Another matter of perspective
« on: January 06, 2019, 06:43:27 PM »
Disappearing ships on the horizon is often used and disputed as evidence for the curvature of the Earth surface. RE believers contend that the gradual 'sinking' of the ship into the sea on the horizon is proof of curvature whereas FE believers will contend that this is due to light refraction effects etc.

I was thinking about this from a different approach. The Burj Khalifa is the tallest man-made structure in the world. I believe from base to tip of spire it is about 2,717ft high give or take a bit. Looking from above the tower the spire forms a line that takes you vertically down the centre of the building and so forms a line XY say where x is at ground level. I stand at the base of the tower and start to move away from it (direction unimportant). If XY is the opposite side of a triangle and XZ is the horizontal line that represents my distance from it. If I am moving away from the tower across an infinitely flat plane of the Earths surface then by simple trigonometry I should be able to calculate how high the tower should look from whatever distance I am from it.

If on the other hand I am walking away from it along a curved surface then not only will the tower will look shorter at a given distance but I would also see the tower appearing to tip away from me due to the curved path I am following. The height of the tower means that this would be quite easy to test out from quite a distance away without atmospheric refraction becoming a significant issue.

Offline edby

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Re: Another matter of perspective
« Reply #1 on: January 06, 2019, 06:53:12 PM »
Isn't this the same as the lighthouse question? The standard function v = sqrt(7h)/2 tells you that for h = 2,717ft, v = 68.1 miles. Therefore, at about 68 miles away, you would only be able to see the tip of the Burj.

Re: Another matter of perspective
« Reply #2 on: January 06, 2019, 09:15:30 PM »
Point is that if you were moving away from it along a flat surface your perspective on the tower would remain the same but it would get vanishingly small.  If you were moving away from it along a curved surface it would appear to be tipping over away from you.

If that is the same as the lighthouse question then fair enough but it just seemed like a reasonable point.