Talk:Atmospheric refraction/Archive 1

Anonymity
What is the point is in creating links to pages that don't exist. [not signed, actually by 83.245.40.135]


 * Um, I don't understand... what is your problem, exactly? This page exists, it's not linking to any red-links, so what is it you are trying to say? Oh, and I should add that it's common courtesy to sign your Talk/Discussion contributions so people know who says what. Master Thief Garrett 23:29, 23 Apr 2005 (UTC)


 * 83.245.40.135 is how I wish to be known. Who I am is irrelevant.


 * nonono, your anonymity is fine, but you need to sign with your IP so people can tell the difference between the comments of multiple anon users. You can auto-sign your name by typing four tildes ( ~ ) after your comment. Hope that helps you. Master Thief Garrett 01:58, 28 Apr 2005 (UTC)

VfD
On April 23, 2005, this article was nominated for deletion. The result was keep. See Votes for deletion/Atmospheric refraction for a record of the discussion. Mindspillage (spill yours?) 14:25, 6 May 2005 (UTC)

Does atmospheric refraction account for discrepancies in the Moon's "arrow" to the sun?
This is a hard thing to find on Google.

When the moon is a crescent, a triangle could be drawn between its two points and a point equidistant from them on its lit horizon. This triangle should point directly at the sun. However, it always points to a point several degrees away from the sun (it's noticable).

Is this effect due to atmospheric refraction? If so, should it be mentioned here as another example? It is an observable example of the sunset phenomenon.

--Dan Kuck (talk) 18:19, 16 October 2009 (UTC) edited: 21:24, 18 October 2009 (UTC)


 * [From Terry0051] Is there any reliable source to show that this suggested triangle/arrow thing is real, and to describe more clearly what it is? Terry0051 (talk) 21:52, 18 October 2009 (UTC)


 * I haven't been able to find it. The fact that the lit side of an orb "points" at its light source is verifiable, and it's observable that the moon doesn't appear to do this (the triangle is my own explanation; frankly a crescent shape already makes an arrow, but it's a curved one so it's less-clear in words).  I'm probably just Googling the wrong terms.  I realize that without sources it's WP:OR.  Or does ease of observability change that? --Dan Kuck (talk) 14:30, 19 October 2009 (UTC)


 * [From Terry0051] Hmm: there are questions about observability, and they naturally include "what accuracy is achievable in the measurement?", and "is the achievable accuracy enough to support any suggested conclusion?". Here, particularly, I would think that an absence of sources is likely to bring a risk of OR in any conclusions offered.  Terry0051 (talk) 17:05, 19 October 2009 (UTC)


 * On Oct 26, 2009 at 6:15 PM local time you could see this effect was the reverse of what is described in this article. The moon was facing a point in the sky higher than the sun whereas the article indicates that at this time of day the sun is somewhat lower than the point where it appears.  I'm not sure atmospheric refraction can account for this phenomenon. --Dan Kuck (talk) 13:19, 27 October 2009 (UTC)

Latter
The phrase "the latter" apppears in the article. It is not clear exactly what it refers to. —Preceding unsigned comment added by 78.105.36.65 (talk) 13:47, 8 December 2009 (UTC)

Values section
The formula for additional distance to the horizon is unsourced, and appears at odds with formulas in Horizon and other sources such as Andrew Young and the Explanatory Supplement to the Astronomical Almanac. The formula given here seems to confuse astronomical refraction of a celestial body (which depends on the body's apparent altitude) with terrestrial refraction of the horizon for an elevated observer (which depends on the observer's height). JeffConrad (talk) 08:06, 7 October 2010 (UTC)

I removed the formula above because it doesn't appear to be correct. If we think this article should mention the effect of refraction on the distance to the horizon, I think we should simply use Young's explanation (as a recognized authority in the field, his personal web pages should be citable): for the simple treatment with common values, the distance to the horizon is increased by a factor of $$\sqrt {7/6}$$, or about 1.08.


 * I've discussed the distance to the horizon in more detail on Talk:Horizon. JeffConrad (talk) 06:01, 26 October 2010 (UTC)

I've made a few other changes in attempt to clarify this section, and added two references. I removed mention of correction of the times of Moon rise and set for phase because I've not seen this mentioned in any published source. The appearance/disappearance of the illuminated part of the Moon's disc may vary with phase, but every source I've seen still refers to the appearance/disappearance of the Moon's upper limb (so this holds even for a new moon). JeffConrad (talk) 00:57, 8 October 2010 (UTC)

I think discussion of distance to the horizon is best covered in Horizon; if it's mentioned here, the mention should be brief, perhaps as suggested above. It might be reasonable to add some quantitative discussion of refraction, perhaps with both some simple formulas (e.g., Bennett) and a more general treatment that includes the refraction integral, preferably with some mention of the method of Auer and Standish that changes the variable of integration to the angle between the radius vector and the light ray to allow easier calculation near the horizon and for zenith angles greater than 90°.

As I suggested above, I think we should be clear on the difference between the astronomical refraction of a celestial body for a sea-level observer, and the additional effects of dip and refraction for an elevated observer. What's added would depend on how technical this article should be. A starting point might be brief descriptions and direction of the reader to sources that cover the subject in more detail. JeffConrad (talk) 10:02, 21 October 2010 (UTC)

Precision of rise and set times
I just made a change to the accuracy discussion. As an example of what I'm referring to, if sunrise is rounded to the nearest minute and the calculated sunrise time on Day 1 is 7:14:30 and on Day 2 is 7:15:29, both days' sunrise times will be listed as 7:15. In reality, however, sunrise will occur on Day 2 59 seconds later on average. So, while, in a given year, sunrise may actually occur earlier on Day 2 than Day 1, it is nonetheless useful to show times to the nearest second. Rodneysmall (talk) 17:10, 11 January 2011 (UTC)


 * This change is in conflict with the cited reference (Meeus 1991), which states


 * . . . it should be mentioned here that giving rising or setting times of a body more accurately than to the nearest minute makes no sense.


 * Were we concerned strictly with the geometrical position of a body (e.g., times of twilight), I would agree with your statement. But we are not; this article is about refraction, so although the differences you cite are theoretically correct, for practical purposes, there are no differences. Absent a reliable source to support the current wording, we shoud go back to a wording consistent with the source. JeffConrad (talk) 21:54, 11 January 2011 (UTC)

On his website, former NASA scientist Paul Lutus shows sunrise/sunset tables with times to the nearest second for any location. Dr. Lutus's tables also lists the earliest and latest sunrise/sunset times to the nearest second. See http://arachnoid.com/lutusp/sunrise/index.html. I understand the point Meeus is attempting to make -- that one should not assume that the calculated time is accurate to the nearest second -- but, then, in some cases it will not be accurate to the nearest minute, either. Further, terrain variations can also make a difference of several minutes in sunrise/sunset times in a given city, so any sunrise/sunset table should not be blindly relied upon. In sum, I think it's better to show sunrise/sunset times to the nearest second with an explanatory note rather than showing times only to the nearest minute with no explanatory note. Rodneysmall (talk) 02:41, 12 January 2011 (UTC)


 * I also have programs that will show the times of Sun and Moon rise and set to the nearest second, but the precision is meaningless—day-to-day variations in atmospheric refraction can result in variations of 20 seconds in the times of rising and setting. Lutus is using a very low-precision algorithm for the Sun’s equatorial coordinates, and he doesn’t consider ΔT, so I doubt that even the geometrical positions are accurate to a second. The USNO, who have access to arguably the most precise algorithms, give times only to the nearest minute. Terrain does not enter into the time of rise or set, which is the time that the Sun’s upper limb would appear to be on the geometrical horizon: in other words, the official time of Sun rise or set is when the geometrical altitude of the Sun’s center is −50′, as indicated in the article. And again, this article is about refraction, not time of rise and set. The times of rise and set are affected by elevation (because air density changes), but few calculators take this into account.


 * The current wording is essentially WP:OR, so without support from a reliable source (and not just an example of a calculator that gives results to the nearest second), that wording cannot stand. JeffConrad (talk) 04:32, 12 January 2011 (UTC)

I'm not sure what you're objecting to. Are you saying that the following statement is inaccurate, or only that no reliable source has explicitly stated it? "However, such calculations can be useful for the purpose of specifying changes to rise and set times, if it is understood that the changes are average values that may not hold in a given year."Rodneysmall (talk) 14:25, 12 January 2011 (UTC)


 * In general, I object on both counts. The statement is personal opinion unsupported by a reliable source; nearly all reliable sources for rise and set times give them only to the nearest minute, so they apparently don’t see greater accuracy as useful. Arguably, then, the statement is at odds with reliable sources. Giving times to the nearest second (or millisecond or whatever) might be useful if one were to plot the times of rise and set (the resulting curve would be smoother; the usefulness is questionable), but this or anything similar has nothing whatsoever to do with this article. The point of the paragraph is that although a standard true altitude of rising and setting is generally assumed, the refraction allowance is so variable that it makes no sense to give times to greater accuracy than the nearest minute. As I mentioned, most programs that calculate rise and set times accordingly don’t incorporate enough terms to provide one-second accuracy even if atmospheric refraction were constant, so showing times to that accuracy is illusory and simply ludicrous. Take, for example, the USNO’s MICA, which uses the JPL DE405 ephemeris to calculate positions of bodies; it give positions to the nearest 0.1 arc second, but only gives times of rise and set to the nearest minute. Moreover, positional calculations do not take refraction into account because of its variability. I have been told that future versions will provide the option to include the effect of refraction; the precision to which refracted positions will be given remains to be seen.


 * Again, I concede the possible usefulness of giving times to sub-minute accuracy in an article about the motion of the Sun or some other body, but this is not that article, and the statement quoted above simply muddies the waters here. JeffConrad (talk) 21:26, 12 January 2011 (UTC)

The main problem I have with the previous version of the article is the assertion with no context that "it is essentially meaningless to calculate rise and set time to greater accuracy than the nearest arcminute." I don't think it is meaningless for purposes of showing daily changes to sunrise and sunset times, which is why I believe Paul Lutus shows those times to the nearest second. However, let me run both the previous version and my suggested edits by an astronomer and get his opinion as to which version is better. [I am not an astronomer, which you probably already figured out ;-).]   I'll get back to you with his opinion.Rodneysmall (talk) 01:53, 13 January 2011 (UTC)


 * I’m not an astronomer, either, but I am reasonably familiar with computational astronomy. “Arcminute” (added on 26 November 2010 by Joe Kress, and which I had not noticed) is clearly wrong; it should be “minute”. Perhaps the previous wording could be slightly revised, but nonetheless, the added sentence is unsupported personal opinion, and it’s essentially unrelated to this article. We have a citation from Meeus, who’s a recognized authority on computational astronomy, supporting the previous wording. By example, we also have nearly all reliable sources giving times only to the nearest minute.


 * Unless the astronomer to whom you refer is a recognized authority who is published and can be cited on this point, he or she doesn’t count as a reliable, verifiable source. I’m not big on ceremony; as I’ve tried to imply, my objection to the current wording is primarily that it is potentially misleading and is only one editor’s opinion. My objection to the lack of a source is largely pro forma, but I nonetheless insist on a source if the current wording is to remain; it’s the way we resolve disagreements on WP. And I return yet again to the most fundamental point: this article is not about day-to-day changes in rise and set times, so the possible usefulness of giving times to the nearest second is irrelevant. JeffConrad (talk) 07:14, 13 January 2011 (UTC)


 * I don't know what I was thinking when I changed "minute" to "arcminute". Sorry for the error. — Joe Kress (talk) 07:21, 17 January 2011 (UTC)

Here is the e-mail correspondence that I just had with Dr. David McNaughton; see http://dlmcn.com

Subject: Wikipedia Article About Atmospheric Refraction

"Dear Dr. McNaughton: "I obtained your name from the Internet in connection with a friendly debate I'm having with someone about a small portion of the above article. Without telling you which of us prefers which version of the article, I would like to get your opinion as to the version that is better, if you have the time to briefly take a look at the below: "Version 1: Day-to-day variations in the weather will affect the exact times of sunrise and sunset as well as moonrise and moonset, and for that reason it is essentially meaningless to calculate rise and set time to greater accuracy than the nearest arcminute (Meeus 1991, 103). "Version 2: Day-to-day variations in the weather will affect the exact times of sunrise and sunset as well as moonrise and moonset, and for that reason it can be misleading to calculate rise and set time to greater accuracy than the nearest arcminute (Meeus 1991, 103). However, such calculations can be useful for the purpose of specifying changes to rise and set times, if it is understood that the changes are average values that may not hold in a given year."

Dr. McNaughton's response was: "In the reference you give, I'm pretty sure that Meeus means [that we should quote rising and setting times only to the nearest] clock-minute ... i.e., we must not read that as 'arc-minute'.

"During one clock-minute, the sun or moon can descend/ascend by up to 15 arc-minutes.

"According to Schaefer (in the paper cited by Meeus) we must accept an uncertainty of +/- 20 arc-minutes in very low-level refraction, at a 95% level of confidence ... which seems to be why Meeus insists that rising and setting times should be published only to the nearest clock-minute.

"However, Schaefer implies that the problem is due to variations in temperature profile - which indicates that it will be more serious at sunrise. So, by way of compromise, I would suggest that we could usefully publish rising/setting times to the nearest half a clock-minute, together with a warning that natural meteorological variations of up to about one clock-minute can sometimes be expected.

"In any event, as your version 2 suggests, there are occasions when it can be illuminating to calculate with even greater accuracy. For example, one of the Saudi Arabian criteria for commencing Ramadan is that the sun should set before the moon [at Mecca, presumably] ... and there was one year when the difference was only a matter of clock-seconds. So I wrote to Meeus explaining the reasons why we wanted more precise values - and he understood, and sent them to us. In this instance, it was important only to look at the comparative setting-times; i.e., [almost] the same refraction correction would have applied to the sun and the moon.

"In a comparable vein, you may have seen my answer to question 11 in http://dlmcn.com/questions9q.html" Rodneysmall (talk) 14:07, 13 January 2011 (UTC)


 * More info on the Saudi Arabian criteria is at Islamic calendar. — Joe Kress (talk) 07:21, 17 January 2011 (UTC)

The Meteorological/Astronomical Office in Zimbabwe used to (and maybe still does) receive inquiries as to the (theoretical) shortest and longest day of the year. This varies from year to year (and from decade to decade) - but we did need to consider whether or not it also depended on the latitude of the place concerned, because Zimbabwe lies within the tropics. To answer the question properly, it was necessary to calculate sunrise and sunset times to the nearest second – whilst emphasizing that the date could easily change through unpredictable variations in the degree of atmospheric refraction. Indeed, Jean Meeus himself adopts this tactic on page 315 of his "More Mathematical Astronomical Morsels" (Willmann-Bell, 2002). DLMcN (talk) 20:59, 13 January 2011 (UTC)


 * I have no real disagreement with David McNaughton’s comments, though I’m not sure they really answer the main question here. Times given to the nearest half minute would usually be reasonable, but there is no way to make this precision obvious from the values given (unless perhaps they were decimal minutes rounded to the nearest 0.5 minute). I suspect that this would confuse rather than enlighten most readers.


 * I yet again return to the main point: the utility of showing times to the nearest second is personal opinion tangential to this article. It might be appropriate for an article dealing specifically with the motion of the Sun or some other body. Even so, the sentence


 * However, such calculations can be useful for the purpose of specifying changes to rise and set times, if it is understood that the changes are average values that may not hold in a given year.


 * would need some careful rework. The changes aren’t necessarily “average” values; the standard value for refraction at the horizon is based on a theoretical atmosphere that presumably reflect average values of temperature, pressure, and most important as David and Schaefer note, temperature lapse rate. And these conditions and the resulting rise and set times may not hold at any given time, not necessarily linked to a given year. And we still might be venturing into WP:OR, so I think we’d be better off sticking to the topic at hand.


 * There are other pitfalls to excess precision. For example, Paul Lutus’s Solar Computer gives times to the nearest second, yet for the default latitude and longitude, the rise and set times for 1 January 2011 seem to be off by over a minute (to be fair, the day-to-day changes seem much accurate). So unless all assumptions are carefully stated, precision needs to be taken with a grain of salt.


 * I’ve changed the wording to distinguish between the precision of calculation and the precision to which results are given (consistent with what Meeus actually says); the rounding should be the last step. JeffConrad (talk) 00:56, 14 January 2011 (UTC)

I'm fine with your edits. Rodneysmall (talk) 01:34, 14 January 2011 (UTC)


 * The issue of the second sentence remains. To even be correct, it would need to be changed to the effect of


 * However, such calculations can be useful for indicating day-to-day changes in rise and set times that would occur if refraction were constant.


 * If you lived here, you’d be home by now . . . refraction isn’t constant. In an article describing the effects of Earth’s orbit about the Sun, perhaps this statement would be appropriate, but I fail to see it as anything but a distraction here.


 * No major source of which I’m aware gives the times to greater precision than a minute. It isn’t just Meeus. In the Explanatory Supplement to the Astronomical Almanac, Bernard Yallop (former director of the RGO), calls for the iterative solution of the equation for rising and setting to continue until the difference between successive iterations is less than 0.008 h (0.48 min). The USNO’s MICA states


 * MICA tabulates rise and set times to a precision of one minute only (i.e. no seconds are tabulated). This is because the observed times of rise and set are affected by random changes in local atmospheric conditions and other local variables which cannot be accurately modeled. Thus, tabulating the times to a higher precision is not practical or normally useful.


 * David McNaughton gives an interesting example of the Sun setting just before the Moon when both are presumably subject to the same refraction, but that is a very special case that is quite different from the statement here, which gives a personal opinion that’s not reflected by the published sources (and in fact, is generally in conflict with them), and is in any event tangential to the article. Per WP:BURDEN, it needs a source if it is to remain. JeffConrad (talk) 04:41, 14 January 2011 (UTC)

OK then - so you can include my above-mentioned reference to page 315 of Jean Meeus's "More Mathematical Astronomical Morsels" (Willmann-Bell, 2002) as an illustration of the usefulness of times calculated to the nearest clock-second? DLMcN (talk) 06:59, 14 January 2011 (UTC)


 * Your example is certainly a better one than implied by the current wording. In fact, I take a similar approach at www.largeformatphotography.info/sunmooncalc/, where I calculate the time difference between Sun and Moon events before rounding. I stop iterating when the difference between successive iterations is 0.005 h (0.3 minute), but the convergence criterion could easily be adjusted to any arbitrary value (at the cost of increased computational overhead, of course). Again, though, I wonder if this is the place for it; we’re talking about refraction, and the mention of giving rise and set times only to the nearest minute is really incidental—what we’re really saying that’s relevant to this article is that the standard allowance of 34′ at the horizon is a nominal value that varies unpredictably.


 * I have several books by Meeus, but not this one, so I can’t mention it here or even really assess how well it supports whatever wording we might decide on. You apparently have the source, so you could of course mention it. As I suggested above, though, that really is a very special case, so if we do include it, we should make that specialness clear. JeffConrad (talk) 08:33, 14 January 2011 (UTC)

That new Meeus reference has now been added, and to me it seems to support the present wording. DLMcN (talk) 17:18, 14 January 2011 (UTC)

Yes, the latest "02:13, 15 January 2011 JeffConrad" edit looks fine, particularly now that I've put the reference earlier in the sentence. DLMcN (talk) 06:20, 15 January 2011 (UTC)


 * I had thought of similarly moving the reference, but doing so without having read it seemed a bit off the wall.


 * For the record, the current wording almost seems to say that very precise calculations are useful as long as we recognize that they have little relation to reality (a correct statement, in my opinion, but one whose point I question). For example, using the calculator I linked above modified to iterate until successive iterations differ by less than 1×10−8 h, the shortest day in 2011 for a location at on the Greenwich meridian at the equator is on 19 September, with a duration of 12:06:31.35; on 20 September, the duration is 12:06:31.36. Here more precise calculations (to the nearest tenth of a millisecond) produce different numbers, but do the numbers really mean anything? It should be further noted that I use the formulas of Van Flandern and Pulkkinen, which are only good to about an arcminute in ecliptic longitude, and probably don’t support the precision that I show.


 * I still would prefer that we give the example of the near-simultaneous setting of the Sun and Moon, for which precise calculations are meaningful, but it’s probably not worth belaboring the point. JeffConrad (talk) 08:13, 15 January 2011 (UTC)

Your description - that [precise calculations] "have little relation to reality" - is perhaps a bit strong, i.e., not really fair?

I am sure you could find a way of borrowing that 2002 book by Meeus, on Inter-Library Loan, maybe? ... or else just ask a library to copy the entire section for you, which runs from pages 314-319. (Page 315 contains a Table of rising and setting times for Paris, given to the nearest second). You may well find the topic interesting - Meeus is looking at the daily variation in times of sunrise and sunset at different latitudes, and discovers that the curves (particularly for 60 deg N) are double-peaked, something completely unexpected, and to my knowledge not yet explained. That analysis would of course have been impossible without Meeus's very precise calculations.

I am not aware of any publication which mentions that example of near-simultaneous setting of the sun at moon at Mecca, unfortunately. DLMcN (talk) 11:46, 15 January 2011 (UTC)


 * Can’t comment on fairness, though “little relation to reality” is admittedly (and not unintentionally) a bit strong. Key, I think, is what is meant by “reality”. If we confine ourselves to mathematical astronomy, at which Meeus is an acknowledged master (if he’s not nonpareil), I overstate the issue. But if we look at actual events, I’d probably stand by the statement.


 * The closest library that has this book is 300 miles away. My local library hasn’t been too impressive on inter-library loans in the past, but perhaps I just happened to ask the wrong people, and perhaps it’s worth another try. I’m sometimes interested in topics that are strictly mathematical astronomy, including this one, but I’m just not curious enough to cough up $25 USD to pursue it further (and I would be out a small fortune if I were to get all five works in the series).


 * I’ve never been able to see a double peak in plots I’ve made, but this may be a limitation of using Meeus’s 0.01° positional formulas or Van Flandern and Pulkkinen’s 1′ formulas.


 * The cause of a double peak is probably not rocket science; it likely results from changes in RA as well as declination. We tend to concentrate on the formula for the hour angles of rise and set while perhaps overlooking changes in RA. Of course, this really describes the effects of Earth’s motion about the Sun rather than observable phenomena that are subject to variations in atmospheric refraction.


 * Absent something we can cite, we probably can’t discuss the moonset–sunset time differences. JeffConrad (talk) 06:27, 16 January 2011 (UTC)

I return to the example that I used to initiate this discussion: If sunrise is rounded to the nearest minute and the calculated sunrise time in a given place on Day 1 is 7:14:30 and on Day 2 is 7:15:29, both days' sunrise times will be listed as 7:15, even though the change that occurs from Day 1 to Day 2 averages 59 seconds. Rodneysmall (talk) 15:27, 15 January 2011 (UTC)


 * I am quite familiar with how rounding works, as I assume are folks like USNO and HMNAO, who give times to the nearest minute despite having the the most accurate known ephemerides available. Indeed, there is a theoretical 59-second difference in the rise times for the two days, but the difference between actual times may be no where near that great. The issue here is the difference between physical science and pure mathematics. It’s a simple matter to express rise and set times to the nearest picosecond, but doing so is little more than an exercise in mental masturbation. Again, I go to the example I gave of the shortest day of the year at zero longitude and zero latitude: it’s reasonable to say that it occurs sometime between 31 July and 5 November, but choosing a specific day from that period is largely meaningless. I’d probably agree with David that giving times to the nearest half minute would be reasonable, but for good or for ill, we normally do it either to the nearest minute or the nearest second.


 * Again, though I concede the potential usefulness of sub-minute precision to the mathematician, I question the appropriateness of discussing it in a very basic article about atmospheric refraction. JeffConrad (talk) 06:27, 16 January 2011 (UTC)

Jeff Conrad -

Purely for the record, and because it does interest you, here is the mail I received from from Meeus in January 2000 discussing the date of that very unusual event - when only seven seconds separated moonset and sunset at Mecca:

"For Mecca on 2000 Feb 5 I obtain the following times (UT) for the upper  limbs of the bodies :

moonset 15:12:26 ... sunset 15:12:33

So definitely the moon sets before the Sun.

Best regards. Jean Meeus"

2. I cannot quite remember what graphs we managed to produce showing variations in lengths of day in Zimbabwe - but it was several decades ago, and we did not have access to accurate software. When I have the time and inclination, I may take another look to see whether the [theoretical] shape of the graph is [slightly?] influenced by the dates when the sun is exactly overhead - e.g., dispaying a point of inflexion, perhaps. If so, I would find that interesting ... and that will of course need calculations to the nearest second. However, despite being in the tropics, the longest day in Zimbabwe (and Zambia etc. etc.) is still that of the solstice, i.e., close to December 21st.

You are probably right that the Equation of Time is a factor we could usefully consider when discussing this topic, and when trying to explain the double peaks found by Meeus. DLMcN (talk) 11:09, 17 January 2011 (UTC)


 * 1. Using MICA, with zenith distance based on actual semidiameters but standard refraction of 34′, I get
 * Moonset: 15:12:29
 * Sunset: 15:12:36


 * Though the difference here is the same, the actual times differ by three seconds. That two presumptively very reliable sources differ by this much, even without variations in refraction would seem to raise questions about making calculations to the nearest second. For the same date, using Meeus’s positional formulas (and a similar rise/set algorithm), I get
 * Moonset: 15:12:28
 * Sunset: 15:12:36


 * so I’m closer to the USNO times but my difference differs from the other two sources by a second. Now if we threw in actual refraction . ..


 * Incidentally, moonset–sunset time differences less than 30 seconds appear to be fairly rare; I found about 8 dates between 1981 and 2020 meeting this criterion (on 21 November 1987, the difference was only 5.41 seconds—if the calculations are to be believed).


 * 2. Can you give me the date range(s) in which which Meeus (2002) finds a double peak in times? Also, does he just look at rise and set times? I probably could attempt to replicate his work with MICA, though because I’d need to calculate positions and look for ones that correspond to standard altitude crossings, the task would be much easier if the range could be restricted. Alternatively, I could code the limited VSOP87 formulas at the end of Meeus (1991), but this is honestly not at the top of my list.


 * Getting back to the matter at hand: it would seem appropriate to cite Schaefer and Liller (1990) on the variability of refraction (unless there’s a better source) because it speaks directly to the topic of this article. There then would be the issue of reconciling the statement


 * First, the time of sunrise can only be predicted with an accuracy of 4 min, despite all the extreme accuracy of modern positional astronomy.


 * with our statement that very precise measurements can be useful (the actual ±2σ was 3.62 minutes for the “typical” conditions cited on p. 803). I think we probably would agree that Schaefer and Liller presented the absolute worst case; for at least a few of the observations, there appeared to be different average refractions for sunrise and sunset, with smaller variations for sunrise and sunset times. But those constituted only a small number of the observations. Because, in retrospect, the experiment was not designed as carefully as it might have been had the extent of the variations been considered (it’s always easier to design once one has the results . . .), I’d hardly say that article is the last word on the subject. Nonetheless, the caveat is in accord with the overwhelming consensus of the published sources, and I think WP:WEIGHT may come into play. Perhaps it’s still reasonable to retain the statement that I question, but I think it needs further qualification. JeffConrad (talk) 03:43, 18 January 2011 (UTC)

Perhaps the discrepancy of 3 seconds between your times and Meeus's, could be due to you using slightly different longitude values for the location? DLMcN (talk) 09:03, 18 January 2011 (UTC) /// ... Meeus was calculating the day-to-day variations in times of sunrise and set. At latitude 60N the daily sunrise change attained a maximum of +154 seconds on 5th November, but there was also a secondary max of +145 secs on 14th August. For sunset variation, the two maxes were on 8th February (+159 secs) and 27th April (+149 secs). Negative variations were much better 'behaved', with just one extreme value in each case: -182 secs on 26th March for sunrise, and -183 secs on 18th September for sunset. At lower latitudes, the dates of the double-peaks are slightly different; in addition, the phenomenon is weaker. DLMcN (talk) 12:39, 18 January 2011 (UTC)


 * The difference could easily be the result of differences in longitude, and latitude as well. Taking “Mecca” to be the center of the Kaaba (probably reasonable in this context), the differences are less but remain.


 * Thanks for the summary of Meeus’s calculations . . . an ILL costs as much as buying the book from Willmann-Bell, so it’s not an attractive option. The results are easily replicated; I’ve included a plot for 60° N in 2001. It is readily seen that the local minima in the peaks correspond very closely to the maximum rates of change in the equation of time.


 * Rise and set times used to generate the plot were calculated to the nearest millisecond; although the local minima are evident when times are calculated to the nearest second, the curves are jagged because the differences for many days are identical. The local minima are not apparent when the times are calculated to the nearest minute; of course, whether they are normally apparent to an observer is also questionable.


 * I’ve added Schaefer and Liller (1990) as a reference, and slightly changed the wording—see if it works. JeffConrad (talk) 04:38, 19 January 2011 (UTC)


 * Meeus calculated his times for 2002, not 2001. Of course, Meeus' graphs used different scales, +170 instead of +200; and Jan. 1, April 1, July 1, Oct. 1, Dec. 31 instead of day of year. Otherwise, your graph is virtually identical to those on page 318 of More mathematical astronomy morsels (your right-hand scale should be minutes for equation of time). Besides the equation of time, its derivative, the length of the true solar day, also affects the difference in the times of sunrise and sunset. See (red: equation of time, blue: length of true solar day) and . — Joe Kress (talk) 06:09, 19 January 2011 (UTC)


 * Kinda hard to guess the year without having read the chapter, and I just couldn’t justify the $25 to read it (there are interesting items in each of the five volumes, and I learned long ago that I simply can’t buy everything that suits my fancy) . . . I’ve fixed the right-hand axis; hopefully, I’ve finally got it right. We’re getting way off the topic of refraction, but I suppose this material could be useful in some other article. JeffConrad (talk) 07:26, 19 January 2011 (UTC)


 * Agreed that this is off-topic, but the right-hand axis should state "Equation of time, minutes" or a suitable abbreviation, not "Time difference", to avoid confusion with the axis for the other two lines. — Joe Kress (talk) 19:48, 19 January 2011 (UTC)

I'm reasonably happy with the new wording, including the addition of the Schaefer/Liller reference, although I'm inclined to prefer: "precise calculations can be useful for determining average day-to-day changes" - i.e. use the word: average ? [rather than "theoretical"] /// ... It is indeed illuminating to include the Equation of Time Graph in the same diagram as Meeus's Daily Variations of Sunrise and Sunset ... Well done! DLMcN (talk) 15:13, 19 January 2011 (UTC)

I agree about using "average" rather than "theoretical." In the example that I gave, there would be a high degree of confidence that sunrise on Day 2 would be later than on Day 1. I also agree that the Equation of Time Graph is a good addition. Rodneysmall (talk) 16:37, 19 January 2011 (UTC)

Theoretical > Average ... have made the change. DLMcN (talk) 21:07, 19 January 2011 (UTC)

Looks good to me. I just deleted an extra "that" before "actual changes".Rodneysmall (talk) 23:32, 19 January 2011 (UTC)


 * Perhaps “theoretical” isn’t quite the right word, but absent supporting data (e.g., tabulated observations of rise and set times rather than just calculations), I still have a problem with “average”. Perhaps Schaefer and Liller overstate the case with an uncertainty of 3.6 minutes (that value varies a bit with latitude and declination), but they certainly seem to have the support of the people who publish almanacs (and their electronic equivalents). If one calculates times to the nearest second, the ±2σ variation due to changes in refraction is 216 times the purported precision. Even with times rounded to the nearest half minute, the variation is 7.2 times the precision. I’d not have got away with that in a freshman engineering lab. Perhaps a later study has more comprehensive data; I would like to see daily plots of refraction at various locations, but doing this in a manner to remove the effect of weather unique to a given location may be no small undertaking.


 * As has been discussed, there appear to be two different patterns associated with sunrise and sunset, with potentially smaller ranges for each. But those data are limited, and in any event, such a grouping works only for the Sun; the times of Moon rise and set change by an average of 50 minutes per day, so the full range of variation may well apply.


 * The difference between the maximum and the local minimum in the plot of sunrise time differences is about 14 seconds; it is far from clear that such a difference would be physically observable. As I had mentioned, to get the smooth curves, I had to calculate the times to the nearest millisecond, which clearly is not physically meaningful. For illustration, I’ve added plots of the times calculated to the nearest second, the nearest 3.6 seconds, the nearest 0.6 minute, and the nearest minute. The curve at 1-second precision is jagged but the phenomenon is clearly visible; at 3.6-second precision, the curve is more jagged, but the phenomenon is still clearly visible. At 1-minute precision, the phenomenon cannot be seen at all; however, it is far from apparent that the 1-minute curve is unrepresentative of actual physical phenomena: for an extended period, sunrise is essentially at the same time. At 0.6-minute precision, the curve looks more reasonable, but the phenomenon is still not visible.


 * It could be argued that the very concept of “official” rise and set times is purely theoretical, for at least two reasons:
 * Variations in actual refraction, which we’ve discussed.
 * For most locations not on large bodies of water to the east or west, the horizon is occluded, so that the “official” time of rise or set cannot be observed, whatever the actual refraction.


 * That said, those theoretical values are nearly always given only to the nearest minute, with those who publish them stating in no uncertain terms that additional precision is essentially meaningless. It’s obvious that several of the participants in this discussion have considerable experience in astronomical calculations, and presumably understand the limitations of such calculations; however, I suspect that few readers of this very elementary article have such experience, and accordingly may not understand the limitations. Most important, perhaps, is that we seem to be going against the overwhelming consensus of high-quality sources. This article originally just said that almanacs only give times to the nearest minute; I added Meeus (1991) to provide a reference, and perhaps erred in interjecting judgment. But at least that judgment is supported by the sources; with the additional wording, we approach WP:OR. And yet again: this article is about refraction, not astronomical calculations. What is illustrated by the more precise calculations is indeed the effect of orbital motion, but not necessarily anything to do with actual times of rise and set, and certainly nothing to do with refraction.


 * Again, perhaps it’s a matter of fine tuning the wording; though I think we’re on untenable ground describing precise calculations as anything but theoretical (or if you prefer, times at which a body’s true altitude crosses a standard parallel), perhaps there’s another way of putting it that would be acceptable to everyone. Ultimately, a better approach might be to put this material in a different article to which it’s more directly related.


 * Off topic, but perhaps of interest: plotting daily changes in the times of Moon rise and set shows similar inflections in the curves, and it’s hard for me to see how they could relate to the equation of time. I’m still sure there’s a fairly straightforward explanation, but its identification will need to await the efforts of someone more dedicated and more astute than me. JeffConrad (talk) 01:45, 20 January 2011 (UTC)


 * A difference between the last chart and the two that precede it that I probably should have mentioned: the last chart is the difference of times given to one minute, while the others are the differences rounded to the indicated values, and accordingly are free of the oscillations shown in the last chart. Obviously, one should save the rounding for the last step, as I do in the program of mine that I mentioned above; the question then remains as to what precision in the time differences is meaningful. Ultimately, I’m not sure the two approaches really work to different ends.


 * I suppose I must concede that when one does not have a program that calculates differences before rounding, the only alternative is to calculate differences from times that aren’t rounded; the problem then is that many will take the added precision as meaningful for the times themselves, which is probably why most sources avoid it. JeffConrad (talk) 10:13, 20 January 2011 (UTC)

Regarding the wording, how about: "> ... it generally is not meaningful to give rise and set times to greater precision than the nearest minute (Meeus 1991, 103), but despite that it can sometimes be fruitful to calculate them with much greater accuracy (for example Meeus 2002, 315)." - or something such. ... 2. You should write to Meeus, attaching your graphs of daily changes in Moon rise and set times, showing the inflections - and asking for his comments or suggestions for an explanation? DLMcN (talk) 15:44, 20 January 2011 (UTC)




 * I think removing mention of average would go a long way.


 * I still question the usefulness for describing physical phenomena, though. Schaefer and Liller give a ±2σ range for refraction of 0.64°, which translates to time range of about 3.6 minutes for the “typical” conditions cited. This has always struck me as mighty large, but I’m not aware of anyone who has debunked those values, either. For the moment, let’s accept them. Theoretically, the rise and set times on successive days, could be at opposite ends of the range, giving a maximum variation in the time difference of 7.2 minutes due to refraction changes. I think this is highly unlikely, but if we take the time differences as subject to ±0.9 minute, I think we’re being reasonable. I’ve added two more plots to illustrate this, one with rise and set times rounded to the nearest minute, and the other with rise and set times given to the nearest millisecond, and the daily differences rounded to the nearest minute. In both plots, the smooth curve resulting from calculating the time differences to the nearest millisecond are shown in red; values that differ the nominal values by ±54 seconds are shown in blue.


 * The plot that results from rounding before calculating the time differences is more jagged, probably illustrating Rodney’s original point. And the smoother curve that results from rounding after calculating the time differences hints at a peak that’s very close to the one in 1-millisecond curve. But in both cases, nearly all values are well within the fairly narrow range of uncertainty, so is there any real difference in the calculated time differences for sunrise (as opposed to the times at which the Sun’s true altitude crosses the parallel at approximately −50′)? It seems to me that it’s not meaningful to say anything more than that the actual differences are likely to be somewhere in the region between the upper and lower blue curves. This would seem in accord with the statements by the former RGO, the USNO, Schaefer and Liller, and in Meus (1991).


 * So yes, precise calculations can be useful for some things; what’s less obvious (or what we may not completely agree on) is what such “things” are. I still maintain that calculations like the one discussed here are essentially theoretical events that, while perhaps of interest to a few, including some of us in this discussion, are at best marginally related to this article. JeffConrad (talk) 23:29, 20 January 2011 (UTC)

The thing I find most useful about showing sunrise/sunset tables to the nearest second is that they immediately make obvious the calculated daily changes. Consider, first, the USNO 2011 sunrise/sunset table for Washington, DC; see http://aa.usno.navy.mil/data/docs/RS_OneYear.php. For the first ten days of January, that table shows sunrise as 0727; and for both January 2nd and 3rd, shows sunset as 16:58. Now consider Paul Lutus's 2011 sunrise/sunset table for Washington, DC; see http://www.arachnoid.com/lutusp/sunrise/index_old.html. That table shows a different sunrise time for each of the first ten days of January, with the latest sunrise occurring on January 5 at 7:27:48; and shows sunset times of 4:57:45 on January 2nd and 4:58:35 on January 3rd. Now, I understand your points, Jeff, that the USNO model may be more sophisticated than Lutus's and that -- without additional analysis -- it cannot be concluded that January 5, 2011 was the latest sunrise in Washington, DC or even that sunset there occurred later on January 3, 2011 than January 2, 2011. On balance, though, I think Lutus's table, with the accompanying tutorial, is more educational to the average person because it better illustrates the daily sunrise/sunset changes. Rodneysmall (talk) 02:55, 21 January 2011 (UTC)


 * It may well be interesting, but nearly all the sources unequivocally state that it is not useful, and I don’t see how we can contradict them. Be assured that HMNAO and the USNO could easily give times to the nearest second; they do not do so because the extra precision would be meaningless. What the USNO results for 2 and 3 January show is that for practical purposes, the Sun rises at the same time on both days. When the time of an event is subject to essentially random variations that can easily be half a minute or more, giving the time to the nearest second just doesn’t make sense. Imagine the times being given by a thick line that extends between the upper and lower blue lines in the last two plots—in essence, the signal is masked by the noise. I’ve photographed hundreds of Sun and Moon rises and sets, and the limitations described by the sources are entirely consistent with my experience. And though Dr. Lutus’s calculator give the times to the nearest second, the time of sunrise for 5 January 2011 is off by 55 seconds even without accounting for variations in refraction. Is there not a disconnect here?


 * We’re repeating essentially the same discussion for about the third time. Though precise calculations help illustrate phenomena such as described in Meeus (2002), they are essentially purely theoretical.


 * We could perhaps use wording to the effect of


 * More precise calculations can be used to predict average day-to-day changes in rise and set times (for example Meeus 2002, 315) if it is understood that actual changes may differ because of unpredictable variations in atmospheric conditions.


 * I’m not OK with calling them useful when the USNO and most other sources insist they are not (acknowledging Meeus [2002] as an exception). As I’ve said several times, we’d be better off omitting the statement entirely, because it has nothing to do with refraction. It appears to me that it was added to express disagreement with the citation of Meeus (1991). For us to reasonably do so would require that we impeach the credibility of sources like HMNAO, the USNO, and Schafer and Liller, which would be tough to accomplish even if we were so inclined. JeffConrad (talk) 05:08, 21 January 2011 (UTC)

We probably hold the Wikipedia record for the length of discussion required to resolve so few words! .... Anyway, here we could perhaps recall the examples of sunset and moonset differing by just a few seconds: they certainly were useful - and if absolutely necessary, I'm sure we could find a way of citing that point in a manner which is acceptable to Wikipedia .... Incidentally, the word "fruitful" [which I suggested earlier] is not quite the same as "useful". DLMcN (talk) 08:16, 21 January 2011 (UTC)


 * Don’t be so quick to beat the drums of victory . . . I think you misunderestimate Tweakipidia.


 * Perhaps another possibility, to the effect of


 * More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with standard atmospheric conditions (for example Meeus 2002, 315) if it is understood that actual changes may differ because of unpredictable variations in actual atmospheric conditions.


 * Repetition of “atmospheric conditions” is a bit painful, but I don’t have any great ideas that would avoid “theoretical”, which doesn’t seem to find much favor.


 * Finding a way to mention the small moonset–sunset time difference would be worthwhile regardless of what we decide for the statement in question. If you look at my calculator that I linked above, you’ll see that finding dates on which that (and other time differences for phenomena for the Sun and Moon) was one of the main objectives. JeffConrad (talk) 08:33, 21 January 2011 (UTC)

I would be fine with simply saying: "More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with standard atmospheric conditions (for example Meeus 2002, 315), if it is understood that actual changes are unpredictable." Rodneysmall (talk) 16:11, 21 January 2011 (UTC)

OK, or maybe something like: ["... if it is understood that actual changes are unpredictable] due to uncertainty in the value of low-level refraction" DLMcN (talk) 16:35, 21 January 2011 (UTC)


 * I think we need to say why the changes are unpredictable. Looking at it again, it’s probably better to blame it directly on variations in refraction (the actual cause, and the topic of this article). Perhaps something like


 * More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction (for example Meeus 2002, 315) if it is understood that actual changes may differ because of unpredictable deviations from the standard value.


 * If this smacks of inelegant variation, another possibility might be


 * More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction (for example Meeus 2002, 315) if it is understood that actual changes may differ because of unpredictable variations in refraction.


 * Perhaps I’m a pedant, but I think we’re safer with “because of” than with “due to”. Yet another possibility might be


 * More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction (for example Meeus 2002, 315) if it is understood that actual refraction, and actual day-to-day changes, may vary unpredictably.


 * Given the context, I think we’re fine without “low-level”, “at low altitudes”, “near the horizon”, or something similar, and the sentence is already uncomfortably long.


 * We do need to clarify “atmospheric conditions”; in particular, we should mention that in addition to the temperature and pressure, the conditions assume a polytropic lapse rate of 6.5 K/km, deviations from which are the main cause of variations noted by Schaefer and Liller. Of course, this should be sourced, as should the rules for correcting for temperature and pressure. But that’s a different topic than the issue at hand. JeffConrad (talk) 00:06, 22 January 2011 (UTC)

I'm happy with any of Jeff's recent suggestions (above). DLMcN (talk) 07:43, 22 January 2011 (UTC)

Of the three choices, my preference is: More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction (for example Meeus 2002, 315), if it is understood that actual changes may differ because of unpredictable variations in refraction. Rodneysmall (talk) 14:43, 22 January 2011 (UTC)


 * Done. JeffConrad (talk) 20:13, 22 January 2011 (UTC)

Other studies of rise and set times
Not bad at all -- only 11 days to resolve this issue, which, I'm sure we agree, is the most critical one that mankind has ever faced. ;-) By the way, does anyone know if the USNO or other authority has done any studies comparing calculated to actual sunrise/sunset times? Rodneysmall (talk) 22:55, 22 January 2011 (UTC)


 * Many studies have been done, though I’ve only looked at a few. In fact, that’s how Schaefer and Liller determined refraction; a few of their data (in North Carolina in 1968) were obtained by Ken Seidelmann of the USNO. The paper is available in PDF from the NASA Astrophysics Data System. See this article by Harold Exton for another take on Schaefer’s and Liller’s conclusions; though I think he raises some valid questions, especially regarding Cerro Terolo, he also cherry picks the data to suit the result he seems to be looking for. JeffConrad (talk) 03:16, 23 January 2011 (UTC)

Okay, thanks, Jeff. I'll take a look. Rodneysmall (talk) 15:29, 23 January 2011 (UTC)

I've now read these two articles. I'm surprised that the USNO has not followed up on them with a more definitive study. At a minimum, I would think that the USNO could simply have someone record actual sunrise/sunset times in Washington, DC for a year and compare the data with what their model predicts. Rodneysmall (talk) 16:50, 25 January 2011 (UTC)


 * Probably because there’s never enough time, money, or people. But others have done studies, in some cases arguably better than Schaefer and Liller (as I said, it’s always easier to see what you need to do after you have the results).


 * Sampson et al. (“Variability in the Astronomical Refraction of the Rising and Setting Sun”, Publications of the Astronomical Society of the Pacific 115:1256–1261, 2003 October; hereafter “SLPH03”) analyzed 244 sunrises and 135 sunsets in Edmonton, Alberta, and appear to have carefully looked at several things that Schaefer and Liller (“SL90”) neglected. SLPH03 found variability in refraction at sunrise that was similar to what SL90 found for sunsets, but found considerably less variability in refraction at sunset. Sampson et al. have done later studies in Barbados that found considerably less variability, comparable to that found by Liller at Viña del Mar (for the second study, in 2008, I've only read the abstract).


 * Keller and Hall (“Using a digital terrain model to calculate visual sunrise and sunset times”, 2000) concluded that by using atmospheric models more specific to location and season, they could predict times of sunrise and sunset in Israel within about 15 seconds. They noted that Cerro Tololo is far above the sea horizon (2215 m), with a longer optical path, and consequently is subject to greater variability. They claimed it can be shown that when the greater path length is taken into account, Schaefer’s Cerro Tololo data can be corrected to reduce the variability to values similar to what they found in Israel (though they did not actually show it). As SLPH03 noted, SL90 did not address terrestrial refraction (i.e., refraction of the horizon), so the mean values (and perhaps the variability), especially for Cerro Tololo, are probably a bit high.


 * It probably can be concluded, that at least for some locations, with use of specific atmospheric models, possibly adjusted for morning and evening, times of sunrise and sunset can be predicted with much greater accuracy than SL90 suggests. Of course, the times of moonrise and moonset vary over the course of a month, so adjustments for early morning and late evening cannot generally be used. Andrew T. Young sums it up quite well in “Sunset Science. IV. Low-Altitude Refraction” (Astronomical Journal, 127:3622–3637, 2004 June):


 * Users of the Standard Atmosphere should recognize that such models are extremely unrealistic: the real atmosphere is never in such a state. This model averages out diurnal variations, which are particularly large over land. . . . Thus there is never a time when the whole boundary layer has the constant temperature gradient of the Standard Atmosphere: some parts of the boundary layer are near the adiabatic lapse rate, while others have an inverted lapse rate. (emphasis in original).


 * And of course, diurnal variations are in addition to variations that result from climate region and season. So again, with specific data on the variability of refraction for specific locations at specific times, it’s probably possible to predict times to better accuracy than the nearest minute (like David, my general impression would be something like half a minute), but applying  such data would be complex and tedious, and in many cases, even obtaining the data would be nearly impossible. So in general, the practice of not giving times to precision greater than the nearest minute is probably reasonable.


 * Perhaps we could include some of this information in the article, but at this stage, the emphasis might be disproportionate, and the material would probably be of interest to only a handful of readers. I think it would be more important to work on better sourcing, and perhaps including a few simple formulas (e.g., Bennett 1982) than to make a dissertation on refraction variability (what I’ve written in this post is almost as long as the article). JeffConrad (talk) 23:50, 25 January 2011 (UTC)

I agree that you're getting pretty deep into the weeds, but it's very informative. However, to clarify one point: Am I correct in believing that the more sophisticated sunrise/sunset tables incorporate diurnal, regional, and seasonal factors? Rodneysmall (talk) 02:38, 26 January 2011 (UTC)


 * In some cases, information specific to region and time can probably give better estimates of mean refraction. If the variability is low (e.g., Viña del Mar and Barbados), times can probably be predicted with greater accuracy. But if the variability is large (e.g., Cerro Tololo and Edmonton), even the one-minute precision may be illusory, regardless of the atmospheric model. In the case of the Moon, diurnal factors probably aren’t much help unless the granularity is hourly. JeffConrad (talk) 05:43, 26 January 2011 (UTC)

Okay, thanks. Rodneysmall (talk) 14:02, 26 January 2011 (UTC)

Quotation marks
Were the MOS recommendation a mandate, there would of course be no question about using straight quotation marks. But that's not the case; the editors of this article made the choice to follow conventional typographical practice, and it would seem that decision, like most other arbitrary but acceptable stylistic choices, should be respected. It particularly makes no sense to change one instance and leave the other in the previous style. Moreover, the article similarly uses normal typographical apostrophes; given the frequent occurrence of the minutes (′) and seconds (″) marks, it would seem sensible to carefully distinguish among ", “”, and ″, and among ', ‘’, and ′.

The MOS assertion that “There have traditionally been two styles concerning the look of the quotation marks” is dubious; typewriter-style quotes have been used with typewritten material (or anything printed in monospace font), while typeset material (using proportionally spaced fonts) almost exclusively use typographical quotes. This isn't a random choice; a font comprises a set of glyphs that are designed to harmonize with each other, and straight quotes do not harmonize with the other characters in a proportionally spaced font. The clash isn't quite as glaring with the default sans-serif Wikipedia typeface, but it's painfully obvious with a serif typeface, which a user can specify for printing, display or both.

There is probably some validity to the use of typographical quotes complicating searches, but the same is true for any non-ASCII character, such as en and em dashes, minus signs, multiplication symbols, minute and second symbols, accented characters, and so on.

An extended discussion obviously belongs on the MOS Talk page rather than here. But if the intent is to forbid typographical quotes, the MOS should explicitly do so. Because it does not, the use of typographical quotes in this article would seem allowable, and changing them without better reason would seem inappropriate. JeffConrad (talk) 21:19, 28 November 2010 (UTC)

Citation tag added 24 March 2011
I simply do not understand the edit summary, “References are of books which cannot be verified. Web references sought for such important phenomenon”. These books are all readily available; Wikipedia imposes no requirement whatsoever for web references, which in many cases are far less reliable than books. WP:V makes this quite clear:


 * The principle of verifiability implies nothing about ease of access to sources: some online sources may require payment, while some print sources may be available only in university libraries.

Absent a much better explanation, I’m going to remove the tag. JeffConrad (talk) 02:09, 25 March 2011 (UTC)


 * I added a link to Refraction near the horizon. Although the 3rd edition of Astrophysical quantities does not appear to be online, the 4th edition is, entitled Allen's Astrophysical Quantities. However, after reading the article's statement that refraction "quickly increases as the horizon is approached", I expect to see something more obvious than a separate equation for a zenith distance greater than 80° at Atmospheric refraction and air path (pp.262–264). Neither of Jean Meeus' cited books appears to be online, Astronomical Algorithms and More mathematical astronomy morsels. — Joe Kress (talk) 03:02, 25 March 2011 (UTC)


 * The link you added is certainly helpful, and I should have included it initially. I’ve also searched for online versions of some of the other works, with results similar to yours. The 4th ed. of AQ is quite different from the 3rd ed.; I didn’t have the former handy at the time (and it doesn’t cover the topic quite as well—the 3rd ed. includes a table.)
 * There arguably are several statements in the article that need additional support, such as the specific values of refraction, and the temperature and pressure corrections. If we think that is the case, we should tag them individually (or at least list them here); a tagging with no specifics is essentially impossible to address. My objection to this tag is that the stated reasons are clearly invalid; moreover, this editor seems to have a penchant for capricious tagging and in some cases, capricious edits. So absent clarification, I’m still inclined to remove the tag. We should, of course, flag specific statements (such as those I’ve suggested) if necessary, and address them when we can. JeffConrad (talk) 07:26, 25 March 2011 (UTC)


 * If we think citations are needed for the items I’ve mentioned above, we could probably cite temperature correction formulas given in Meeus (1991) or similar formulas in the Explanatory Supplement to the Astronomical Almanac. If reference to the tables in AQ, 3rd ed. are not sufficient, we could give the empirical formulas by Bennett (and perhaps Sæmundsson). We could also mention more rigorous methods such as those of Garfinkel (1967) or Auer and Standish (2000), but I think this might be getting carried away, and given the variability of actual atmospheric conditions, the additional accuracy is somewhat illusory anyway. JeffConrad (talk) 21:03, 25 March 2011 (UTC)


 * Although I agree that online sources are not required, if available they should be provided. The refraction section of the Explanatory Supplement to the Astronomical Almanac, pp.140-144 is available online. The Atmospheric Refraction Applet by J. Giesen includes Saemundsson's formula and pressure/temperture corrections from Meeus, as well as several graphs and a table of atmospheric refraction. Specific values given in the article may be exempt under WP:CALC. We should not tag anything unless we plan to provide a citation within a year or so, otherwise the 'challenged' text is subject to deletion by anyone. — Joe Kress (talk) 02:40, 26 March 2011 (UTC)


 * The Explanatory Supplement gives fairly good coverage to Auer and Standish (the paper was written in 1979 but not accepted until 2000), but it’s very difficult for an average reader to see how that supports the rapid increase in refraction is approached; the table in AQ 3rd ed. gives calculated values, so the support is more obvious. The published paper is also available from the Harvard Astrophysics System. I think Geisen is pushing it with regard to WP:RS (I don’t see how it’s any better than just giving the same formulas here), though it’s probably fine as an external link. I’d rather cite Bennett, Sæmundsson, or both, either directly or via Meeus (1991); though direct citation is ostensibly better, Meeus is usually easier to find than the Journal of Navigation (Bennett). Sæmundsson’s Sky and Telescope article is available in many public libraries.
 * I’m not big on tagging unless I really question a statement. Because User:रामा|रामा hasn’t responded, I’ve removed the general tag. Again, if we think certain statements need support, we should indicate what they are; I think a listing here would suffice. Absent additional comment, I’ll look at adding the temperature correction and simple refraction formulas. JeffConrad (talk) 07:02, 26 March 2011 (UTC)


 * I’ve added a section with this information; I’ve cited the original sources. I think this addresses any significant concerns about unsupported statements (though I don’t suggest that additional references would not help). Two comments:
 * I gave the pressure in mbar because that’s how it’s given in Meeus (1991); if we’re comfortable with conversion to kPa, we can change to this for consistency with the previous section.
 * I retained the calculated changes and moved them to the end of the new section, though I’m not sure they add all that much now that we have the formulas. If desired, we can remove them.
 * See if this works. JeffConrad (talk) 08:50, 26 March 2011 (UTC)