH, in a ClockWise direction. The following can be obtained, by direct inspection (no need to calculate): >From "A" the North direction is AN (0 Deg Azimuth). The direction of "B" from "A" is "North-East" (N-E), ( 45 Deg Azimuth). The direction of "C" from "A" is "North" (N), ( 0 Deg Azimuth). The direction of "D" from "A" is "North-West" (N-W), (315 Deg Azimuth). >From "B" the North direction is BN (0 Deg Azimuth). The direction of "C" from "B" is "North-East" (N-E), ( 45 Deg Azimuth). The direction of "D" from "B" is "North" (N), ( 0 Deg Azimuth). The direction of "A" from "B" is "North-West" (N-W), (315 Deg Azimuth). >From "C" the North direction is CN (0 Deg Azimuth). The direction of "D" from "C" is "North-East" (N-E), ( 45 Deg Azimuth). The direction of "A" from "C" is "North" (N), ( 0 Deg Azimuth). The direction of "B" from "C" is "North-West" (N-W), (315 Deg Azimuth). >From "D" the North direction is DN (0 Deg Azimuth). The direction of "A" from "D" is "North-East" (N-E), ( 45 Deg Azimuth). The direction of "B" from "D" is "North" (N), ( 0 Deg Azimuth). The direction of "C" from "D" is "North-West" (N-W), (315 Deg Azimuth). Since the circle has the North Pole as its center, the points on the circle can be considered as a having the same latitude, the latititude being very close to 90 Deg (but smaller than 90 Deg, since the Latitude of the North Pole is exactly 90 Deg, by definition). We note some VERY INTERESTING facts: ************************************ All points on the circle have the SAME LATITUDE. Even though "B", "C", and "D" are on the same latitude as "A", "B" is North-East (N-E) of "A", C is N of A, and D is N-W of A. Similarly, C, D, and A are on the same latitude as B, C is N-E of B, D is N of B, and A is N-W of B; and similarly, D is N-E of C, A is N of C, and B is N-W of C; A is N-E of D, B is N of D, and C is N-W of D. ******************************************************************* * When "B" is North-East (N-E) of "A", for this small circle, * * "A" is North-West (N-W) of "B" !!! (NOT S-W !!!) * ******************************************************************* The direction from "A" to other points on the same Latitude circle is along points that are on the LINE-of-the-SHORTEST-DISTANCE joining that particular point and the point "A". The Line of the Shortest Distance is along the GREAT CIRCLE. The direct direction is NOT along points on the same Latitude. (Only exception is for points on the equator). The SHORTEST (Direct) DISTANCE between any two points on the surface of the earth is along the Great Circle. We also note that at the point "A", due "East" is 90 Degrees ClockWise (CW) from the North direction (N is along the radius AN), hence is perpendicular to the radius AN, and hence tangential to the circumference of the circle. If a person travels due East from point "A", and that person travels in a "straight line" (along the Great Circle) and does not change direction, then he would be travelling along the tangent (at"A") to the circle, and hence moving "away" from the circle. This would cause the latitude of the person to change while traveling in the "straight line" !! As the person travels in the "straight line" the direction of East would no longer be "straight ahead" since the North direction would change and hence the Ease direction would also change ! Consider again the "small" circle around the North Pole. For a person to "FACE" Point "A" from Point "D", that person would have to face in the North-East (N-E) direction at "D". When that person travels in a "STRAIGHT LINE" along DA, the person is INITIALLY ORIENTED towards the NORTH-EAST direction (defined at Point D) while AT POINT D. Continuing to travel from D, WITHOUT CHANGING THE DIRECTION OF TRAVEL IN THE "STRAIGHT LINE" to an intermediate point E (note that NE is perpendicular to DEA), the INTERMEDIATE ORIENTATION is DUE EAST AT POINT E, to continue from E towards A. Further continuing to travel from E, WITHOUT CHANGING THE DIRECTION OF TRAVEL IN THE "STRAIGHT LINE" to a final pint A, the FINAL ORIENTATION is SOUTH-EAST at POINT A. ********************************************** * TRAVEL EVEN IN A "STRAIGHT LINE" CAUSES * * THE ORIENTATION TO CHANGE WHILE TRAVELLING * ********************************************** STRAIGHT LINE TRAVEL FROM POINT "D", THROUGH POINT "E", TO POINT "A": LOCATION POINT: Point D Point E Point A ORIENTATION: North-East East South-East NORTH DIRECTION: DN EN AN If the person travelled a little distance due East from Point D, since direction East is no longer in the person's line of travel (the North direction changes from point to point) the person re-orients towards due East and again travels a short distance, and again re-orients towards the new East direction and travels a short distance, then that person WOULD BE TRAVELLING IN A CIRCLE (from Point D, to Point F, to Point A) and would NOT be travelling in a "straight line" from Point D, to Point E, to Point A. EXAMPLE D-2: Points around the North Pole (NP), on constant Latitudes, ====================================================================== upto the EQUATOR ================ This is the general case of Example D-1 and D-3. We will consider only four (4) points on each Latitude, at Longitudes 0, 90E, 180, 90W Degrees. Since both the points are on the same latitude, the equation for the Azimuth (given in Section C) is reduced to: __ __ -1 | 1.000 | C = TAN | ------------- | |__ sin (PHI) __| where ANGLE PHI = Latitude Near NP Near Equator N Latitude: 89.99 89.9 89 85 80 70 60 50 40 30 21 20 10 00 Direction "A from D": 45.00 45.0 45 45 45 47 49 53 57 63 70 71 80 90 "B from D": 00.00 00.0 00 00 00 00 00 00 00 00 00 00 00 00 "C from D": 315.00 315.0 315 315 315 313 311 307 303 297 290 289 280 270 (All Directions are Azimuthal, ie E of N.) 180 /------|------\ / B | \ / | \ ( | ) 90 | | N A | 90 West |-----------+-----------| East | C | | ( | ) \ | / \ | D / \------|------/ 0 Deg | West East | "P L A N" 90N /------|------\ ... [Full Article...]
