# Aruch Hashulchan's moon-distance estimate

Aruch Hashulchan (1829–1908), Orach Chayim 397:1, says that a מיל is the same as a Russian верста (verst) or 500 сажен (sazhen), which comes to 1066.8 meters. In 426:2, he says the distance to the moon is about 43,000 פרסה. A פרסה is four מיל, so 43,000 פרסה come to about 183,500,000 meters.

In fact, though, the distance is about 384,400,000 meters (as had been known, at least approximately, for millenia by his day), which according to the Aruch Hashulchan is 384,400,000÷4267.2 פרסה, or about 90,000 פרסה.

His estimate of 43,000 is off by a scale factor of 2! What gives?

• Doesn't he also seem to say that the moon is bigger than Mercury? May 23 '13 at 8:36
• @DoubleAA, yes. (Well, as big or bigger.) I don't know what the state of the science was in his days about that. If you do and are bothered, by all means ask. `:-)`
– msh210
May 23 '13 at 14:01
• @msh210 My point was I don't know if he's trying to be accurate or just to quote some old statement (midrash? rambam?) from before it was known precisely. May 23 '13 at 15:36
• @DoubleAA re "I don't know if he's trying to be accurate or just to quote some old statement": the latter may well be true, and evidence of such a statement would make a great answer.
– msh210
May 23 '13 at 15:49
• Even if had been estimated before, it doesn't mean people knew about it in Eastern Europe. (Columbus would have never tried to sail to India if he knew the Earth was as large as Eratosthenes had calculated.) May 23 '13 at 15:49

This might simply have been a confusion of units. Sizes.com claims that a Russian verst is equal to 500 sazheni, but a Moscovy verst is 1000 sazheni. The sazhen was fixed at 7 English feet (2.134m) in both systems way back during the 1700s in Peter the Great's rule.

In 397:1, the Aruch HaShulchan says that specifically, he is talking about the Russian verst (and therefore, in order to eliminate confusion and to inform heimisch readers how long the official verst is), he says 500 sazheni.

This perspective makes the end of 397:1 much clearer and less redundant:

ואלפים אמה הוא מיל, ולפי מדת מדינתינו רוסיא היא פרסה רוסית שקורין ווייארסט, שהם חמשה מאות סאזנעס. וכל סאזען הוא ד' אמות שבגמרא, כמו שבארנו בחושן משפט סימן רי"ח.

My translation:

And two thousand amot is a mil, and according to the laws of our country, Russia, that is a "Russian parasa" which is called "verst", which are 500 sazheni. And all sazheni [i.e., Russian, Moscovy, Litovskaia] are 4 amot in the gemara, as we explained in Choshen Mishpat, siman 218.

When he talks about the distance to the moon, he says:

מ"ג אלף פרסה

43,000 parasa

We have an ambiguity there. He might be talking about the Russian "parasa" (2000 amot), the Moscovy "parasa" (4000 amot), or the Talmudic parasa (8000 amot). But all of these definitions are off. Even the Talmudic parasa would be, as @msh210 said:

43000 * 8000 amot = 43000 * 2000 sazheni = 43000 * 14000 ft. = 183,500 km

Perhaps, the Aruch HaShulchan heard that the moon is ~180,000 versts away. The speaker was speaking in Moscovy versts:

= 180,000 * 1000 sazheni = 180,000 * 213.4 m = 385,000 km

... but the Aruch HaShulchan understood 180,000 Russian versts

= 180,000 * 500 sazheni = 180,000 * 2000 amot = 180,000 mil = 45,000 Talmudic parasa

...which is just about right. Turns out, the moon's distance from the earth goes from around 363,000km to 405,000km, so we have some wiggle room.

• Interesting idea. What language does he use regarding the measurement to the moon? May 24 '13 at 1:54
• @DoubleAA "_אינה רחוקה מן הארץ רק בערך _מ"ג אלף פרסה" May 24 '13 at 1:57
• (re your last comment.) Maybe so, but then haikar chaser min ha answer.
– msh210
May 24 '13 at 2:19
• @CharlesKoppelman, yes, I think the math works out that way. All we need to do now is find a Russian publication that expresses the distance to the Moon in Moscovy versts, preferably one that doesn't specify. May 24 '13 at 2:20
• Actually, more googling seems to yield (not super-strong) evidence against this hypothesis. `"180000 верст" Луна` (= `"180000 versts" moon`) yields only the PDF I linked above, and I don't think the measurement there is referring to the distance to the moon. `"360000 верст" Луна` yields 8 results including multiple references to books from the 1800s that do seem to be telling us the distance to the moon (noting the appearance of apparent conjugations of "расстояние" = "distance"). May 24 '13 at 15:42