# I How much would time pass between watching the sun set ...?

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1. Sep 12, 2017

### Xarzu

How much would time pass between watching the sun set from ground level and then watching it set again from the top of a sky scraper?

I heard once that this could be done using one of the towers of the World Trade Center. So I assume one could also do this using the Sears / Willis Tower in Chicago. Someone also told me that the world's tallest tower in Dubai is so huge that the local weather broadcast tells of two times for sunset. One time is for the observed sunset at ground level and another time is for the observed sunset from the observation deck near to the top of the tower.

unfortunately, I have recently gotten involved in a debate with someone who believes or claims to believe that the earth is flat and he has challenged me for proofs. I gave him some observations that any one can do, but that did not seem to be good enough for him. He wanted the mathematical predictions of an event and then a demonstration that showed that reality matches the mathematics.

Well, my math skills are a bit rusty on this sort of level since I have been out of college. Although I could probably do this, I figure it would be a greater ease for me to just ask one of the math majors or grad students that frequent online mathematics forums for the equations. So I think what I will do is list my ideas one at a time in this mathematical forum. And now, here is the first one.

The rapper B.O.B. has come out saying that he thinks the earth is flat. Neil Tyson gave him a reply and PBS offered an Op Ed piece explaining some simple tests anyone can do to prove the earth is round. One of them was to lay on the beach on your back and with your head pointed towards the sun set (do this on the pacific coast of course. The moment you see the sun set, immediately stand up and you can see the sun set again -- or so says the op ed piece from PBS. I have herd that something similar can be done with large buildings. If you watch the sun set on the ground level, (let's say from the point of view of a 6ft 4 man. Or some measured eye level from the ground) and then you take an elevator to the top floor, you will be able to see the sun set a second time.

The problem is this, if you know all of the variables, how long would it take to see the sun set a second time.

I hope I have posed this question well enough. Let me know if you have any questions. After this one is answered, I have at least one more question I will start in a second thread.-->

2. Sep 12, 2017

### Staff: Mentor

By my calculation, about 2 minutes difference for a 1000 foot skyscraper.

Edit: you don't have to measure time difference. Just look at the building or a mountain from a distance around sunset. You can watch the shadow climbing from bottom to top. The simplest explanation for that is that the Earth is round.

3. Sep 12, 2017

### Drakkith

Staff Emeritus
Unfortunately there is likely nothing you can present to him that would change his mind. I can't guarantee this, but in my experience, 99% of everyone I've ever dealt with who believed in non-scientific "theories" will not change their mind, regardless of the evidence or arguments you present to them. It's mind boggling to think that some people have developed an elaborate and nonsensical explanation for something as simple as the day-to-night cycle of the Earth when I can take a flashlight and a basketball and explain the cycle in 5 seconds. If they don't believe that the reason the Sun and star-field moves across the sky is because the Earth is round and rotating, something which absolutely screams "round earth" and requires nothing but a basic clock to measure, I don't know what would convince them.

4. Sep 12, 2017

### Staff: Mentor

You are wasting your time. Of course, there are far worse ways to waste your time, so if you are enjoying the conversation then proceed. But the only participant that your arguments will convince is yourself.

5. Sep 13, 2017

### A.T.

Did he present those for his theory?

6. Sep 13, 2017

### CWatters

7. Sep 25, 2017

### Xarzu

I am going to go through with this. It is a good mental exercise if nothing else.

I did the math on my own. It took a while of pondering. And there is a good visualization tool that helped. Using this web site https://www.desmos.com/calculator/zs5wfg9uem I was able to put in the equations for a circle, X 2 + Y 2 = radius 2 and then I put a line for where the light from the sun would be tangent to the circle ( Y = radius). Then with some calculations and trial and error and even a bit of C++ code, I came up with a function that would represent the straight line on which the CN Tower would reside and intersect the sunlight with the sky pod (the highest observation deck) on the CN tower would see the sun light. Now I only need to know one thing (and I might start a separate discussion thread for it). Here it is:

If I have an X and Y point on a grid that represents the intersection of two formulas: A straight line (aX = Y) where "a" represents a constant number with a circle (X 2 + Y 2 = radius 2, how would I convert that point into a degree of an angle?