Zone1 which direction does a priest face at the altar?

[Zebra]

to the east!?

or to the church goers?

 

[frigidweirdo]

to the east!?

or to the church goers?

Depends where the alter boy is, I guess.

 

[gtopa1]

to the east!?

or to the church goers?

Towards the church goers unless it's a traditional mass at the actual altar; not some table.

Greg

 

[Zebra]

to the east!?

or to the church goers?

asking again

 

[frigidweirdo]

asking again

You mean you don't like my answer?

 

[Zebra]

any other?

 

[Godboy]

to the east!?

or to the church goers?

I cant imagine a more boring question than this. What the fuck is with your threads? They are always about the most useless possible thing a human can discuss.

 

[BULLDOG]

to the east!?

or to the church goers?

In the Baptist church I grew up in, he always looked toward the busty young woman with a short skirt sitting in the front row.

 

[Hellokitty]

to the east!?

or to the church goers?

Why do you ask?

 

[BULLDOG]

Jerry Fallwell always faced toward his wife and the pool boy having sex. It was the only way he could keep the camera focused.

 

[Zebra]

Why do you ask?

because there are different rules or sysstems

 

[gtopa1]

This is very important wrt Islam.

The qibla (Arabic: قِبْلَة, lit. 'direction') is the direction towards the Kaaba in the Sacred Mosque in Mecca, which is used by Muslims in various religious contexts, particularly the direction of prayer for the salah. In Islam, the Kaaba is believed to be a sacred site built by prophets Abraham and Ishmael, and that its use as the qibla was ordained by God in several verses of the Quran revealed to Muhammad in the second Hijri year. Prior to this revelation, Muhammad and his followers in Medina faced Jerusalem for prayers. Most mosques contain a mihrab (a wall niche) that indicates the direction of the qibla.

The qibla is also the direction for entering the ihram (sacred state for the hajj pilgrimage); the direction to which animals are turned during dhabihah (Islamic slaughter); the recommended direction to make du'a (supplications); the direction to avoid when relieving oneself or spitting; and the direction to which the deceased are aligned when buried. The qibla may be observed facing the Kaaba accurately (ayn al-ka'ba) or facing in the general direction (jihat al-ka'ba). Most Islamic scholars consider that jihat al-ka'ba is acceptable if the more precise ayn al-ka'ba cannot be ascertained.

The most common technical definition used by Muslim astronomers for a location is the direction on the great circle—in the Earth's Sphere—passing through the location and the Kaaba. This is the direction of the shortest possible path from a place to the Kaaba, and allows the exact calculation (hisab) of the qibla using a spherical trigonometric formula that takes the coordinates of a location and of the Kaaba as inputs (see formula below). The method is applied to develop mobile applications and websites for Muslims, and to compile qibla tables used in instruments such as the qibla compass. The qibla can also be determined at a location by observing the shadow of a vertical rod on the twice-yearly occasions when the Sun is directly overhead in Mecca—on 27 and 28 May at 12:18 Saudi Arabia Standard Time (09:18 UTC), and on 15 and 16 July at 12:27 SAST (09:27 UTC).

Before the development of astronomy in the Islamic world, Muslims used traditional methods to determine the qibla. These methods included facing the direction that the companions of Muhammad had used when in the same place; using the setting and rising points of celestial objects; using the direction of the wind; or using due south, which was Muhammad's qibla in Medina. Early Islamic astronomy was built on its Indian and Greek counterparts, especially the works of Ptolemy, and soon Muslim astronomers developed methods to calculate the approximate directions of the qibla, starting from the mid-9th century. In the late 9th and 10th centuries, Muslim astronomers developed methods to find the exact direction of the qibla which are equivalent to the modern formula. Initially, this "qibla of the astronomers" was used alongside various traditionally determined qiblas, resulting in much diversity in medieval Muslim cities. In addition, the accurate geographic data necessary for the astronomical methods to yield an accurate result was not available before the 18th and 19th centuries, resulting in further diversity of the qibla. Historical mosques with differing qiblas still stand today throughout the Islamic world. The spaceflight of a devout Muslim, Sheikh Muszaphar Shukor, to the International Space Station (ISS) in 2007 generated a discussion with regard to the qibla direction from low Earth orbit, prompting the Islamic authority of his home country, Malaysia, to recommend determining the qibla "based on what is possible" for the astronaut.

Theoretical basis: the great circle[edit]​

The great circle passing through two points (A and B) indicates the shortest path (bold) between them.
A great circle, also called the orthodrome, is any circle on a sphere whose centre is identical to the centre of the sphere. For example, all lines of longitude are great circles of the Earth, while the equator is the only line of latitude that is also a great circle (other lines of latitude are centered north or south of the centre of the Earth).[22] The great circle is the theoretical basis in most models that seek to mathematically determine the direction of the qibla from a locality. In such models, the qibla is defined as the direction of the great circle passing through the locality and the Kaaba.[23][24] One of the properties of a great circle is that it indicates the shortest path connecting any pair of points along the circle—this is the basis of its use to determine the qibla. The great circle is similarly used to find the shortest flight path connecting the two locations—therefore the qibla calculated using the great circle method is generally close to the direction of the locality to Mecca.[25] As the ellipsoid is a more accurate figure of the Earth than a perfect sphere, modern researchers have looked into using ellipsoidal models to calculate the qibla, replacing the great circle by the geodesics on an ellipsoid. This results in more complicated calculations, while the improvement in accuracy falls well within the typical precision of the setting out of a mosque or the placement of a mat.[26] For example, calculations using the GRS 80 ellipsoidal model yields the qibla of 18°47′06″ for a location in San Francisco, while the great circle method yields 18°51′05″.[27]

Calculations with spherical trigonometry[edit]​

The great circle model is applied to calculate the qibla using spherical trigonometry—a branch of geometry that deals with the mathematical relations between the sides and angles of triangles formed by three great circles of a sphere (as opposed to the conventional trigonometry which deals with those of a two-dimensional triangle).

For example, the qibla from the city of Yogyakarta, Indonesia, can be calculated as follows. The city's coordinates, 𝜙

, are 7.801389°S, 110.364444°E, while the Kaaba's coordinates, 𝜙𝑄

, are 21.422478°N, 39.825183°E. The longitude difference Δ𝐿

is (110.364444 minus 39.825183) 70.539261. Substituting the values into the formula obtains an answer of approximately 295°, or 25° north of west.[28]
If a location 𝑂

, the Kaaba 𝑄

, and the north pole 𝑁

form a triangle on the sphere of the Earth, then the qibla is indicated by 𝑂𝑄

, which is the direction of the great circle passing through both 𝑂

and 𝑄

. The qibla can also be expressed as an angle, ∠𝑁𝑂𝑄

(or ∠𝑞

), of the qibla with respect to the north, also called the inhiraf al-qibla. This angle can be calculated as a mathematical function of the local latitude 𝜙

, the latitude of the Kaaba 𝜙𝑄

, and the longitude difference between the locality and the Kaaba Δ𝐿

.[29] This function is derived from the cotangent rule which applies to any spherical triangle with angles 𝐴

, 𝐵

, 𝐶

and sides 𝑎

, 𝑏

, 𝑐

:



Greg

 

[gtopa1]

Had to split it.


cos⁡𝑎cos⁡𝐶=cot⁡𝑏sin⁡𝑎−cot⁡𝐵sin⁡𝐶

[30]

Applying this formula in the spherical triangle △𝑁𝑂𝑄

(substituting 𝐵=∠𝑞=∠𝑁𝑂𝑄

)[30] and applying trigonometric identities obtain:

tan⁡𝑞=sin⁡Δ𝐿sin⁡𝜙cos⁡Δ𝐿−cos⁡𝜙tan⁡𝜙𝑄

, or
𝑞=arctan⁡(sin⁡Δ𝐿sin⁡𝜙cos⁡Δ𝐿−cos⁡𝜙tan⁡𝜙𝑄)

[29]

This formula was derived by modern scholars, but equivalent methods have been known to Muslim astronomers since the 9th century (3rd century AH), developed by various scholars, including Habash al-Hasib (active in Damascus and Baghdad c. 850), Al-Nayrizi (Baghdad, c. 900),[31] Ibn Yunus (10th–11th century),[32] Ibn al-Haytham (11th century),[32] and Al-Biruni (11th century).[33] Today spherical trigonometry also underlies nearly all applications or websites which calculate the qibla.[23]

When the qibla angle with respect to the north, ∠𝑞

, is known, true north needs to be known to find the qibla in practice. Common practical methods to find it include the observation of the shadow at the culmination of the sun—when the sun crosses exactly the local meridian. At this point, any vertical object would cast a shadow oriented in the north–south direction. The result of this observation is very accurate, but it requires an accurate determination of the local time of culmination as well as making the correct observation at that exact moment.[34] Another common method is using the compass, which is more practical because it can be done at any time; the disadvantage is that the north indicated by a magnetic compass differs from true north.[16][35] This magnetic declination can measure up to 20°, which can vary in different places on Earth and changes over time.[16]

Shadow observation[edit]​

Main article: Qibla observation by shadows
Twice a year, the Sun passes directly above the Kaaba, allowing the observation of its direction from the shadow of a vertical object.
As observed from Earth, the Sun appears to "shift" between the Northern and Southern Tropics seasonally; additionally, it appears to move from east to west daily as a consequence of the Earth's rotation. The combination of these two apparent motions means that every day the Sun crosses the meridian once, usually not precisely overhead but to the north or to the south of the observer. In locations between the two tropics—latitudes lower than 23.5° north or south—at certain moments of the year (usually twice a year) the Sun passes almost directly overhead. This happens when the Sun crosses the meridian while being at the local latitude at the same time.[36]

The city of Mecca is among the places where this occurs, due to its location at 21°25′ N. It occurs twice a year, firstly on 27/28 May at about 12:18 Saudi Arabia Standard Time (SAST) or 09:18 UTC, and secondly on 15/16 July at 12:27 SAST (09:27 UTC).[36][37]https://en.wikipedia.org/wiki/Qibla#cite_note-39 As the sun reaches the zenith of the Kaaba, any vertical object on earth that receives sunlight cast a shadow that indicates the qibla (see picture).[36] This method of finding the qibla is called rasd al-qiblat ("observing the qibla").[38][28] Since night falls on the hemisphere opposite of the Kaaba, half the locations on Earth (including Australia as well as most of the Americas and the Pacific Ocean) cannot observe this directly.[39] Instead, such places observe the opposite phenomenon when the Sun passes above the antipodal point of the Kaaba (in other words, the Sun passes directly underneath the Kaaba), causing shadows in the opposite direction from those observed during rasd al-qiblat.[36][40] This occurs twice a year, on 14 January 00:30 SAST (21:30 UTC the previous day) and 29 November 00:09 SAST (21:09 UTC the previous day).[41] Observations made within five minutes of the rasd al-qiblat moments or its antipodal counterparts, or at the same time of the day two days before or after each event, still show accurate directions with negligible difference.[36][37]

On the world map[edit]​

A map generated using the Craig retroazimuthal projection centered on Mecca. Unlike most map projections, it preserves the direction from any other point on the map to the center.
Spherical trigonometry provides the shortest path from any point on Earth to the Kaaba, even though the indicated direction might seem counterintuitive when imagined on a flat world map. For example, the qibla from Alaska obtained through spherical trigonometry is almost due north.[23] This apparent counter-intuitiveness is caused by projections used by world maps, which by necessity distort the surface of the Earth. A straight line shown by the world map in using the Mercator projection is called the rhumb line or the loxodrome, which is used to indicate the qibla by a minority of Muslims.[42][c] It can result in a dramatic difference in some places; for example, in some parts of North America the flat map shows Mecca in the southeast while the great circle calculation shows it to the northeast.[23] In Japan the map shows it to the southwest, while the great circle shows it to the northwest.[43] The majority of Muslims, however, follow the great circle method.[23]

A retroazimuthal projection is any map projection which preserves the angular direction (the azimuth) of the great circle path from any point of the map to a point selected as the center of the map. The initial purpose of its development was to help finding the qibla, by choosing the Kaaba as the center point.[44] The earliest surviving works using this projection were two astrolabe-shaped brass instruments created in 18th-century Iran.[45] They contain grids covering locations between Spain and China, label the locations of major cities along with their names, but do not show any coastline.[45][46] The first of the two was discovered in 1989; its diameter is 22.5 centimetres (8.9 in) and it has a ruler with which one can read the direction of Mecca from the markings on the instrument's circumference, and the distance to Mecca from the markings on the ruler.[46][d] Only the second one is signed by its creator, Muhammad Husayn.[47] The first formal design of a retroazimuthal projection in the Western literature is the Craig projection or the Mecca projection, created by the Scottish mathematician James Ireland Craig, who worked at the Survey Department of Egypt, in 1910.[48] His map is centered in Mecca and its range is limited to show the predominantly Muslim lands.[48] Extending the map further than 90° in longitude from the center will result in crowding and overlaps.[49][50]

Traditional methods[edit]​

Historical records and surviving old mosques show that throughout history the qibla was often determined by simple methods based on tradition or "folk science" not based on mathematical astronomy. Some early Muslims used due south everywhere as the qibla, literally following Muhammad's instruction to face south while he was in Medina (Mecca is due south of Medina). Some mosques as far away as al-Andalus to the west and Central Asia to the east face south, even though Mecca is nowhere near that direction.[51] In various places, there are also the "qiblas of the companions" (qiblat al-sahaba), those which were used there by the Companions of the Prophet—the first generation of Muslims, who are considered role models in Islam. Such directions were used by some Muslims in the following centuries, side by side with other directions, even after Muslim astronomers used calculations to find more accurate directions to Mecca. Among the directions described as the qiblas of the companions are due south in Syria and Palestine,[52] the direction of the winter sunrise in Egypt, and the direction of the winter sunset in Iraq.[53] The direction of the winter sunrise and sunset are also traditionally favoured because they are parallel to the walls of the Kaaba.[54]

Development of methods[edit]​

Pre-astronomy[edit]​

The determination of qibla has been an important problem for Muslim communities throughout history. Muslims are required to know the qibla to perform their daily prayers, and it is also needed to determine the orientation of mosques.[55] When Muhammad lived among the Muslims in Medina (which, like Mecca, is also in the Hejaz region), he prayed due south, according to the known direction of Mecca. Within the few generations after Muhammad's death in 632, Muslims had reached places far away from Mecca, presenting the problem of determining the qibla in new locations.[56] Mathematical methods based on astronomy would develop only at the end of the 8th century or the beginning of the 9th, and even then they were not initially popular. Therefore, early Muslims relied on non-astronomical methods.[57]

There was a wide range of traditional methods in determining the qibla during the early Islamic period, resulting in different directions even from the same place. In addition to due south and the qiblas of the companions, the Arabs also knew a form of "folk" astronomy—called so by the historian of astronomy David A. King to distinguish it from conventional astronomy, which is an exact science—originating from pre-Islamic traditions.[53] It used natural phenomenon, including the observation of the Sun, the Moon, the stars, and wind, without any basis in mathematics. These methods yield specific directions in individual localities, often using the fixed setting and rising points of a specific star, the sunrise or sunset at the equinoxes, or at the summer or the winter solstices.[58] Historical sources record several such qiblas, for example: sunrise at the equinoxes (due east) in the Maghreb, sunset at the equinoxes (due west) in India, the origin of the north wind or the fixed location of the North Star in Yemen, the rising point of the star Suhayl (Canopus) in Syria, and the midwinter sunset in Iraq.[58] Such directions appear in texts of fiqh (Islamic jurisprudence) and texts of folk astronomy. Astronomers (aside from folk astronomers) typically do not comment on these methods, but they were not opposed by Islamic legal scholars.[59] The traditional directions were still in use when methods were developed to calculate the qibla more accurately, and they still appear in some surviving medieval mosques today.[52]

From Wiki

Who knew such a simple question would lead to spherical maths??

 

[Zebra]

Had to split it.


cos⁡𝑎cos⁡𝐶=cot⁡𝑏sin⁡𝑎−cot⁡𝐵sin⁡𝐶

[30]

Applying this formula in the spherical triangle △𝑁𝑂𝑄

(substituting 𝐵=∠𝑞=∠𝑁𝑂𝑄

)[30] and applying trigonometric identities obtain:

tan⁡𝑞=sin⁡Δ𝐿sin⁡𝜙cos⁡Δ𝐿−cos⁡𝜙tan⁡𝜙𝑄

, or
𝑞=arctan⁡(sin⁡Δ𝐿sin⁡𝜙cos⁡Δ𝐿−cos⁡𝜙tan⁡𝜙𝑄)

[29]

This formula was derived by modern scholars, but equivalent methods have been known to Muslim astronomers since the 9th century (3rd century AH), developed by various scholars, including Habash al-Hasib (active in Damascus and Baghdad c. 850), Al-Nayrizi (Baghdad, c. 900),[31] Ibn Yunus (10th–11th century),[32] Ibn al-Haytham (11th century),[32] and Al-Biruni (11th century).[33] Today spherical trigonometry also underlies nearly all applications or websites which calculate the qibla.[23]

When the qibla angle with respect to the north, ∠𝑞

, is known, true north needs to be known to find the qibla in practice. Common practical methods to find it include the observation of the shadow at the culmination of the sun—when the sun crosses exactly the local meridian. At this point, any vertical object would cast a shadow oriented in the north–south direction. The result of this observation is very accurate, but it requires an accurate determination of the local time of culmination as well as making the correct observation at that exact moment.[34] Another common method is using the compass, which is more practical because it can be done at any time; the disadvantage is that the north indicated by a magnetic compass differs from true north.[16][35] This magnetic declination can measure up to 20°, which can vary in different places on Earth and changes over time.[16]

Shadow observation[edit]​

Main article: Qibla observation by shadows
Twice a year, the Sun passes directly above the Kaaba, allowing the observation of its direction from the shadow of a vertical object.
As observed from Earth, the Sun appears to "shift" between the Northern and Southern Tropics seasonally; additionally, it appears to move from east to west daily as a consequence of the Earth's rotation. The combination of these two apparent motions means that every day the Sun crosses the meridian once, usually not precisely overhead but to the north or to the south of the observer. In locations between the two tropics—latitudes lower than 23.5° north or south—at certain moments of the year (usually twice a year) the Sun passes almost directly overhead. This happens when the Sun crosses the meridian while being at the local latitude at the same time.[36]

The city of Mecca is among the places where this occurs, due to its location at 21°25′ N. It occurs twice a year, firstly on 27/28 May at about 12:18 Saudi Arabia Standard Time (SAST) or 09:18 UTC, and secondly on 15/16 July at 12:27 SAST (09:27 UTC).[36][37]Qibla - Wikipedia As the sun reaches the zenith of the Kaaba, any vertical object on earth that receives sunlight cast a shadow that indicates the qibla (see picture).[36] This method of finding the qibla is called rasd al-qiblat ("observing the qibla").[38][28] Since night falls on the hemisphere opposite of the Kaaba, half the locations on Earth (including Australia as well as most of the Americas and the Pacific Ocean) cannot observe this directly.[39] Instead, such places observe the opposite phenomenon when the Sun passes above the antipodal point of the Kaaba (in other words, the Sun passes directly underneath the Kaaba), causing shadows in the opposite direction from those observed during rasd al-qiblat.[36][40] This occurs twice a year, on 14 January 00:30 SAST (21:30 UTC the previous day) and 29 November 00:09 SAST (21:09 UTC the previous day).[41] Observations made within five minutes of the rasd al-qiblat moments or its antipodal counterparts, or at the same time of the day two days before or after each event, still show accurate directions with negligible difference.[36][37]

On the world map[edit]​

A map generated using the Craig retroazimuthal projection centered on Mecca. Unlike most map projections, it preserves the direction from any other point on the map to the center.
Spherical trigonometry provides the shortest path from any point on Earth to the Kaaba, even though the indicated direction might seem counterintuitive when imagined on a flat world map. For example, the qibla from Alaska obtained through spherical trigonometry is almost due north.[23] This apparent counter-intuitiveness is caused by projections used by world maps, which by necessity distort the surface of the Earth. A straight line shown by the world map in using the Mercator projection is called the rhumb line or the loxodrome, which is used to indicate the qibla by a minority of Muslims.[42][c] It can result in a dramatic difference in some places; for example, in some parts of North America the flat map shows Mecca in the southeast while the great circle calculation shows it to the northeast.[23] In Japan the map shows it to the southwest, while the great circle shows it to the northwest.[43] The majority of Muslims, however, follow the great circle method.[23]

A retroazimuthal projection is any map projection which preserves the angular direction (the azimuth) of the great circle path from any point of the map to a point selected as the center of the map. The initial purpose of its development was to help finding the qibla, by choosing the Kaaba as the center point.[44] The earliest surviving works using this projection were two astrolabe-shaped brass instruments created in 18th-century Iran.[45] They contain grids covering locations between Spain and China, label the locations of major cities along with their names, but do not show any coastline.[45][46] The first of the two was discovered in 1989; its diameter is 22.5 centimetres (8.9 in) and it has a ruler with which one can read the direction of Mecca from the markings on the instrument's circumference, and the distance to Mecca from the markings on the ruler.[46][d] Only the second one is signed by its creator, Muhammad Husayn.[47] The first formal design of a retroazimuthal projection in the Western literature is the Craig projection or the Mecca projection, created by the Scottish mathematician James Ireland Craig, who worked at the Survey Department of Egypt, in 1910.[48] His map is centered in Mecca and its range is limited to show the predominantly Muslim lands.[48] Extending the map further than 90° in longitude from the center will result in crowding and overlaps.[49][50]

Traditional methods[edit]​

Historical records and surviving old mosques show that throughout history the qibla was often determined by simple methods based on tradition or "folk science" not based on mathematical astronomy. Some early Muslims used due south everywhere as the qibla, literally following Muhammad's instruction to face south while he was in Medina (Mecca is due south of Medina). Some mosques as far away as al-Andalus to the west and Central Asia to the east face south, even though Mecca is nowhere near that direction.[51] In various places, there are also the "qiblas of the companions" (qiblat al-sahaba), those which were used there by the Companions of the Prophet—the first generation of Muslims, who are considered role models in Islam. Such directions were used by some Muslims in the following centuries, side by side with other directions, even after Muslim astronomers used calculations to find more accurate directions to Mecca. Among the directions described as the qiblas of the companions are due south in Syria and Palestine,[52] the direction of the winter sunrise in Egypt, and the direction of the winter sunset in Iraq.[53] The direction of the winter sunrise and sunset are also traditionally favoured because they are parallel to the walls of the Kaaba.[54]

Development of methods[edit]​

Pre-astronomy[edit]​

The determination of qibla has been an important problem for Muslim communities throughout history. Muslims are required to know the qibla to perform their daily prayers, and it is also needed to determine the orientation of mosques.[55] When Muhammad lived among the Muslims in Medina (which, like Mecca, is also in the Hejaz region), he prayed due south, according to the known direction of Mecca. Within the few generations after Muhammad's death in 632, Muslims had reached places far away from Mecca, presenting the problem of determining the qibla in new locations.[56] Mathematical methods based on astronomy would develop only at the end of the 8th century or the beginning of the 9th, and even then they were not initially popular. Therefore, early Muslims relied on non-astronomical methods.[57]

There was a wide range of traditional methods in determining the qibla during the early Islamic period, resulting in different directions even from the same place. In addition to due south and the qiblas of the companions, the Arabs also knew a form of "folk" astronomy—called so by the historian of astronomy David A. King to distinguish it from conventional astronomy, which is an exact science—originating from pre-Islamic traditions.[53] It used natural phenomenon, including the observation of the Sun, the Moon, the stars, and wind, without any basis in mathematics. These methods yield specific directions in individual localities, often using the fixed setting and rising points of a specific star, the sunrise or sunset at the equinoxes, or at the summer or the winter solstices.[58] Historical sources record several such qiblas, for example: sunrise at the equinoxes (due east) in the Maghreb, sunset at the equinoxes (due west) in India, the origin of the north wind or the fixed location of the North Star in Yemen, the rising point of the star Suhayl (Canopus) in Syria, and the midwinter sunset in Iraq.[58] Such directions appear in texts of fiqh (Islamic jurisprudence) and texts of folk astronomy. Astronomers (aside from folk astronomers) typically do not comment on these methods, but they were not opposed by Islamic legal scholars.[59] The traditional directions were still in use when methods were developed to calculate the qibla more accurately, and they still appear in some surviving medieval mosques today.[52]

From Wiki

Who knew such a simple question would lead to spherical maths??

Is that all?