MadSci Network: Physics
Query:

Re: How far can you see, horizon-to-horizon, from an airplane at 37,000 feet?

Date: Wed Jul 28 12:06:33 1999
Posted By: Demian Bertozzi, Grad student, Physics, UFSC
Area of science: Physics
ID: 934812662.Ph
Message:

   Hey, Joe! The way I see, It's a pure geometrical question, not Physics. 
Look at the picture.




 We want to know the length of the arc AB. We only need to know the angle 
 which determines the arc, so  l = .R , where R is the Earth radius. R 
is aproximatelly equal to 6.400 km, but I don't know this value on  ft , 
so itís an exercise to you. The  angle is easy to determine. Note that cos
(/2) = R/(R+h). The angle is exactly /2 because the two triangles are 
equivalent. With a calculator, you can imediatelly obtain . However, you 
can use this relation

Cos (/2) = ( (1+ cos ) / 2 )Ĺ

to take directly the cos .

	You may want to know that I did a rough aproximation on solving 
this question. I put the plane to travel right above the equator line, 
following its direction, because at that point the section (cut) of the 
Earth is a circle with R=6.400 km. If the plane, for instance, were 
travelling perpendicularly to equator, the section would be na elipsis, 
but I think my way is a reasonable aproach for what you need.

Hope this helps.

D..!


Any doubts to escrutinador@hotmail.com





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