Twilight: The Final Analysis
G.D.O'Bradovich III
July, 2017
[extensive, but incomplete]
There are three versions or definitions for the term “twilight”.
Astronomical Twilight: the sun is 12° to 18° below the horizon.
Nautical Twilight: the sun is 12° to 6° below the horizon.
Civil Twilight: the sun is 6° below the horizon.
The three twilights are each six degrees and, together, they total eighteen degrees below the horizon before sunrise and fter sunset.
Astronomical Twilight: the sun is 12° to 18° below the horizon.
Nautical Twilight: the sun is 12° to 6° below the horizon.
Civil Twilight: the sun is 6° below the horizon.
The three twilights are each six degrees and, together, they total eighteen degrees below the horizon before sunrise and fter sunset.
The following information is for Quito, Ecuador; Cairo, Egypt; and Terre Haute, Indiana. Quito Is within one degree of the equator, Cairo is near 30° north and Terre Haute (39°29’) has a similar latitude both to Rome, Italy and Istanbul.
In the following table, solar noon has been adjusted to 12pm and the other times have been adjusted accordingly. We have done this so that the effects of daylight saving time is eliminated and solar noon becomes the fixed point of reference.
In the following table, solar noon has been adjusted to 12pm and the other times have been adjusted accordingly. We have done this so that the effects of daylight saving time is eliminated and solar noon becomes the fixed point of reference.
Start Time
Quito
March 20 June 20 September 22 December 21 |
Astronomical
4:48 4:42 4:48 4:41 |
Nautical
5:12 5:02 5:12 5:07 |
Civil
5:36 5:34 5:36 5:33 |
Sunrise
5:57 5:57 5:57 5:56 |
Cairo
March 20 June 20 September 22 December 21 |
Astronomical
4:39 3:21 4:36 5:28 |
Nautical
5:05 3:57 5:04 5:57 |
Civil
5:33 4:30 5:32 5:56 |
Sunrise
5:56 4:58 5:56 6:53 |
Terre Haute
March 20 June 20 September 22 December 21 |
Astronomical
4:26 3:21 4:25 4:42 |
Nautical
4:58 3:57 4:57 5:15 |
Civil
5:29 4:30 5:28 5:49 |
Sunrise
5:56 4:58 5:55 6:19 |
Duration (in minutes)
Quito
March 20 June 20 September 22 December 21 |
Astronomical
:24 :22 :24 :26 |
Nautical
:24 :22 :24 :26 |
Civil
:21 :22 :21 :22 |
Total Twilight
:69 1:09 :64 1:04 :69 1:09 :75 1:15 |
Cairo
March 20 June 20 September 22 December 21 |
Astronomical
:26 :36 :28 :29 |
Nautical
:28 :33 :28 :30 |
Civil
:22 :28 :24 :26 |
Total Twilight
:77 1:17 :97 1:37 :80 1:20 :84 1:24 |
Terre Haute
March 20 June 20 September 22 December 21 |
Astronomical
:32 :47 :32 :33 |
Nautical
:31 :42 :31 :34 |
Civil
:27 :32 :27 :30 |
Total Twilight
:90 1:30 :121 2:01 :90 1:30 :107 1:47 |
The duration for each city’s respective astronomical and nautical twilight are the similar; we observe that the higher latitudes have longer twilights. Interestingly, civil twilight, which is also six degrees, is less time than either astronomical or nautical twilight. Since the three twilights are six degrees, we expect the three durations to be equal, or nearly equal. Yet, civil twilight is always a shorter duration than either astronomical or nautical twilight. We are uncertain of the reason for this discrepancy.
Before our investigation, we presumed that throughout the solar year, sunrises and sunsets moved in tandem, however, this is not reality.
For Terre Haute, the earliest the sun sets is at 5:25 pm in December from the fourth through the tenth, whereas the latest the sun rises is at 8:10 am in January, from the second to the seventh.
The earliest the sun rises is 6:21am from June 12 to the 15; the latest the sun sets is 9:20pm from June 20 to July 4.
The following table lists the changes in the amount of daylight for five days before and five days after the beginning of the seasons for Terre Haute.
For Terre Haute, the earliest the sun sets is at 5:25 pm in December from the fourth through the tenth, whereas the latest the sun rises is at 8:10 am in January, from the second to the seventh.
The earliest the sun rises is 6:21am from June 12 to the 15; the latest the sun sets is 9:20pm from June 20 to July 4.
The following table lists the changes in the amount of daylight for five days before and five days after the beginning of the seasons for Terre Haute.
March 15-19
March 21-25 June 15-19 June 21-25 September 17-21 September 23-27 December 16-20 December 22-26 |
12:58
12:45 1:09 :34 12:45 12:45 1:03 :47 |
We now understand the frustration of 16th century astronomers in their attempts to determine the dates of the solstices and equinoxes, and the length of the solar year.
For the eleven days surrounding the summer solstice, there is a difference in daylight of 45 minutes (the difference between an increase of 69 minutes and a decrease of 34 minutes); for the winter solstice, 16 minutes (the difference between a decrease of 63 minutes and an increase of 47 minutes).
For the eleven days surrounding the spring equinox there is an increase of daylight of 25:43; for the autumnal equinox, a decrease of 25:30. Although the measuring of shadow lengths of upright sticks or poles are suggested as a method to determine the seasons, such attempts cannot determine the exact day. Clearly, accurate clocks are necessity to determine the amount of daylight to determine the exact day, and not a range of days, for the commencement the seasons.
Capricious Nature has not provided equal seasons, therefore, even with an accurate knowledge of the solar year (exactly 1,461 days in four years), dividing the year into four equal seasons is not the correct manner of assigning the start of the seasons, as there are no partial days.
For the eleven days surrounding the summer solstice, there is a difference in daylight of 45 minutes (the difference between an increase of 69 minutes and a decrease of 34 minutes); for the winter solstice, 16 minutes (the difference between a decrease of 63 minutes and an increase of 47 minutes).
For the eleven days surrounding the spring equinox there is an increase of daylight of 25:43; for the autumnal equinox, a decrease of 25:30. Although the measuring of shadow lengths of upright sticks or poles are suggested as a method to determine the seasons, such attempts cannot determine the exact day. Clearly, accurate clocks are necessity to determine the amount of daylight to determine the exact day, and not a range of days, for the commencement the seasons.
Capricious Nature has not provided equal seasons, therefore, even with an accurate knowledge of the solar year (exactly 1,461 days in four years), dividing the year into four equal seasons is not the correct manner of assigning the start of the seasons, as there are no partial days.
The cross quarter days for Terre Haute, 2017 (Adjusted to solar noon)
Terre Haute
February 3 May 4 August 6 November 6 |
Astronomical
5:20 3:17 3:14 5:19 |
Nautical
5:51 3:55 3:53 5:50 |
Civil
6:23 4:31 4:29 6:22 |
Sunrise
6:51 5:00 4:59 6:50 |
Duration
Terre Haute
February 3 May 4 August 6 November 6 |
Astronomical
:31 :38 :39 :31 |
Nautical
:32 :36 :36 :32 |
Civil
:28 :29 :30 :28 |
Total Twilight
91 1:31 103 1:43 105 1:45 91 1:31 |
Seasons and Cross Quarters for Terre Haute
Date
February 3 March 20 May 4 June 20 August 6 September 22 November 6 December 21 |
Astronomical
5:20 4:26 3:17 3:21 3:14 4:25 5:19 4:42 |
Nautical
5:51 4:58 3:55 3:57 3:53 4:57 5:50 5:15 |
Civil
6:23 5:29 4:31 4:30 4:29 5:28 6:22 5:49 |
Sunrise
6:51 5:56 5:00 4:58 4:59 5:55 6:50 6:19 |
Sunrise, Sunset, (in degrees) and Solar Elevation (in degrees and minutes°)
Date
February 3 March 20 May 4 June 20 August 6 September 22 November 6 December 21 |
Sunrise
111 89 68 58 68 89 110 120 |
Sunset
249 271 292 302 292 271 249 240 |
Elevation
34°18' 50°42' 66°42' 74° 67° 50°36' 34°24' 27° 6' |
It is impossible to determine the day of the solstice based exclusively either on the location, in degrees, of the rising sun, or the elevation, at solar noon, of the sun. The reason this method cannot provide a single day is that there are multiple days that have the same degrees for sunrise and for the sun's elevation at solar noon. Therefore, the only method is to measure the amount of daylight, which fluctuates on the days before and after a solstice. We remind the Gentle Reader that the time difference is only a few seconds, hence, accurate clocks are necessary.
It sometimes occurs that restaurants are critically understaffed and employees are sent from another location to help out. Invariably, the manager who sends an employee, sends the individual who is deemed the most expendable, that is, the less productive or least desirable employee. This technique of sending the worst employee may have its origin in card playing, where one discards an unwanted card.
As an experienced manager, Yours Truly always sent the best available employee. The “best” person was not chosen on completely objective grounds; nor the reasoning for the choice always justifiable: it may be said that we have our favorites, where favoritism is understood as likability and the likelihood that they would benefit from the experience. At this point in our career, we can acknowledge that “some employees are more equal than others”: those with virtues were favored to the detriment of the mediocre.
There were two reasons for Yours Truly’s nonconformist behavior when sending aid to other stores, firstly, from previous experience, the staff and management at the other store would know the arriving employee is the worst employee, therefore, they would wonder what my other, and presumably better, employees were capable of accomplishing.
Secondly, I would always tell the person I sent to “help out” to observe that store’s operation and compare it to our store’s adherence to policy and procedure; furthermore, I said that I didn't care what happened at the other store: I don't want a report on how the management performed or how employees worked, or anything else.
Invariably, upon their return, they would seek me out and enthusiastically ejaculate: “You wouldn't believe what...” as their new experience was a personal revelation that cried out to be shared. Now armed with the invaluable experience of working in another location, I would tell them to compare both stores, and reach their own conclusions. Again, I'd say that I didn't want to know their opinions. Of course, my capable employees, or those who could do more than one thing well, would reach one valid conclusion: our store was better.
For all my quirks and oddities, my shifts were better ran, more productive (as we positioned staff according to both corporate guidelines and in accordance with my insights into astrology) and, as a direct consequence, were busier. I repeatedly explained during the shift that the reason we were busier than other shifts is that “People are coming by to see what I'll do next.”
While running the fry station I would declare that “Some people call me the Fry Master.” and few crew, less than a handful over several years, ever approached me for my lack of originality. [Disclosure: FryMaster is a manufacturer of restaurant equipment and their name and logo were displayed on almost all the equipment located in the kitchen.]
In conclusion to this part, firstly, we sent our most capable employee to impress upon managers and staff at various locations that we were the better store and, secondly, the origin of our name “Fry Master” was a better kept secret than why Dick and Mac were obsessed with counting the number of hamburgers sold.
Recently, it came to our attention that Apprentice Denver will be living in Wiley Hall (no doubt as an homage to a great mentor: Yours Truly) and has been offered the possibility of studying abroad. Upon experiencing the unenthusiastic reaction of Apprentice Denver, we suspected that our naïve and non cosmopolitan colleague did not understand the significance of this opportunity. Therefore, we expressly stated to Apprentice Denver in clear and simple words that world class universities send their best students abroad, and while we do not doubt Apprentice Denver will benefit from this experience, Great Occultists know that any benefit to Apprentice Denver is of a secondary nature: the primary reason for sending Apprentice Denver is to impress upon the instructors at the receiving university that all undergraduates at Purdue University have similar attributes as Apprentice Denver. After the receiving university is duly impressed with Apprentice Denver, the faculty at the respective university can only imagine what abilities and potentials the doctoral candidates at Purdue University posses.
Gentle Researcher, it seems in the wonderful world of the Occult that the differences in the understanding between the modus operandi of world renowned universities and infrequent opportunities available at exceptional restaurants are by degrees, not kinds.
As an experienced manager, Yours Truly always sent the best available employee. The “best” person was not chosen on completely objective grounds; nor the reasoning for the choice always justifiable: it may be said that we have our favorites, where favoritism is understood as likability and the likelihood that they would benefit from the experience. At this point in our career, we can acknowledge that “some employees are more equal than others”: those with virtues were favored to the detriment of the mediocre.
There were two reasons for Yours Truly’s nonconformist behavior when sending aid to other stores, firstly, from previous experience, the staff and management at the other store would know the arriving employee is the worst employee, therefore, they would wonder what my other, and presumably better, employees were capable of accomplishing.
Secondly, I would always tell the person I sent to “help out” to observe that store’s operation and compare it to our store’s adherence to policy and procedure; furthermore, I said that I didn't care what happened at the other store: I don't want a report on how the management performed or how employees worked, or anything else.
Invariably, upon their return, they would seek me out and enthusiastically ejaculate: “You wouldn't believe what...” as their new experience was a personal revelation that cried out to be shared. Now armed with the invaluable experience of working in another location, I would tell them to compare both stores, and reach their own conclusions. Again, I'd say that I didn't want to know their opinions. Of course, my capable employees, or those who could do more than one thing well, would reach one valid conclusion: our store was better.
For all my quirks and oddities, my shifts were better ran, more productive (as we positioned staff according to both corporate guidelines and in accordance with my insights into astrology) and, as a direct consequence, were busier. I repeatedly explained during the shift that the reason we were busier than other shifts is that “People are coming by to see what I'll do next.”
While running the fry station I would declare that “Some people call me the Fry Master.” and few crew, less than a handful over several years, ever approached me for my lack of originality. [Disclosure: FryMaster is a manufacturer of restaurant equipment and their name and logo were displayed on almost all the equipment located in the kitchen.]
In conclusion to this part, firstly, we sent our most capable employee to impress upon managers and staff at various locations that we were the better store and, secondly, the origin of our name “Fry Master” was a better kept secret than why Dick and Mac were obsessed with counting the number of hamburgers sold.
Recently, it came to our attention that Apprentice Denver will be living in Wiley Hall (no doubt as an homage to a great mentor: Yours Truly) and has been offered the possibility of studying abroad. Upon experiencing the unenthusiastic reaction of Apprentice Denver, we suspected that our naïve and non cosmopolitan colleague did not understand the significance of this opportunity. Therefore, we expressly stated to Apprentice Denver in clear and simple words that world class universities send their best students abroad, and while we do not doubt Apprentice Denver will benefit from this experience, Great Occultists know that any benefit to Apprentice Denver is of a secondary nature: the primary reason for sending Apprentice Denver is to impress upon the instructors at the receiving university that all undergraduates at Purdue University have similar attributes as Apprentice Denver. After the receiving university is duly impressed with Apprentice Denver, the faculty at the respective university can only imagine what abilities and potentials the doctoral candidates at Purdue University posses.
Gentle Researcher, it seems in the wonderful world of the Occult that the differences in the understanding between the modus operandi of world renowned universities and infrequent opportunities available at exceptional restaurants are by degrees, not kinds.