Bismillah hir-Rahman nir-Rahim
(In the Name of ALLAH, THE MOST BENEFICENT, THE MOST MERCIFUL)
FACE TOWARDS KABAH (QIBLAH)
(Direction for Daily Prayers)
1 Safr 1418 AH
7 Jun 1997 CE
Revised 15 Feb 2003 CE
Dr.Mohib.N.DURRANI,
mailto:Durrani@Hilal-Sighting.Com
Alternate
mailto:mnd0@columbia.edu
Webpages at http://Hilal-Sighting.Com
National Coordinator (Since 1987),
for Astronomical Information
Islamic Society of North America (ISNA)
Islamic Shura Council of North America
Shariah Scholars Association of North America (SSANA)
Copyright (c) 1997-2003
The Muslim Students Association of Columbia University
102 Earl Hall, Columbia University
NEW YORK, NY 10027
"FACE TOWARDS KABAH - What is that direction ?"
As Salamu alaikum (Peace) to all.
The following is a continuation of the information to determine the
direction for salaat (prayers), which is the direction to "Face Kabah"
(in Makkah), from any place on the world.
The previous information (article) was generated in 1997 and
was titled "Direction for Kabah (Mathematical) - from anywhere".
This article can be electroninally viewed on the homepage at
http://www.Hilal-Sighting.Com/Qibla-Direction-Mathematical
A general question (which is an incorrect question) that is sometimes
asked and which could lead to an incorrect answer is:
"What direction do I need to travel to reach Kabah (in Makkah) ?"
The precise question that should be asked is:
"What direction do I need to travel, WITHOUT HAVING TO TURN TOWARDS
THE RIGHT OR TOWARDS THE LEFT, to reach Kabah (in Makkah) ?"
This precise question leads to the correct direction, towards the North-of-East
for most places in USA/Canada. The precise direction can be easily calculated
and was given for many places, in a table, in the previous article.
This precise direction is also calculated in this article for one city
(Lawrence, KS), as a complete worked-out example.
This North-of-East direction for the Kabah from USA/Canada can also be quite easily
and clearly seen by taking a large diameter globe of the earth and marking on
the globe both the point representing the city (from where the direction for the
Kabah is to be determined), and marking the point representing the Kabah. Then a
string could be connected between these points on the surface of the globe. The
initial direction to the Kabah from the city can be easily (and approximately)
determined with respect to the North and East directions at the city, by looking
at the direction of the string from the city to Kabah.
The SUMMARY of this article is that IF we are truly "Facing the Kabah",
we should be able to "TRAVEL (forward) WITHOUT TURNING" towards the right
or towards the left, and we should be able to finally touch the Kabah.
This true direction of "Facing the Kabah" is also along the "Great Circle".
The incorrect "Rhumb Line" direction of "apparant straight line" travel on a
special map projection, the Mercator Map, involves a CONTINUOUSLY TURNING TRAVEL.
If the initial Rhumb Line direction is followed, without turning, we WILL NOT
reach the Kabah !!!
Direction for Kabah from TRUE NORTH or True East for Lawrence, KS is:
43 deg 49 min 10.5 sec East of True North (more precise Ellipsoid Model)
43 deg 15 min 55.9 sec East of True North (Spherical Trigonometry)
46 deg 10 min 49.5 sec NORTH of True East (more precise Ellipsoid Model)
46 deg 44 min 04.1 sec NORTH of True East (Spherical Trigonometry)
Direction for Kabah from MAGNETIC NORTH or Magnetic East for Lawrence, KS is:
39 deg 32 min 22.5 sec East of Magnetic North (more precise Ellipsoid Model)
38 deg 59 min 07.9 sec East of Magnetic North (Spherical Trigonometry)
50 deg 27 min 37.5 sec NORTH of Magnetic East (more precise Ellipsoid Model)
51 deg 00 min 52.1 sec NORTH of Magnetic East (Spherical Trigonometry)
The information for this article is presented in the following sections:
1. Basis for "Turn" our "Face" towards Kabah, from the Quran and Hadith.
"Turn our Face towards Kabah" would be the Qiblah, direction for prayers.
2. The result of "Face the Kabah" is to be able to TRAVEL WITHOUT TURNING,
in the direction we are "Facing", and to be able to finally touch the Kabah.
3. Determining "true" direction of STRAIGHT TRAVEL (WITHOUT TURNING).
Properties of Latitudes and Longitudes on a "spherical" earth.
4. The INCORRECT "RHUMB-LINE" DIRECTION OF TRAVEL, REQUIRES CONTINUOUS TURNING
(continuous corrections to direction of travel).
Properties of a Mercator Projection, where Rhumb-Lines are projected
as Straight Lines.
5. Examples of places at different distances from Kabah.
6. Qibla direction for Lawrence, KS (USA), calculated result.
7. Conclusions for USA/Canada.
1. Basis for "Turn" our "Face" towards Kabah, from the Quran and Hadith.
"Turn our Face towards Kabah" would be the Qiblah, direction for prayers.
The Quran orders us in many places to "Turn" our "Face" towards the Sacred
Mosque (Kabah, in Makkah) for our Salaat (prayers), Ref. 1.
This "Facing the Sacred Mosque" is the Qiblah (the direction of Salaat).
2:144 .. Surely, We shall turn you (Muhammad, sws) to a Qiblah (prayer direction)
that shall please you, so turn your face in the direction of the Sacred Mosque
(at Makkah). And where ever you people are, turn your faces (in prayer)
in that direction. ..
2:149 And from where ever you start (for prayers), turn your face in the
direction of the Sacred Mosque (at Makkah); that is indeed the truth from your
Lord. And Allah is not unaware of what you do.
2:150 And from where ever you start (for prayers), turn your face in the direction
of the Sacred Mosque (at Makkah), and where ever you are, turn your faces
towards it (when you prayer) ..
There also exist various Saheeh hadith that also guide us to face the Qiblah.
Vol. 1 - Salat - Chapter 31, Ref. 2.
(31) CHAPTER. During the prayer one should face the Qiblah wherever one may be.
Narrated Abu Huraira: The Prophet (SAW) said, "Face the Qiblah and say,
'Allahu Akbar.' 393.
Narrated Jabir: Allah's Apostle (SAW) used to pray (optional, non-obligatory prayer)
while riding on his mount (Rahila) wherever it turned, and whenever he wanted to pray the compulsory prayer he dismounted and prayed facing the Qiblah (Kabah at Makkah).
2. The result of "Face the Kabah" is to be able to TRAVEL WITHOUT TURNING,
in the direction we are "Facing", and to be able to finally touch the Kabah.
Based on the the Quran and Hadith, let us understand the implications of "Face"
the Kabah. This understanding of "Face" the Kabah is IMPORTANT. We will consider
three cases:
2A. When we can see the Kabah.
2B. When we are just beyond seeing the Kabah,
but we are not too far from the place from where the Kabah can be seen.
2C. When we are quite far from the Kabah (the Kabah is not visible even if
we travel towards it for a long time).
2A. When we can see the Kabah.
When we can see the Kabah, "Facing the Kabah" means being able to look directly at
the Kabah, with our face perpendicular to the line of sight, the line of sight
being from our face to the Kabah. It is IMPORTANT to note that this also means
that if we are at some distance from the Kabah (the Kabah is still clearly
visible in front of us) and IF we are "Facing the Kabah", then if we TRAVEL
WITHOUT TURNING, in the direction we are facing, we can finally touch the Kabah.
Hence, the travel has to be without any turning towards the right or towards the
left, and if we are facing the Kabah, we will be able to finally touch the
Kabah.
***************************************************
* The IMPORTANT point is "TRAVEL WITHOUT TURNING" *
***************************************************
2B. When we are just beyond seeing the Kabah, but we are not too far from
the place from where the Kabah can be seen.
In this situation, we start from a place where we can see the Kabah, and while
facing the Kabah, walk straight backwards (without turning) for a short
distance, so that the Kabah is now not visible. In this section, we are assuming
that there are no walls between us and the Kabah. It is only the curvature of
the round earth that has made the Kabah to disappear from view when we move
backwards (without turning) for the short distance from the place where the
Kabah was visible. The important point to note here is that, if we TRAVEL
WITHOUT TURNING from the place where the Kabah cannot be seen, and IF we are
really "Facing the Kabah", then we will be able to finally touch the Kabah.
Please note that the "TRAVEL IS WITHOUT TURNING" !!!
Another extension is that if the Kabah is not directly visible
(as stated in this section, the Kabah is just beyond the curved horizon),
and we are "Facing the Kabah", and if there is an imaginary tall vertical rod
at the center of the Kabah with the top of this
vertical rod visible in our line of sight, we are then still "Facing the Kabah".
This extension is used at the times when the Sun is directly above the Kabah,
then the direction to the Kabah would be the direction towards the Sun, if the
Sun was visible.
Due to the revolution of the Earth around the Sun, the Sun is
"above" the Kabah only two times in a year. The actual time varies slightly from
year to year because of the addition of a day (in February) in a leap year.
Utilizing the Sun is presented in a companion electronic article
"WHEN IS THE SUN ABOVE KABAH ?"
and can also be electronically viewed at the same homepage address mentioned above.
The conclusion of that article is that the Sun is above Kabah only two times in a year.
1. May 28 at 9:18 am (UT), that is 12:18 pm local Makkah time, and
2. July 15 at 9:27 am (UT), that is 12:27 pm local Makkah time.
2C. When we are quite far from the Kabah (the Kabah is not visible even if
we travel towards it for a long time).
The criteria that we are truly "Facing the Kabah", in this case, is an extension of
case (B), explained above.
Again, IF we are really "Facing the Kabah", and if we TRAVEL WITHOUT TURNING,
we should be able to finally touch the Kabah.
Please note that the "TRAVEL IS WITHOUT TURNING" !!!
3. Determining "true" direction of STRAIGHT TRAVEL (WITHOUT TURNING).
Properties of Latitudes and Longitudes on a "spherical" earth.
Let us consider TRAVEL WITHOUT TURNING. Considering the Earth as a "round sphere",
we know that if we "Travel Without Turning" we should be able to RETURN TO THE
STARTING POINT, when we have traveled around the Earth.
[The "round earth" approximation for the earth causes an error of approximately
only one degree, in the direction of the Kabah, from any point on the earth.
The more precise approximation is of an ellipsoid, that is, an oblate spheroid.]
"Travel Without Turning" on a round sphere would also automatically imply that the
path is along a "Great Circle". A Great Circle is the circle formed, on the surface
of the sphere, by the intersection of a sphere with a plane passing through the center
of the sphere.
This Great Circle path would also automatically be the shortest distance between
any two points (on the Great Circle) on the surface of the earth.
Some simple explanations of longitudes, latitudes, North, South, East,
and West are now presented. The explanations are kept simple so that the main
concepts can be easily understood. Hence the "round earth" model has been
adopted for the explanations.
LONGITUDES ARE CONSTANT DIAMETER CIRCLES passing through both the North and the
South Poles. All the longitudes are automaticaly
Great Circles. All the longitudes "point" towards a pole, either the North Pole
or the South Pole.
Hence, THE LONGITUDES ARE NOT PARALLEL TO EACH OTHER, since
they converge towards a Pole (either the North or the South Pole). When the
places are closer to the poles, the convergence of the longitudes is more
apparant.
All longitudes at the Poles intersect at the pole, hence the
longitudes are NOT parallel !
[The only exception is for points on the equator,
where the longitudes are parallel to each other and they point towards the North
Star. Hence, North and South directions are parallel to each other only for
points on the equator.]
This implies that the NORTH DIRECTIONS ARE DIFFERENT
(NOT PARALLEL) AT DIFFERENT PLACES !!! Hence, the other directions (East, West,
and South) are ALSO different at different places. That also implies that East
at one place is not parallel to East at another place. [It is to be noted that
even on the equator, East at one place is NOT parallel to East at another place.
This is because of the curvature of the round earth.]
LATITUDES ARE VARIABLE
DIAMETER CIRCLES which are parallel to the equator. The largest diameter of a
latitude circle is that of the Equator (zero latitude). The diameters of the
latitude circles decreases as the latitudes approach the poles (North Pole or
South Pole). The latitude circle at the pole has zero diameter. Of all the
latitudes, only the equator is a Great Circle.
If we travel WITHOUT TURNING along the equator, we would reach the starting point
when we have gone around the world.
If we travel along a line of constant latitude, which is NOT the equator,
we have to be CONTINUOUSLY TURNING to be on the line of constant latitude.
This is easily evident if we take a latitude close to the North Pole.
This line of constant latitude, near the pole, would be a circle. Hence, to
travel along the circle (line of constant latitude) we would have to be
continuously turning !!!
If, on the other hand, we initiated travel along a line
of constant latitude and we travel without turning, then we would automatically
no longer be along the line of constant latitue !
The direction of travel is usually indicated as an "Azimuth".
An Azimuth is the angle measured in degrees
between a base line from the point of interest (usually the line pointing North)
to another line from the point of interest. The angle is usually measured in the
clockwise direction (from the local North).
It is IMPORTANT to note that the
Azimuth is measured from the North direction AND again it is important to
remember that the North directions are NOT parallel to each other at differnet
points of interest. [The only exception is for points on the equator.]
This leads to an IMPORTANT CONCLUSION.
IF A PERSON TRAVELS WITHOUT TURNING, then THE
AZIMUTH of the direction of travel, at different points along the travel, WOULD
GENERALLY CHANGE CONTINUOUSLY ! [The exeptions are for travel along a longitude
or along the equator. For travel along a longitude, the individual is traveling
either North or South. For travel along the equator, the individual is traveling
either East or West.]
4. The INCORRECT "RHUMB-LINE" DIRECTION OF TRAVEL, REQUIRES CONTINUOUS TURNING
(continuous corrections to direction of travel).
Properties of a Mercator Projection,
where Rhumb-Lines are projected as Straight Lines.
Now let us consider TRAVEL WITH TURNING. This would be the "Rhumb-line" travel
which requires CONTINUOUS TURNING from the start to the finish. In the olden
days, sea travel was done with the aid of stars and the magnetic compass. The
magnetic compass gave an approximation to the true North direction. The
approximation is because of the difference between the true north and the
magnetic north. An easy way to determine the direction of travel (but with
continuous turning) was found by adopting a special map projection which uses
the North direction (approximately indicated by the magnetic compass). This
special map projection is the Mercator Projection.
The Mercator projection has
the property that when any two points on the Mercator projection map is joined
with a straight line, the travel path between them is an "apparant straight
line" with constant Azimuth, but THE TRAVEL REQUIRES CONTINUOUS TURNING TO
MAINTAIN THE CONSTANT AZIMUTH. It was a small price to pay, for the additional
longer travel path, that required continuous turning, as compared to maintaining
a simple constant Azimuth direction, that did not require constant calculations
to determine azimuthal direction of travel.
We also noted that the North
directions were different at different places (not parallel to each other).
The direction of the "apparant straight line" of a Mercator map is also called the
"Rhumb-line" direction. This is the "constant direction" line. The "constant
direction" implies that travel along a Rhumb-line would have a constant Azimuth
(angle from the changing North direction). Travel along the "aparant straight
line" indicated on a Mercator map is NOT A TRAVEL WITHOUT CONTINUOUS TURNING.
The only exceptions are for travel along a longitude or along the equator. In
these exceptions, the "Rhumb-line" direction is also the great circle direction
and hence there is no turning while traveling along points on the same longitude
or for points on the equator.
It is interesting to note that latitudes are showm
as horizontal straight lines on a Mercator map. We know from the previous
section on lines of constant latitude that we have to turn continuously to
travel along a latitude. Hence, traveling along an "apparant horizontal straight
line" (other than the equator) on the Mercator map is actually traveling with
continuous turning !!
5. Examples of places at different distances from Kabah.
We will be considering some examples for determining the direction of Kabah.
5A. Traveling from a point North of Kabah, on the Longitude through Kabah.
5B. Traveling from a point North of Kabah, from beyond the North Pole.
5A. Traveling from a point North of Kabah, on the Longitude through Kabah.
In this example, let us approximate (for the sake of discussion) the longitude of
Kabah as 40 Degrees East of Greenwich (39 deg 49 min is more precise). We know
the approximate latitude of Kabah to be 21 Degrees North of the Equator (21 deg
26 min is more precise).
If we stand at a point which has a greater latitude
than Kabah (>21 deg), and on the same longitude (40 deg E) as Kabah, then in
order to "Face the Kabah" we would have to face directly South. This would
continue until the latitude is 90 deg North (North Pole) where, to "Face the
Kabah" we would still have to face due South.
Now, an interesting extension
takes place. Suppose we are standing at longitude 40 deg E and latitude 89.999
deg N (close to the North Pole), and "Facing the Kabah", that is facing due
south, then when we TRAVEL WITHOUT TURNING in the direction we are facing, we
would be able to finally touch the Kabah.
5B. Traveling from a point North of Kabah, from beyond the North Pole.
In this example, let us start from the longitude 40 deg E (of Kabah) and at the North
Pole. The direction is due South for the Kabah, as mentioned above. Now, while
"Facing Kabah" we move backward a few steps, without turning, then we would be
on the longitude 140 deg W (180 - 40 = 140 deg). We are still "Facing Kabah"
since we have NOT turned while steping (traveling) backwards, but our direction
is due NORTH, since the North Pole would be a few steps ahead of us, in the
direction we are facing, which is also the direction for the Kabah, since we did
not turn !
This is an IMPORTANT conclusion:
There are POINTS on the earth THAT
ARE AT A LATITUDE NORTH OF THE KABAH AND THE DIRECTION TO FACE FOR THE KABAH
WOULD BE NORTH AGAIN (not south) !!
This has been shown for points on the
longitude 140 deg West (which is an extension of the longitude of Kabah, 40 deg
E, beyound the North Pole).
Hence, IT IS INCORRECT TO GENERALIZE THAT FOR ALL
POINTS THAT ARE AT A LATITUDE NORTH OF KABAH (latitude greater than 21 deg
North), THE DIRECTION FOR KABAH FROM ALL THESE POINTS WOULD BE IN THE SOUTHERLY
DIRECTION !
6. Qibla direction for Lawrence, KS (USA), calculated result.
The correct direction for Lawrence, KS is calculated from the folowing:
Coordinates of Lawrence: 38 deg 58 min 18 sec North, ( = 38.971666)
95 deg 14 min 06 sec West. ( = 95.235)
Coordinates of Makkah:
21 deg 27 min North, ( = 21.45) .
39 deg 49 min East. ( = 39.816666)
Let us consider a spherical triangle with the North Pole at vertex A,
the Kabah at vertex B, and
the City at vertex C.
The angles at the vertices are denoted by the UPPERCASE LETTERS A, B, and C.
The sides of the spherical triange, opposite to the vericies, are denoted by the
lowercase letters a, b, and c.
The compliment (90 deg minus the latitude) of the latitude
of Makkah is the side b, and the compliment of the latitude of the City is side
c. Therefore, side b is equal to 51.028333, and side c is equal to 68.55.
The angle at the North Pole, ANGLE A is equal to 135.051666 deg ( = 95.235 +
39.816666).
Angle C is the required direction towards the Kabah.
Hence the direction for the Kabah is ANGLE C, which is given by:
ANGLE C = TAN [ SIN A / ( sin b cot c - cos b COS A ) ]
= TAN [SIN 135.051666 / (sin 51.028333 cot 68.55 - cos 51.028333 COS 135.051666)]
ANGLE C = 43.2655287 deg East of North (Spherical Trigonometry)
= 43 deg 15 min 55.9 sec East of North (Spherical Trigonometry)
ANGLE C = 43 deg 49 min 10.5 sec East of North (Ellipsoid Model)
ANGLE C = 46.7344713 deg NORTH of East (= 90 - 43.2655287)
= 46 deg 44 min 04.1 sec NORTH of East (Spherical Trigonometry)
Direction for Kabah from True North or True East for Lawrence, KS is:
43 deg 49 min 10.5 sec East of True North (more precise Ellipsoid Model)
43 deg 15 min 55.9 sec East of True North (Spherical Trigonometry)
46 deg 10 min 49.5 sec NORTH of True East (more precise Ellipsoid Model)
46 deg 44 min 04.1 sec NORTH of True East (Spherical Trigonometry)
Magnetic Variations for Lawrence, KS (Ref.3):
The Magnetic Variation is:
5.7 deg East (for Nov 1985)
5 deg 42 min East (for Nov 1985)
The Annual Variation is:
7.1 min West (from Nov 1985)
The Total 12 year Variation is:
85.2 min West (1997 to 1985)
1 deg 25.2 min West (from Nov 1985)
The Total Magnetic Variation is:
4 deg 16.8 min East (for Nov 1997)
4 deg 16 min 48 sec (for Nov 1997)
Direction for Kabah from Magnetic North or Magnetic East for Lawrence, KS is:
39 deg 32 min 22.5 sec East of Magnetic North (more precise Ellipsoid Model)
38 deg 59 min 07.9 sec East of Magnetic North (Spherical Trigonometry)
50 deg 27 min 37.5 sec NORTH of Magnetic East (more precise Ellipsoid Model)
51 deg 00 min 52.1 sec NORTH of Magnetic East (Spherical Trigonometry)
The approximate radius of the earth as 3960 miles. The distance of
Kabah from Lawrence, KS is approximately 73.61 degrees. The distance of Kabah
from Lawrence, KS is approximatley 5,090 miles.
If we travel, WITHOUT TURNING, from Lawrence, KS to Kabah for 5,090 miles
along the initial CORRECT (Great Circle) direction of:
43 deg 15 min 55.9 sec East of True North (Spherical Trigonometry),
the half-way point would be at:
Latitude of 30.2108 deg North = 30 deg 12 min 39 sec North
Longitude of 27.7092 deg West = 27 deg 42 min 33 sec West and
the final destination point (Makkah) would be at:
Latitude of 21.45 deg North = 21 deg 27 min North
Longitude of 39.8167 deg East = 39 deg 49 min West
If we travel, WITHOUT TURNING, from Lawrence, KS to Kabah for 5,090 miles
along the initial INCORRECT (Rhumb-Line) direction of:
98 deg 44 min 13.3 sec East of True North (Mercator Projection),
the half-way point would be at:
Latitude of 21.3777 deg North = 21 deg 22 min 40 sec North
Longitude of 59.2702 deg West = 59 deg 16 min 13 sec West and
the final destination point (in the Atlantic Ocean) would be at:
Latitude of 3.7837 deg North = 3 deg 47 min 13 sec North
Longitude of 23.3055 deg East = 23 deg 18 min 20 sec West
7. Conclusions for USA/Canada.
For most of USA/Canada the direction for prayers is towards the NORTH-OF-EAST.
The actual direction can be easily calculated. This direction of travel,
WITHOUT ANY TURNING, would lead us directly to the Kabah.
The incorrect Rhumb-Line direction, from the Mercator Map Projection, gives
a direction that requires continuous turning during the travel even though the
azimuth of the direction of travel is constant. The continuous turning in the
Rhumb-Line travel is due to the not parallel (different) North directions from
different points on the path of travel.
REFERENCES:
1. QuranBase Search on "Turn" and "Face", QBase by Sound Vision (ICNA)
2. HadithBase Search on Qibla, HBase by Sound Vision (ICNA)
3. "Direction for Kabah (Mathematical) - from anywhere", by Dr.Mohib.N.Durrani