During my walks that I have undertaken to maintain my physical and mental well-being I have taken a standard 3x3x3 cube and looked for places to photograph it. People who are local to the Blackburn-with-Darwen area might recognise some of the places.
Having a cube in my pocket means I have an excuse for a short breather. I can solve it in random places. Not being a speed cuber means I get a little longer.
There is one heliocentric model, just one. This model is used to describe our tiny piece of the cosmos. It is used to make predictions. It does this very well.
There is no singular and consistent flat-Earth model that can do the same. If the flat-Earth community is genuinely serious in its convictions then it should be able to present a model that explains the Universe we observe and can make accurate predictions. So where is it?
Here is a summary of all of the things that this hypothetical model must include and be able to explain. Just one failure and the model is incorrect and is disproved and discarded.
The sun rises in the morning from below the horizon. It travels across the sky at a constant speed and maintains a constant angular size. In the evening, it sets below the horizon. Observers at the same latitude see the sunrise and set at the same time. All observers see the same face of the Sun.
The angular size of the sun does change by a minute amount during the course of the year. It is ever so slightly larger in January than it is in July.
The Moon is slightly more complicated. While observers on earth see the same face of the Moon, this is only approximately true. The flat-Earth model needs to explain libration. We can, in fact, see just over half of the Moon's surface from the Earth, with a slightly different portion of the surface being visible depending on its position its orbit. Also, the angular size of the moon varies, giving rise to super moons, etc.
The Moon has phases. All observers on Earth witness the same phase.
There are two types of eclipse. A solar eclipse is when the disc of the sun completely or almost completely obscured. A lunar eclipse is when a shadow passes over the moon preventing the sun from illuminating the moon. The flat-Earth needs to not only explain these two phenomena but also be able to predict when they will occur.
North of the equator, the sky is seen to rotate in an anti-clockwise direction around the north celestial pole. South of the equator, it rotates clockwise around the south celestial pole. Specific stars are either visible or invisible depending on an observer's latitude. For example, no Southern stars can be seen from the Earth's North pole and Polaris cannot be seen south of the equator.
Finally, we need to see a working map of the whole world. This map must be good enough for use as a navigational aid. All distances between any two locations must be accurate and precise. The flat-Earth maps we usually see are arimuthal equidistant projections. Distances from the pole (or centre) to other places on the mao are all correct, but distances between any two other locations are distorted.
Toppling the heliocentric model will require more than a collection of distorted "black swan" photographs. The flat-Earth community needs to present a singular model of the flat-Earth that is 100% consistent with the reality that we observe and has predictive power. Handwavery and evasion are not going to cut it. If you cannot explain all of the above with your model, your model is incomplete or wrong. Go away and come back when you have one that can.
Once you have succeeded, you can then work on advanced features of the model, such as vulcanism, plate tectonics, earthquake shadows (the ones explained by a hot iron core in the globe model), jet streams, the length of the day changing by a fraction of a second depending on the time of year, and any other phenomena you might wish to tackle.
