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I know we're supposed to face towards Jerusalem when praying/davening. For most of us in the Europe or the Western Hemisphere, we're used to facing "Mizrach", east.

How precise should we be? If I'm in Hotzenplotz and a straight line to Jerusalem is 5 degrees south of east, do I just face east, or 5 degrees south of east?

Similarly, if my house isn't strictly compass-oriented (e.g. it faces an avenue in Manhattan, 29 degrees east of north), do I daven towards a corner, or just pick the wall in the room that's most oriented towards Jerusalem?

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It seems pretty universal that this question only applies outside of a בית כנסת and that inside one the rule is to face the front/ארון קודש. I once asked a local פוסק about which way to face in a V-shaped shul and he instructed me to be perpendicular to my row of seats. –  WAF Nov 18 '10 at 15:09
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@WAF I don't know if everyone agrees with that. In the YU B"M, don't they face East, even though the Aron is on a different wall? I've heard R' Rakeffet noting this and saying that in his day, everyone faced the Aron. –  Isaac Moses Nov 18 '10 at 15:52
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See the discussion here: vbm-torah.org/archive/halak67/18halak.htm –  Dave Nov 18 '10 at 16:19
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4 Answers

Practically speaking, there is no difference between "east" and "5 degrees south of east." You probably have a variation of 20 degrees just depending on where your siddur is on the table, or the way you "shukkel." One prominent posek said (half-jokingly) about this topic: לא ניתנה תורה למהנדסים - The Torah was not given to engineers. Therefore, you're probably safe if you aim for the nearest half-quadrant (e.g., N, NE, E, SE, etc.). With regard to a house that does not have a wall facing Jerusalem, it would depend how much of a discrepancy there is. It would only make sense to face a corner if there is a difference of more than 20 degrees or so, as mentioned above. This seems to be the "common custom" in shuls worldwide.

Two more points: (1) There are differences of opinion as to whether one should face towards the direction that would be indicated by a standard Mercator Projection map, or rather following a Great Circle route, which is really a "straight line" towards Jerusalem. The difference in NY is more than 40 degrees! See here and here for good summaries of this topic. (2) A compass is not a precise way of determining direction, since the Earth's magnetic field is not completely parallel to its axis. There is an offset that depends on one's location, and that varies over time due to activity in the earth's core. It is therefore better to use a map with a "true north" indicator.

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I heard from a former resident of South Africa recently that where he davened they basically faced north but called it "מזרח". –  WAF Nov 18 '10 at 15:06
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לא ניתנה תורה למהנדסים. I think the Arabic "al-handasa" meant geometry, and Hebrew eventually picked up the word as "engineering." See Sefer HaChinuch on לא תונו איש את עמיתו, a good Jew needs to know geometry so he can buy/sell land by its actual area, even if it's not shaped like a rectangle. –  Shalom Nov 18 '10 at 17:00
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Sefer HaChinuch says you need to know "al-handasa." –  Shalom Nov 18 '10 at 17:00
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@Shalom - the posek I quoted probably meant it in its modern sense, but either way the point is the same: Ordinary people, even those who can calculate the area of a triangle, are generally clueless WRT spherical trigonometry, so the Torah apparently requires only a good approximation. –  Dave Nov 18 '10 at 18:09
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Dave, agreed. Just trying to be (too) clever. –  Shalom Nov 18 '10 at 18:47
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To expand on Dave's points a bit:

R' Shneur Zalman of Liadi points out in his siddur that the practice of facing eastward goes back to when the major (Ashkenazic) center of Jewish settlement was in France, which is west of Jerusalem. "In our countries [Poland and Russia], which are much further north," he says that the angle should be SSE - a heading of about 150 degrees.

From this we see two things:

  1. The angle indeed doesn't have to be precise - after all, going due west from Jerusalem would get you to North Africa, not France.

  2. On the other hand, you should try to be at least somewhat accurate - the difference between SE (135 degrees) and his recommended 150 degrees is significant. (In his Shulchan Aruch (94:2) he goes so far as to say that "the calculation is easy for those who are familiar with spherical trigonometry" - implying that someone, at least, ought to be making such calculations.)

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It is clear from the Shulchan Aruch HaRav that he uses the Great Circle calculation. Note that the Great Circle route from Paris would only be about 22 degrees south of east. –  Dave Nov 18 '10 at 16:44
    
Wouldn't it be north of East, since both Paris and the Har Habayit are in the Northern Hemisphere? –  Isaac Moses Nov 18 '10 at 16:54
    
Jerusalem is at a lower latitude than Paris, so the direction is towards south. See this map: gcmap.com/… –  Dave Nov 18 '10 at 18:14
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In the NY area the GC route is 54 degrees from north, whereas the "traditional" direction is 96 degrees (i.e., 6 degrees south of east). My comment about Jerusalem being at a lower latitude than Paris was only because they are not separated by enough degrees of longitude to change the direction to northeast. But you are correct about the US and other places farther from EY. –  Dave Nov 18 '10 at 20:00
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BTW, Myzemanim.com has a calculator that computes the proper direction for any location. –  Dave Nov 18 '10 at 20:01
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Rabbi Gissingers Shul in Lakewood faces North. Rabbi Gissinger holds that you should face the way the flights take off towards Israel which in the NY/NJ area is North.

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In other words -- the Great Circle route. –  Dave Nov 18 '10 at 20:02
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Responding from another angle (sorry) to the question of how much accuracy is called for: Shulchan Aruch Orach Chayim 94:1, q.v., indicates that those outside Israel should face Israel (not Jerusalem) and merely have more precise coordinates in mind.

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True, though I think that's just because when you're outside Israel, that doesn't really make much of a difference. Using the calculator that Dave linked to in his comment, if you're in Paris (CDG), the difference between facing Kiryat Shemona (KSW) and Eilat (ETH) is only about six degrees. –  Alex Nov 18 '10 at 19:01
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@Alex: True, but when you're in Amman.... –  msh210 Nov 18 '10 at 19:15
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