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This site (see the paragraph starting with "accuracy") says that no one can predict the times for sunrise and sunset to within a minute accurately for a given location because of certain atmospheric fluctuations. If so, how do some people predict zemanim (times of day with halachik significance) to a number of seconds, or even the end of shabbat to within a minute? Also, I have been to hanetz minyanim who are very careful to start at the moment of sunrise. But according to this, that's impossible to predict!

I suppose my question is really just looking for some justification for the common practice. Do any rabbis discuss this phenomenon? Do they say if it matters or not?

Note: I know most zemanim services will say "Please don't rely on this till this last moment; these may not be exact" but that sounds more like a legal disclaimer than a statement of fact.

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The times given are always "sea level, on the horizon" , but I have no idea what halachic ramification that has. Although some people like to claim they also take altitude into account, so the top of Har nof has a different shabbat starting time than the bottom of Harnof. –  avi Jan 11 '12 at 6:08
    
I have heard in the name of R' Elazar Kenig shlita of Tzfas that we are ovdei HaShem, not ovdei hashemesh (servants of G-d, not servants of the sun), meaning that it is not necessary to be overly punctilious about zmanim. This is typical of a Breslev approach, but it would seem that he is quoting the Rashash, a very significant mekubal. –  yoel Jan 11 '12 at 6:11
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@avi Issues of elevation are dealt with in the question I link to in the comment above. My question is about the fundamental inability to predict the exact sunrise time for a given location, time, altitude etc. due to unpredictable atmospheric air patterns. See the article I link to for more details. –  Double AA Jan 11 '12 at 6:12
    
I don't think the link is saying what you think it is saying. They are making a general statement about the globe. In places like Alaska, sure you can't predict it to the minute. The refraction in the zone of Israel for instance, is not going to change the time by minutes. (Though Altitude will) Nor will the height of a person. I personally do not rely on the calendars etc, I look at the sky. And in general, the time that people say and what I see in the sky do coincide. –  avi Jan 11 '12 at 6:36
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Today I checked when sunset was using www.myzmanim.com and found that they updated their site to allow you to account for temperature and pressure in determining sunset and sunrise times. Their explanation for the phenomenon is here.

I wonder if one of them has been following Judaism.SE?

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Even with precise Zemanim there can be variances of +-2 minutes due to atmospheric conditions.

http://www.kosherjava.com/zmanim-project/

Please note: due to atmospheric conditions (pressure, humidity and other conditions), calculating zmanim accurately is very complex. The calculation of zmanim is dependant on Atmospheric refraction (refraction of sunlight through the atmosphere), and zmanim can be off by up to 2 minutes based on atmospheric conditions. Inaccuracy is increased by elevation.

Therefore we do our best and do not OCD over it.

I heard that by the Vasikin Minyan in Bnei Brak where HaRav Chaim Kanievsky Shlita Davens they start within 2 minutes of the posted Neitz HaChama Zeman .

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According to this website, the accuracy of the website you linked to is not entirely accurate.

http://www.srrb.noaa.gov/highlights/sunrise/calcdetails.html

They state here that

The calculations in the NOAA Sunrise/Sunset and Solar Position Calculators are based on equations from Astronomical Algorithms, by Jean Meeus. The sunrise and sunset results have been verified to be accurate to within a minute for locations between +/- 72° latitude, and within 10 minutes outside of those latitudes.

It later states that

The effects of the atmosphere vary with atmospheric pressure, humidity and other variables. Therefore the solar position calculations presented here are approximate. Errors in sunrise and sunset times can be expected to increase the further away you are from the equator, because the sun rises and sets at a very shallow angle. Small variations in the atmosphere can have a larger effect.

The +/-72° line is roughly near the arctic circle on both sides of the globe, so for most Halachic zmanim calendars, the margin of error would not be more than a minute.

They also provide an assumped atmospheric refraction level, and some other mathy stuffs.

Now, as to the halachic websites which calculate the zmanyim to the second, they write at the bottom of the list:

**The times for sunrise and sunset have been computed assuming that the horizon is clear of obstructions (see Accuracy).

Later in the Accuracy page they also write:

Rounding in Monthly Printouts In monthly printouts, where seconds have not been provided, all times for Sunrise, Earliest Talis, Earliest Mincha and Nightfall (all opinions) have been rounded later. Accordingly, a listing of "6:12" means "before 6:12" (between 6:11 and 6:12). All other Zmanim times have been rounded earlier. As such, a listing of "5:36" means "after 5:36".

If you follow and read all the instructions on the website, you are left with the suggestion that the seconds on the zman are given so that you can know in which direction to round for the minute and to be cautious in it's accuracy.

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OK and it also says that between 5 and 85 degrees it uses the same atmospheric refraction correction term. So maybe it doesn't change much in its average variance over the whole range of 142 degrees. It could still easily be off by 30-45 seconds at Israel's latitude. –  Double AA Jan 11 '12 at 16:53
    
Also, in fairness, I think the US Naval Observatory is a pretty decent source. –  Double AA Jan 11 '12 at 16:55
    
@DoubleAA I'm not saying the US Naval Observatory isn't a good source, it just wasn't very accurate. It said something true on a global level, but not accurate for Jews who care about sunrise times. –  avi Jan 11 '12 at 17:47
    
@DoubleAA the 5 to 85 degrees, is the solar elevation, not the latitude. –  avi Jan 11 '12 at 17:50
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