Your article handles the "Aristarchus of Samos envisioned our solar system's heliocentric design " well, and this is especially so because you say Aristarchus "presented" the heliocentric layout as a model.
Other writers have fallen into error regarding this bit of history, among them Carl Sagan I seem to recall, in that they have claimed that Aristarchus actually proved it as a theory. IMHO Aristarchus probably never proved out the theory simply because he lacked the tools to do so - specifically he lacked the principles of spherical trigonometry and spherical geometry.
The ancient Greeks were just getting started on the process of discovering these principles during his lifetime.
Moreover, other tools of such math were added to the mix much later in history (SINES for example ~~>"the sine is a trigonometric function of an angle") came into mankind's math tool-kit during the 800's AD - a full millennium after Aristarchus lived & died.
Copernicus relied heavily upon spherical geometry when he proved his theory of a sun-centered solar system to the satisfaction of his contemporaries and to later Renaissance astronomers and mathematicians - - Copernicus spent two whole chapters of his revolutionary book, De Revolutionibus, singing the praises of spherical geometry, crediting it with the proof he made.
Aristarchus didn't have that tool at his disposal, so I don't think he actually could have proven his point mathematically, which would have left his theory rejected by anyone and everyone who trusted their instincts (the earth feels steady underfoot, the sun appears to move across the sky, etc.)
It was only the math that allowed Copernicus to persuade the best minds of his time to re-examine their instinctual prejudices, and even in his era the world almost wasn't ready yet to understand the argument. Way back in Aristarchus' era the world just hadn't evolved far enough yet in terms of principles of math.
Aristarchus Lived too early in history to Prove his Concept
But no doubt Aristarchus was a visionary, and certainly in his mind's eye he beheld the truth about the layout of our neighborhood of the cosmos. But the rest of humanity had to develop for many centuries longer to catch up with his thinking.
Congrats on an artfully written piece.
First of all, thank you for your kind words.
It is true that ancient greeks didn't know almost anything about trigonometry, but they presented their theories in a geometric way that was equivalent to some trigonometric laws and formulas..
For example, there is Aristarchus' inequality, trigonometric law, although Aristarchus didn't posses any knowledge on trigonometry, not to speak about notation, but he was using that law in a more lets say geometric way..
And yes, ancient greeks, without doubt, used primitive math and physics...for example their best argument for non spinning Earth was 'if I jump I will land on a different place, but I am landing always in the same place therefore Earth is static' but they didn't know whatwhat is inertia back then :)
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