More Discussions for this daf
1. Taurus and Scorpio 2. North-South Determination 3. The Vilna Gaon's calculation
4. Rav Ada 5. Tekufos - Halachic vs Secular 6. Vernal Equinox
7. Gra on Tosfos D"H Abaya 8. Rashi's Siman 9. Rashi's inexact calculation
10. Solistice? 11. Rashi, D"H v'Ein Tekufos Tamuz.. 12. Rashi DH Mipnei She'Mafsid - Where does the 28 come from?
13. Bach on amud beis 14. Constellations 15. Akrav is in the South
DAF DISCUSSIONS - ERUVIN 56

Dovid Gottlieb asked:

Why should constelations be given as the way to determine north-south when it is much simpler to observe the direction of the shortest shadow at noon? [The shadow will point north.]

Dovid Gottlieb,

The Kollel replies:

(a) It is not simple to determine the exact moment of midday

(b) Your system does not help at night

M. KORNFELD

Rabbi Gottlieb responds:

Thanks. But - noon is when the shadow is shortest. And you probably would not be measuring the squaring of the city at night.....

The Kollel replies:

(a) That may be true, but it is not at all simple to determine the exact moment when the shadows are shortest. As Rashi writes in Pesachim 94a, between 11:30 and 12:30 (assuming that 12 is noon) the sun is above people's heads. The difference in the length of the shadow is minimal, but the difference in the north to south line based on the shadow may add up to a significant amount, after 2,000 Amos of measuring. This requires a high precision of measurement.

Until today, scientists are amazed at the precision with which the bases of the Great Pyramid line up with NSEW. They are convinced that there is no simple method by which a straight north-south line can be determined with such precision. Chazal's method, then, is certainly in order. (Some mainstream hypotheses involving astronomical calculations that may have been done in order to position the pyramids can be found at http://www.americanscientist.org/template/AssetDetail/assetid/35115. An excerpt is copied below.)

(b) Although the measurers of the Techum may not have measured at night, a north-south orientation is necessary for other measurements as well; perhaps even moving 4 Amos in Reshus ha'Rabim. See Tosfos Eruvin 51a DH Mi.

Best wishes,

Mordecai Kornfeld

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Excerpt from http://www.americanscientist.org/template/AssetDetail/assetid/35115

Astronomy and the Great Pyramid

by J. Donald Fernie

"A long-standing problem relating not only to the Great Pyramid but also its smaller cousins is the question of how the builders managed to orient such colossal structures to the cardinal points with surprisingly high accuracy. The eastern side of the Great Pyramid, for example, points only three arcminutes away from a true north-south line, and other pyramids in the group are not much worse. This makes it virtually certain that some astronomical method was used to establish the local meridian. At first thought this does not seem too difficult a problem, even without a bright star close to the north celestial pole during the millennia of interest. (Even today, Polaris is some 43 arcminutes from the pole, and during this time it was about 25 degrees away.)

"Still, other possibilities spring to mind. An obvious method would be to note the directions of sunrise and sunset on a given day and bisect the angle between the two-the result marks the meridian. But this, and other seemingly straightforward methods, while fine in principle, turn out to be unsatisfactory in practice, at least when accuracies of a small fraction of a degree are called for. For instance, in this case the rising and setting sun must be seen over an absolutely flat horizon, which Giza lacks. Then there is refraction in the earth's atmosphere: When one sees the lower edge of the setting sun just touching the horizon it has in fact already set. The light rays are bent to produce an image above the horizon, thereby shifting the direction in which the sun appears to set. And since the amount of refraction depends on air temperature, pressure and other factors, all of which can differ between morning and evening, the effect may not be consistent between rising and setting. Furthermore, the sun's celestial coordinates will change during the course of the day, spoiling the symmetry of the method. All in all, these practical hurdles have stymied modern astronomers who tried to figure out just how the early Egyptians managed to orient their pyramids as precisely as they did"