If a person was 100,000 feet above Houston, how far could they see
before the curavature of the earth blocked their view?  I need you to
show your work.

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Request for Question Clarification by scriptor-ga on 18 Sep 2005 05:12 PDT

Is it possible that this question is actually a homework assignment or
something similar?

Scriptor

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Clarification of Question by sugarland-ga on 19 Sep 2005 11:17 PDT

No, this is not homework (20 years past that).  I was driving to San
Antonio a couple of weeks ago and I was on the phone with a friend
there.  I made a comment that there were some large rain clouds that
direction (west) and asked if it was raining there.  I about got
laughed on the phone call.  His reply was first no, and then that
there was no way I could see a rain cloud over San Antonio while on
the ground in Houston.  I told him I thought clouds could top out
pretty high (I said 100,000 ft, but a pilot friend has corrected me to
50,000 feet).

So I want to prove to my friend that I could in fact see something
100,000 feet in the air that is 200 miles away (Houston to San
Antonio), and even better if I could show I could see it at 50,000
feet.  Lastly, if I can't see that far then I'll know to quietly leave
the debate behind.

In point of fact the storm was over a city about half way in between, Flatonia.

After reviewing the question I see why you are asking if it's
homework.  The reason I want to understand the calculation is to re-do
it for 50,000 feet.

Check out Google Earth, you will at least see what you are looking for.
 Google Earth + computer = the best view you are going to get without
being there, thats my work. Now you do the math :)

I asked a similer question a while ago.
See if it helps:
http://www.answers.google.com/answers/threadview?id=468086

Horizon problem
http://people.smu.edu/rnhart/horizon.htm

  h = height above the earth
  R = radius of the earth
  d = distance you can see
        ___________
  d = \/ 2Rh + h^2 

Plugging in

  R = 3959.87152 mi
  h = 18.9393939 mi = 100000 ft 

yields

  d = 387.754863 mi