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  1. Path: sparky!uunet!gatech!prism!emperor!collins
  2. From: collins@emperor.gatech.edu (Tom Collins)
  3. Newsgroups: sci.astro
  4. Subject: Re: Distance of horizon
  5. Message-ID: <75439@hydra.gatech.EDU>
  6. Date: 19 Nov 92 14:46:11 GMT
  7. References: <lglhj3INNb0c@appserv.Eng.Sun.COM> <1992Nov19.021430.13833@sfu.ca>
  8. Sender: news@prism.gatech.EDU
  9. Organization: CERL-EE, Georgia Institute of Technology
  10. Lines: 66
  11.  
  12. In article <1992Nov19.021430.13833@sfu.ca> palmer@sfu.ca (Leigh Palmer) writes:
  13. >In article <lglhj3INNb0c@appserv.Eng.Sun.COM> fiddler@concertina.Eng.Sun.COM
  14. >(steve hix) writes:
  15. >>Anyone have handy a function for figuring the distance of the
  16. >>horizon from a viewer based on the viewer's height from the
  17. >>surface?
  18. >                            -1
  19. >Try d = R arccos ( 1 + h/R )
  20. >
  21. >    d = horizon distance
  22. >    h = height above MSL (assuming horizon is at sea level)
  23. >    R = radius of Earth
  24.  
  25.  
  26. Don't think so.  Look at the figure below and see if the answer isn't 
  27. pretty simple.  (Assuming of course, a smooth earth that is round, rather
  28. than pear-shaped).  Don't peek at the answer :-).
  29.  
  30.    __________________________________
  31.    \               d         _   -  |
  32.      \ h              _  -          |
  33.        \           -                |  (lines of tangency are always 
  34.          \     -                    |   perpendicular to radius)
  35.            \/                       |
  36.              \                      |
  37.                \                    | R
  38.                  \                  |
  39.                    \                |
  40.                      \              |
  41.                      R \            |
  42.                          \          |
  43.                            \        |
  44.                              \      |
  45.                                \    |
  46.                                  \  |
  47.                                    \  Center of earth 
  48.  
  49.  Answer below:
  50.  
  51.  
  52.  
  53.  
  54.  
  55.  
  56.  
  57.  
  58.  
  59.  
  60.  
  61.  
  62.  
  63.  
  64.  
  65.        2    2        2
  66. since R  + d  = (R+h)         (Pythagorean theorem)
  67.  
  68.                 2    2
  69. d = sqrt(  (R+h)  - R  )
  70.  
  71. This says that the horizon for a six-foot tall person is about
  72. 3 miles away.
  73. -- 
  74. Tom Collins                               tom.collins@ee.gatech.edu
  75. Georgia Institute of Technology           (404) 894-2509
  76. 400 Tenth St. NW, CRB 384
  77. Atlanta, GA  30332-0540 
  78.