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Earth is roughly 8000 miles in diameter.

 

(a) I'm riding in a hot air balloon 1/2 mile above the surface of earth. Approximately how far away is the horizon? (In other words, how far away is the farthest point on the surface of Earth that I can see.)

 

(b) What if I'm in a plane 10 miles above the surface of the earth?

 

(c) What is I'm in a spaceship 200 miles above the surface of the earth?

 Jan 1, 2021
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There is a very neat formula that you can use:

 

(a) - 1/2 mile =5280 feet / 2=2,640 feet

Distance to horizon =Sqrt[1.5 * 2,640] =sqrt[3,960] =~63 miles

 

Do exactly the same thing for (b) and (c).

 Jan 2, 2021

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