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Do you want to sleep ?

25 Jan

Whenever I travelled, I always wondered if earth is indeed really big or not. Whenever I flew, it will seem to me as if I am seeing the same old stuff through the window and then suddenly I will hear that the flight has reached its destination. Well, I was aware that the farther up you fly, your visibility (in a clear sky) will be much higher and hence, it is possible that you will see more than what you normally do.

For lack of any useful thing to do, I was trying to figure out an answer to this rather mundane question. To do any mathematical calculation on this stuff, I had to assume that the earth was a perfect sphere. I checked up the radius of the earth to be around 6400 kilometers. This would mean that, if you are standing at a height “h” (say 170 cm) from the ground, in a clear sky, you will see things upto 22 kilometers from the point you are standing (actually, you should draw a circle of radius 22 km around you since you can just rotate to see all those objects). You compute this by drawing a tangent from the top of your head on to the sphere. Now, you will have a right-angled triangle with hypotenuse of “r+h” and a side of “r”. The third side is the distance you would see from a height h (d = sqrt(h^2 + 2*h*r)). So, if a flight is hovering at an altitude of 35000 feet (10.668 km), you will be able to see a distance of upto 369.68 kilometres. Given that the circumference of earth is around 40,000 km, you just need approximately 54 positions to see the entire circumference of earth. In other words, if you travel 1000 km, you just need 2 to 3 positions to completely see the whole path. No wonder why I felt the way I did.

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4 Comments

Posted by on January 25, 2006 in From AM-KICKING blog

 

4 responses to “Do you want to sleep ?

  1. BrainWaves

    January 25, 2006 at 6:50 pm

    It took a while for me to visulize the formula you are talking about.
    I was initially visulaizing a right angled triangle with the person standing in the center. So, for people like me, he is talking about person standing on the circumference of the circle.(earth)

    Just to continue your argument after some finite distance number of points must be 2. Same way we can see mooooon (Keerthana’s language) on a full moon day.

    And continuing it further, after another (in)finite point we won’t be able to see it at all πŸ˜‰

     
  2. Mindframes

    January 25, 2006 at 7:22 pm

    In your last para, I am assuming that you are talking about infinite height from the center of the earth…Is that right?

    That brings up an interesting question. I always wonder why objects look smaller when they are at a farther distance. I assume that, if I know the distance an object is from my current position and its apparent size as seen by me, I should be able to somehow calculate its actual size. But, is it entirely true? Consider a small ant. When it looks at a farther object, will it appear bigger than how it appears to me? In that case, is size of the eye (focal length of the lens of the eye) a factor? How would an organism see other things when its focal length tends to zero…infinitely bigger?…Hope u r asleep now…:)

     
  3. BrainWaves

    January 25, 2006 at 7:35 pm

    May be they will see us as we see high rise building in close quarters?

     
  4. Survivor

    January 26, 2006 at 6:04 pm

    No wonder why I am feeling this way now. Feels like a vertigo. πŸ™‚

    Scientists have discovered an earth like small planet . It was in news yesterday..
    http://www.timesonline.co.uk/article/0,,3-2009914,00.html
    If there were to exist life outside our galaxy, I guess at that distance, they should be able to view the whole earth in one shot.

     

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