Great ball of fire

The sun provides us all with light, warmth and food, keeping our home not just liveable but comfortable, all the sun gods throughout history should be no surprise. But we're not here to talk about gods, today's topic is the sun or more specifically the way it moves or appears to.

As we all know the globe earth spins making a stationary sun appear to move across the sky. At the end of the day, the sun appears to drop below the western horizon, travelling under our feet before risings from the eastern horizon the following morning. On flat earth things are very different, the sun and moon float about 4000 miles above the ground moving in a circle that follows the equator. both shine there light down on earth like spotlights only illuminating half (approximately) of the world at any one time.

I have spent quite some time looking in to this and at first I assumed that the sun on a flat earth would orbit over the top and then underneath much like in the Discworld series of book. If you don’t know about the Discworld books I highly recommend you read one or two and I’m shore you will want to read the rest. The Discworld its self is a flat world ten thousand miles across which rests on the back of 4 elephant's which in turn stand on the back of the giant star turtle Great A'tuin. But let's get back on track. The flat earth is very different from the Discworld, for a start the ocean's don't flow off the edge as the Antarctic stretches all the way around the rim, it also doesn't rest on the back of any animals but its exact nature is subject to debate. Some say its a flat disc, others say its a never-ending flat plain, furthermore some say the earth is covered by a dome called the firmament and then it all starts to get complicated with every theory splitting off into two or three others. For my own sanity, I’m going to ignore some of the more outlandish theory's and stick to the basics that most flatheads can agree on. 

When looking at how the sun would work I kept getting the same thoughts and I decided to do some maths to see if things would look the same as I have witnessed time after time from my own back garden. If you look into the distances involved you will come across some quite contradictory figures, most flat heads believe the sun is somewhere between three and four thousand miles high, but I’ve come across as little as 35 miles. To keep things simple I'm going to use the figures that seem to be the most common and to simplify things further I will be calculating the suns movements as if it's at the equinox. This will give me a sun that is 3000 miles high and 32 miles across. Assuming the equator is half way between the north pole and the rim and that the equators circumference is the same as that of a globe earth the earth's diameter must be 25000 miles.

So just to recap the figures I'm going to use are as follow

• Sun’s diameter : 32 miles
• Sun’s height : 3000 miles
• Earth's diameter : 25000 miles
• The Equator from North pole : 6250 miles

I used MS Excel to do the maths involved, mainly because I’m familiar with using formula in Excel but also it would be easy to send the file to any one who wishes to look at my workings. The following is the work sheet I created to show the flat earth model working, the graph at the top shows a representation of the flat earth as viewed from above with the north pole in the centre. positions “A”, “B” and “C” are lined up along the Greenwich prime meridian. the box on the bottom left displays the figures as well as the time. the box on the bottom right gives information about the sun from each of the points labelled.

Let's have a closer look at position “A” the rest will then be self-explanatory. Position “A” is 1250 miles from the north pole and at this time its 5438 miles from the point which the sun is directly over. Using this distance and the suns height (3000 miles) we can work out the angle above the horizon the sun would appear to be, at this time from “A” it would be 28.88° (I’m not going to go in to the maths but if you want to check it you can do so here). The last bit “Sun Angular Size” is simply how small the sun would look with the naked eye. (not that I recommend looking at the sun with the naked eye as it can do some serious damage however if you feel the urge to, please don't let me stop you)  The sun always stays the same size but due to it being further away it will look smaller, so to work this out all I need is the distance to the sun its self (which works out to be 6210 miles) and its diameter, if you assume its a right-angled triangle you can use the same maths as before.

As you advance time on the worksheet you will see the distances and angles change in accordance with how things would appear if you were stood at any one of the three positions marked on the graph.

the following are examples of different times of the day

The first chart shows you the figures for 6pm this should be sunset, but if you look the lowest angle as seen from “C” the sun is still 13.12º above the horizon. Worse still is the apparent size of the sun, if you've ever paid attention to the sun as it passes over your head it always look roughly the same size and yet the maths says that on a flat earth the time of day will drastically affect how big it looks. As you can see the graph on the far right is set to 12 o'clock midnight yet the sun is still above the horizon, infect using these figures the sun will never go below 9° and will always be visible (unless its obscured by something like a building or a big hill) and it appears to have halved its size compared to 3pm. Point “B” sees the sun seemingly accelerating towards you before slowing down as it moves off into the distance more like what you would expect if you watched a passenger jet fly over. The chart to the right shows the angular size and altitude every hour for point “B”, these numbers fly in the face of anything I would see if I was stood at the equator observing the sun.

All my charts and figures are very well and good but not very visual and unfortunately I'm not all that good at animation, however as I was looking into this I stumbled across the following gif file that displayed exactly what I was trying to. I don't know what distances are used so the numbers are a little different but the results are more or less the same. the software used to create it can be found here. Ill let you scrutinise the picture your self as its mostly self-explanatory

After carefully calculating all the angles and distances on a flat earth the results just don't fit with real-world observations. The sun does does not grow visibly as it approaches noon before shrinking off into the distance. Some flatheads may show you photos or videos of the sun shrinking as it setts but this is an artefact of the lens or the sensor being flooded with light in one spot and struggling to deal with the information, any good photographer will know this and should be able to suggest a way or two to fix it. (an ND filter or small aperture, even the use of HDR may help).

In the real world the sun appears to move across the sky at a consistent speed never slowing as it reaches the horizon, but on the flat earth the sun would appear to slow as it approaches the horizon, a horizon it will never actually meet or dip below. but flatheads have this covered as well, saying perspective will make the sun “set” as it travels beyond the vanishing point, however, a vanishing point is simply an imaginary point on a picture or graphical projection to create the correct visual perspective and so making it seem more realistic. Perspective will only make the sun look smaller it will not make it move out of sight as if setting below the horizon.

in conclusion, the sun from our point of view can not move round in a circle 4000 miles above us, it must stay the same distance from us and we spin creating the illusion of the sun moving across the sky. At 93 million miles any change in apparent size due to earth's spin would be unnoticeable with the naked eye and hard to measure with good equipment. The observable sun does not support the flat earth it sits squarely in the globe earth model.