Newton's theory became compelling not because it was simpler or more accurate than rivals, but because a single set of ideas explained three seemingly unrelated phenomena at once: planetary motion, terrestrial projectile motion, and the tides.
Nielsen suggests the real driver behind accepting the new cosmology was explanatory unification — one theory covering orbits, falling objects, and tides — rather than superior accuracy or simplicity, since Copernicus's model was actually neither.
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Michael Nielsen: You have what seem like three very different disconnected phenomena all being explained by this one set of ideas. That starts to feel very compelling, at least to me. I think most people find that very satisfying once they eventually realize it.