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Russell H., Electronics and systems professinal
Category: Homework
Satisfied Customers: 10328
Experience:  Educated in electronics and experienced in multiple technologies, I fix things, and also explain them.
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If this is answered within 72 hours.Assuming optimal conditions,

Customer Question

If this is answered within 72 hours.
Assuming optimal conditions, i.e., moonless night and no artificial illumination, then given the geometric position of the center of the Sun below the horizon what formula would give the magnitude of star a person with 20-20 vision but without the aid of binoculars, telescope, etc. could expect to detect, covering all 3 phases of twilight: civil, nautical, and astronomical.
Submitted: 12 months ago.
Category: Homework
Expert:  Justin Williams replied 12 months ago.
http://i.imgur.com/g6NiJUO.png
Customer: replied 12 months ago.
my understanding of the answer is:6 - (3.98 /1000) = 2.5 log (I subscript 2/ I "something") . (Sorry I don't know how to do sub/superscripts here.)Is this correct? What is I subscript 2? What is the "something?"
Customer: replied 12 months ago.
how do I get your response? through here-like a chat, or separate email, or what?
Customer: replied 12 months ago.
my understanding is that clicking the "View Response" button takes us into a chat situation, but I don't see it happening??
Expert:  Justin Williams replied 12 months ago.
I'm sorry, maybe I am in over my head with this question. I put the equation together using an entry about visible light and magnitude on wikipedia and I fear my answer could be wrong. I am going to opt out of this question in the hopes that someone with more knowledge than me can answer it.
Expert:  Russell H. replied 12 months ago.
Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question. What definitions of civil twilight, nautical ditto, and astronomical ditto, are you using? is the first query I would have to make before answering your question. Also - I need to check - you are assuming the very best of viewing conditions and atmospheric clarity, no fog or mist or smog or smoke, no cloud, etc., and presumably no artificial or man-made lighting obscuration whatever - is that so?And, you are also not taking into account the extinction-with-altitude, I would presume - in other words, you are assuming the star is at the zenith or nearly, since even clear atmosphere obscures the light from stars slightly with lower altitude.
Customer: replied 12 months ago.
Russell,Thank you for your response."What definitions of civil twilight, nautical ditto, and astronomical ditto, are you using? is the first query I would have to make before answering your question."***Please see attached file "Rise, Set, and Twilight Definitions a.pdf" for definitions from the USNO website.Also - I need to check - you are assuming the very best of viewing conditions and atmospheric clarity, no fog or mist or smog or smoke, no cloud, etc., and presumably no artificial or man-made lighting obscuration whatever - is that so?**yes, optimal viewing conditionsAnd, you are also not taking into account the extinction-with-altitude, I would presume - in other words, you are assuming the star is at the zenith or nearly, since even clear atmosphere obscures the light from stars slightly with lower altitude.**I think this condition would be overly restrictive. Since we see stars all over the place, I'm not certain this restriction would be realistic-although I would be amenable to discussing this if you think I'm wrong. Of course, ideal would be to include a correction as the location of the given star departs from the zenith.Thanks.Larry Elewitz
Expert:  Russell H. replied 12 months ago.
Thanks for your response.Maybe I was overly pedantic about definitions of the three twilights. But you've cleared that up for certain.As for extinction-with-altitude... it's significant for amateur astronomers estimating naked-eye stars without instruments, when those stars (or other objects) are at varying altitudes. It's pedantry for amateur astronomers in other words. Now I shall have to figure out how twilight affects stars' visibility. That I admit I don't have a snappy answer for, it will take a little while.
Customer: replied 12 months ago.
Thanks.I just want to make certain you understand that what I'm looking for is that as the Sun is farther and farther below the horizon, one can see higher magnitude stars because of the decrease in residual sunlight, and I'm looking for a formula relating magnitude of star which can be seen with geometric angle below the horizon, from sunset to 18 degrees below the horizon (which, I assume, will be identical with 18 degrees below the horizon going all the way to sunrise).
Expert:  Russell H. replied 11 months ago.
I want to let you know that though I have been busy with other cases, I have managed to at least locate a promising source of info about star extinction during twilight, here (for my own reference at least):https://www.osapublishing.org/josa/abstract.cfm?uri=josa-43-3-177 (Unfortunately I would have to purchase access to read this article.) So far is how far I have gotten with the answer.
Expert:  Russell H. replied 11 months ago.