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Mon 11 Sep, 2017 09:40 pm

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.-->

@Bill Thompson,

Bill, I'm sorry but I couldn't hold back a laugh about you debating someone about whether the earth is flat or round. I'm sure you've heard the question

"What is this world coming to?"

So he wants proof that it's round ? ( I can't believe that in 2017 I'm even writing this.) How about having him Google "Earth from Space"? Ask him why it appears round from every angle. Ask him if he has ever heard of satellites that

go aROUND the earth. Find a globe somewhere, grasp the back of his head so that he is facing the globe, spin it, and say "Look. Do you get it now ?"

@Bill Thompson,

As far as your question about observed time of sunset on the ground versus at the top of a building, why bother with the math, which would involve the height of the building , distance of rotation at the surface versus at the top of the building, etc.? Have your buddy take his phone to the top floor. ( I doubt if they will let him on the roof) You stay on the ground. When you see the sun set, write down the time. Call your buddy and tell him to do the same. Hopefully, you won't have to explain to the security guards what you are doing.

@Ponderer,

You can also calculate the height of a building with an barometer and a piece of string. Go to the top of the building, tie the barometer to the string, and lower it to the ground. Now, measure the string. I think it was Fermi who came up with that bit of genius.

@roger,

Does it have to be a barometer or would a telescope work?

@Ponderer,

Well, the class assignment involved either a barometer or altimeter. I don't think you could sneak in a telescope.

@roger,

Oh. I get it. How 'bout an oil pressure guage?

@Ponderer,

I'm really sure it was Enrico Fermi, and the assignment involved barometer or altimeter. Another neat idea he has was to take your fancy barometer to the building engineer and tell him you would give him a nice, shiny barometer in exchange for the elevation figures.

He was lucky he wasn't kicked out of school for being a dullard.

@roger,

Can you just tie a clock on the string and see how long it takes to let it down?

And then divide by 60?

@Ponderer,

Save the math. Just measure the string.

@roger,

I think Ben Franklin tried to measure electricity like that.

@Bill Thompson,

The distance to the horizon at a height of H (in feet) is around 1.14 nautical miles x sqrt(H).

The ground speed of the sun is 360 degrees/24 hours * 60 nautical miles/degree * cos (latitude) = 900 nm/hour x cos(latitude)

At the equator (latitude = 0)

Time = distance/speed

Time (hr) = 1.14 sqrt(H) / 900