From SelfStandingEvidence:
If you see the problem with the above thought exercise, then the solution to the dilemma is simple. Very little in general and particular on WardsWiki is SelfStandingEvidence. Most educated people on this planet cannot prove by themselves basic facts like that the Earth is round. They trust the authority and the integrity of the scientific community and the scientific processes (publications, peer reviews, criticism, wide adoption of ideas, etc) in trusting that the Earth is round and moves on an elliptical and to take those as facts without complaining about SelfStandingEvidence.
It is uneconomical that the evidence be 100% self-standing. All arguments about non-trivial things rely on a frame of reference generally accepted, because of OnceAndOnlyOnce principle.
It's actually fairly easy to prove that the earth is round without referring to external (i.e. non-personally-verifiable) evidence. There exists a horizon. Beyond the horizon, we cannot see objects regardless of how tall they are. If the earth were flat, all points above its surface would be visible from all other points, assuming there is no hill or other earthly impediment (if that's a problem for you, stand on a beach). Therefore, the earth is round. QED.
I agree with your general viewpoint, but object to your use of the word "prove". It's easy to provide evidence, the easiest and simplest explanation of which is that the Earth is round. However, I have a model in which the Earth is flat and which agrees with all your evidence. Yes, it's more complicated, but it shows that you cannot "prove" that the Earth is round. You can only show that your model to explain the observations is simpler than mine.
[Unless "round" is the best term to describe the "flat" concept in the model, which is presumably the case, since the earth really is round.]
It is not hard to watch a ship sail away, and see it sink below the horizon, the roundness of the earth is quite obvious.
It's possible to compute the circumference of the earth using only personal measurements this way too. Eratosthenes did this in 250 B.C. Why people persisted in thinking it's flat is beyond me. Maybe they're just stupid.
Actually, according to most historians, the 'Flat Earth Myth' is itself a myth. The idea that Terra is flat was never prevalent among the educated classes in Western Europe, nor was it ever the Church's position. The opposition to Columbus' voyage was based on Eratosthenes' estimate of the circumference of Terra (which had been reintroduced to the Europeans by the Moors), versus the calculations Columbus supported which indicated a much smaller circumference. Both were wrong, but Eratosthenes was much closer; if there hadn't been an unknown landmass in his way, Columbus and his crews would have died of thirst long before reaching East Asia. -- JayOsako
Proving that the earth moves in an ellipse around the sun is somewhat more difficult, because in a sense it's not true. Einstein showed that all motion is relative (well, actually this was known intuitively in Galileo's time, but became an issue with Maxwell's calculation of the velocity of light). If you're willing to transform to the rotating, revolving reference frame centered on the earth, the sun does indeed go around the earth, though in a far more complicated way than just a circle or an ellipse. The advantage of the Keplerian formulation is that it's far easier to calculate - I certainly don't want to pull out Einstein's equations just to compute the movement of the earth, and I doubt I could get a closed-form, algebraic answer anyway.
Interestingly, I've heard that when NASA puts people on the moon, they actually do use the Ptolemaic formulation, with epicycles-on-epicycles. That's because the rocket starts out in the earth's reference frame, so if you want to use the Keplerian solar frame, you need to account for the earth and moon's motion too. Ptolemy's epicycles are really just a Fourier decomposition of the observed measurements, so it's mathematically as valid as Kepler's laws. But you have to carry the sum out to infinity in order to get really accurate predictions, while Kepler's laws are simple closed-form equations (modulo relativistic effects and the influences of other planets). -- JonathanTang
I'm not sure I buy that, though it would be rather interesting if it's true. The problem with that claim is that it shouldn't have been necessary. As I understand it, epicycles are the result of a body's orbital motion around Sol as viewed from Terra, but interpreted as orbital motion around Terra; Luna, however, actually does orbit Terra, and thus should not have any epicycles. I could be mistaken, however. -- JayOsako
See also GalileoGalilei NicolausCopernicus