Xref: utzoo talk.politics.misc:8104 sci.misc:932 Path: utzoo!mnetor!uunet!husc6!bloom-beacon!tut.cis.ohio-state.edu!rutgers!mtune!mtgzz!mtgzy!mtuxo!homxb!whuts!orb From: orb@whuts.UUCP (SEVENER) Newsgroups: talk.politics.misc,sci.misc Subject: Re: The Last Word on Friedman, Sevener, and Cuba Message-ID: <3904@whuts.UUCP> Date: 10 Mar 88 23:37:55 GMT References: <3405@bloom-beacon.MIT.EDU> <3895@whuts.UUCP> <3588@bloom-beacon.MIT.EDU> Reply-To: orb@whuts.UUCP (45263-SEVENER,T.J.) Organization: AT&T Bell Laboratories, Whippany, NJ Lines: 94 Summary: More nonsense from JF Carr In article <3588@bloom-beacon.MIT.EDU> jfc@athena.mit.edu (John F Carr) writes: > : my explanation of the principle of refraction, > : I will herein post quotes from "An Introduction to the > : Meaning and Structure of Physics" by Leon N. Cooper. > : It is an introductory college physics textbook. > >And my calculations are based on (besides common sense and scientific >reasoning) the CRC Handbook of Chemistry and Physics, an astronomy >textbook, and class notes for an astronomy course. Which has nothing to do with the issue involved here. We are not talking about an astronomical object - we are not talking about a transition from SeaLevel air density to a practical vacumn. We are talking about a tangent line of sight which at the *maximum* is 2059 feet high out of an atmosphere 180 miles thick. This is *not* the same as the case of the Sun which is 93 million miles away. Now let's talk about the actual atmospheric densities at Sea-Level versus 2059 feet versus the upper atmosphere. According to the Encyclopedia of Atmospheric Science and Astrogeology (p. 781) here are some standard pressures for values of concern here: height pressure refractive index Sea Level 29.92 inches 1.00029 3000 feet 26.81 inches ?? 18000 feet 14.94 inches ?? (mine) Space ~0 inches ~1.00000 What is the refractive index for air pressure of 29.92 inches compared to the refractive index for air pressure of 26.81 inches? I could not find the refractive index for air pressure of 26.81 inches. I *could* find the refractive index for air pressure at Sea Level, i.e. 29.92 inches. That turns out to be the very small value of 1.00029. This is compared to a refractive index of 1.33 for water, and of course, 1.0000 (the standard of measurement) for a perfect vacumn. (New Columbia Encyclopedia, p.2294) Even if we assume some exponential relation between air pressure and the refractive index, we are talking about a very *small* difference here. A crude extrapolation would be we are talking about a refraction index of 1.00015. But we don't even have to get into that to prove John Carr's figures are totally off. And we don't need calculus or differential equations or anything else to prove him wrong. All that is needed is simple geometry,trigononmetry and logic. To make Carr's case the strongest possible, suppose we take his figure for the refraction of the Sun, to wit: >In article <3267@bloom-beacon.MIT.EDU> jfc@athena.mit.edu (me) writes: JFC : The amount of refraction depends strongly on atmospheric conditions. JFC : The only figure I know is the apparent displacement of (for example) JFC : the Sun on the horizon. This is .5 degrees This is the absolute *maximum* refraction that is possible. All this means is that whereas in my original calculations I took the cos of 1 degree and divided the radius of the Earth to obtain the height of the horizon line. Under the best scenario then instead we take the cos of .5 degree which is .99996, then divide the radius of the Earth by that value to obtain the total height we get: 3963.2/.99996 = 3963.36 The height of this line, accounting for a refraction displacement of .5 degrees will then be: 3963.36 (height of line of sight with .5 degree refraction) -3963.20 (radius of the Earth) -------- .16 miles * 5280 feet/mile = 844.8 feet And again, we find that this is unequivocally *higher* than the highest point in Cuba within 90 miles of Key West which is 344 feet high. Of course this is accepting John Carr's figure of 0.5 degrees displacement for the Sun on the horizon which is an *overestimate* for something less than 3000 feet high. You are wrong, wrong, wrong, Mr. Carr. Mr. Swan and the whole bunch of you. Ask any of your Physics professors about it John. tim sevener whuts!orb