Recently I come across a YouTube video “New Proof of a Flat Earth: Distance to the Sun? Shorter Version” Sasha appears in the video and talks about measuring angles from the horizon to the sun and how you can make an
equilateral triangle which is a triangle in which all three sides and all three internal angles are equal. The video and all Sasha’s videos are done in such a way that its hard to take them or her seriously, I can only assume this is intentional as her channel is labelled as comedy but on the other hand she stats that she is passionate about flat-earth, so is she mocking it? I invoke Poe's Law on this and I will assume she is serious and believes the earth is flat.On a flat plain, the equilateral triangle would work well, it will give you the exact distance to the sun and as stated in the video it would disprove the sun’s 93 million mile distance. Sasha gives us two places on earth that are the correct distance apart to see the sun at 60° at the same point in time. One is Macapá in Brazil and the other is Malabo in Equatorial Guinea. She also gives us the distance between them as 4134.6 miles, a quick look on google earth and I got 4144.7 miles so a 10.1 mile difference? I’ll use her figures as 10 miles will make little to no difference and is well within any reasonable margin of error. If you work this out using a triangle solver app like this one you will find it gives you a sun height of 3580.67 miles, a long way short of 93 million. Yep that's it the globe earth is done for the world can only be flat…. “Sparkle Sound”
But wait, wouldn't the curvature of the earth change the angles? Yes and no, from the people standing into two cities
measuring the suns altitude there should be no difference but the horizons they are measuring from will be vastly different in relation to each other. Sasha has thought about this and demonstrates how the curvature of the earth will affect the angles. As you can see in the image to the left (grabbed from her video) the 60° measurements taken from our two cities will diverge and simply get further apart the further you are from earth. one thing bugs me about this drawing, where is the working out? how do we know the drawing is correct? I know its hand drawn and it doesn't need to be exact or to scale, but it would be nice to have a little more than just two points marked with time and angle as our only verification. For a start would 4134.6 miles create that much curvature? I had to check this out for my self, time to do some maths!
Ok to test this for my self and demonstrate my finding I decided to test out a new app I found, its called GeoGebra (if you like maths and/or geometry you seriously need to check this app out) and I was pleasantly
surprised how easy it was to use. At first I simply tried to replicate the above drawing and found I could manipulate positions of the two cities and the curvature of the earth at will and get the lines diverging, parallel or converging with out changing the 60° angle. this was no good at all I needed to know I was getting all the angles and distances right, so I made a circle and set its circumference to 24901 miles, the same as earth equatorial circumference. Next I set points “A” and “B” to slide along the circumference and the green line that lets us know the distance between the two. I then created another point and placed it 93 million miles away in the direction of the red arrow, this I joined to points “A” and “B” with lines and had the angle between them and the imaginary observers local horizon displayed in green. as you can see in the drawing to the right I used the distance Sasha gave us (within a tenth of a mile) and as you can see the altitude of the sun from our two cities would be incredibly close to 60° and converging on a single point. Infect if we want to get it to exactly 60° we only have to move our observers 2.8 miles closer together giving us a distance of 4131.8 miles.
surprised how easy it was to use. At first I simply tried to replicate the above drawing and found I could manipulate positions of the two cities and the curvature of the earth at will and get the lines diverging, parallel or converging with out changing the 60° angle. this was no good at all I needed to know I was getting all the angles and distances right, so I made a circle and set its circumference to 24901 miles, the same as earth equatorial circumference. Next I set points “A” and “B” to slide along the circumference and the green line that lets us know the distance between the two. I then created another point and placed it 93 million miles away in the direction of the red arrow, this I joined to points “A” and “B” with lines and had the angle between them and the imaginary observers local horizon displayed in green. as you can see in the drawing to the right I used the distance Sasha gave us (within a tenth of a mile) and as you can see the altitude of the sun from our two cities would be incredibly close to 60° and converging on a single point. Infect if we want to get it to exactly 60° we only have to move our observers 2.8 miles closer together giving us a distance of 4131.8 miles.
So in short, if you had two people on a globe earth stand 4131.8 miles apart along the equator, one could watch the sun rise to 60° at the same time as the other watches it set to 60° with the sun that is 93 million miles away. “New Proof of a Flat Earth”? New Proof of Bad Geometry more like.
I’m going to leave you with the worksheet I created in GeoGebra. You should be able to have a little play with it.
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