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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.to the east!?
or to the church goers?
asking againto the east!?
or to the church goers?
asking again
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.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.to the east!?
or to the church goers?
to the east!?
or to the church goers?
because there are different rules or sysstemsWhy do you ask?
Is that all?Had to split it.
cos𝑎cos𝐶=cot𝑏sin𝑎−cot𝐵sin𝐶[30]
Applying this formula in the spherical triangle △𝑁𝑂𝑄(substituting 𝐵=∠𝑞=∠𝑁𝑂𝑄)[30] and applying trigonometric identities obtain:
tan𝑞=sinΔ𝐿sin𝜙cosΔ𝐿−cos𝜙tan𝜙𝑄, or
𝑞=arctan(sinΔ𝐿sin𝜙cosΔ𝐿−cos𝜙tan𝜙𝑄)[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??