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.