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”בקומו להתפלל, אם היה עומד בחוץ לארץ יחזיר פניו כנגד ארץ ישראל, ויכוין גם לירושלים ולמקדש ולבית קדשי הקדשים. היה עומד בארץ ישראל יחזיר פניו כנגד ירושלים, ויכוין גם למקדש ולבית קדשי הקדשים. היה עומד בירושלים יחזיר פניו למקדש, ויכוין ג"כ לבית קדשי הקדשים. היה עומד אחורי הכפורת מחזיר פניו לכפורת“ (שו"ע או"ח צד, א)
What is a “straight path”? Perhaps we would say that if one is traveling on a straight path, that means that 1) his compass points in the same direction throughout the entire journey, and 2) he is bearing neither right nor left; he’s traveling straight. Interestingly though, because the surface of the earth is curved, practically any conceivable path, can meet no more than one of the above two criteria (there are exceptions). Otherwise stated, if the traveler is following a straight path (bearing neither right nor left), it is likely that his compass direction is gradually changing, and if his route maintains constant compass direction, then it is likely that he is slightly bearing one way or the other. Accordingly, before one can determine which direction faces the Beis Hamikdash, he must first decide how he will define “straight-ness.”
The term rhumb line is used to describe a route that is straight in the sense that it maintains constant compass direction. The term great circle path is used to describe a route that is straight in the sense that it is neither bearing right nor left. Whether the Torah definition of “straight” follows the rhumb line model or the great circle model, is a subject of disagreement among Rabbonim.
MyZmanim.com provides the Davening Direction according to both views, for anywhere in the world.
Imagine a person traveling to Eretz Yisroel following a rhumb line. He departs from New York heading east (bearing 96 degrees) and continues his journey traveling east all along. After a distance of 6100 miles, he arrives in Eretz Yisroel. Now, although he has been maintaining a constant heading throughout his journey, in doing so, he was also continuously bearing left.
This illustration demonstrates that according to the view that the Torah definition of “straight” follows a rhumb line, one must turn to face east (bearing 96 degrees) in order to be facing the Bais Hamikdash.
Next, imagine a person following a great circle path. He departs from New York with an initial heading of east and continues his journey traveling straight, along a non-bearing course. After traveling the same distance of 6100 miles, he finds himself not in Eretz Yisroel, but in Congo, Africa (see Map #1). Now, although he was maintaining a non-bearing course all along, in doing so, he was also continuously changing heading. Although his initial heading was east, as his journey progresses, his heading approaches south. If he wishes to arrive in Eretz Yisroel, he will need to adjust his initial heading in order to compensate.
This illustration demonstrates that according to the view that the Torah definition of “straight” follows a great circle, if one is facing east, he is not facing the Beis Hamikdash. To follow this view, one would need to face north-east, as shall be shown with a final illustration:
Imagine a person traveling to Eretz Yisroel following a great circle path. He departs from New York initially heading north-east (bearing 54 degrees) and continues his journey traveling straight, along a non-bearing course. He then arrives in Eretz Yisroel, this time after having traveled only 5670 miles (see Map #2). Now, although he was maintaining a non-bearing course throughout his journey, in doing so, he was also continuously changing heading. Throughout the first part of his journey, his heading gradually approaches east. Eventually, his heading reaches and even passes east. Finally, his journey concludes with a heading of south-east. Although his heading is constantly changing, at no point is he bearing to the right or to the left.
Collectively, the rhumb line and great-circle path provide us with two options of “straight” routes to Eretz Yisroel, from New York, or from anywhere else in the world.
How does that work?
Imagine a person standing at a distance of 30 feet from the North Pole. He takes out a compass and begins walking eastward. After about one minute, he finds himself exactly back where he started. He has walked the path of a complete circle. Now, although he was heading east all along, it’s clear that he hasn’t been walking straight. Rather, if he completed the circle, it means he had to have been bearing left.
The same applies when one departs from New York heading east. Here too he is traveling along the path of a circle, albeit a much larger circle. Therefore, he too must be bearing left, albeit less so.
It is noteworthy that the fact that the earth’s axis of rotation is on a tilt has no place in this discussion.
If one finds that in his shul – 1) the direction to which everyone faces is not the correct direction, OR 2) the placement of the Aron Kodesh is such that if he turns to face the Aron Kodesh, the direction to which he is facing is not the correct direction, a Rav should be consulted.
Map #1: Great circle path beginning in New York with initial heading of EAST.
Map #2: Great circle path beginning in New York with initial heading of
Note that great circle routes are also used by ships and aircraft.