You have astronomy as scinece confused with astronomy as historical records. I can't recreate an eclipse in 500 CE but I can calculate when another like it will happen in the same place it did.

The dynamic instability of the solar system puts a limit on that predictability.

In any case, tell me about how you can predict gamma-ray bursts. When will the next detection of extrasolar neutrinos occur? How do we recreate the Big Bang?

I am not confused. I regard historical sciences like astronomy, geology, paleontology and archaeology equally part of science even though there isn't the high level of reproducibility of, say, most chemistry.

I also regard nuclear bomb physics to be a science, even though by law it's impossible to reproduce those tests.

So get better telescopes for the tolerance you want. We have no problems making predictions over thousands of years with current technology when it comes to stellar mechanics that agree extremely well with the historical record.

Yours seems to be a very medieval mindset. Just because we are ignorant of the initial conditions of a system doesn't mean we are ignorant of the equations by which it evolves. And the example of chemistry is just bizarre. If we couldn't reproduce the same reaction down to the atom time and time again our silicone based infrastructure would have filed a very long time ago. Similarly for nuclear bomb tests, if they were truly irreproducible then things like [1] should happen a lot more often than not.

[1] https://en.wikipedia.org/wiki/Castle_Bravo

The solar system is chaotic in the sense that no matter how well you can measure their positions, their future evolution, at about 20 million years in the future, is not predictable. We will never be able to predict an eclipse that far ahead of time. We won't even know when the seasons are.

You claim that I have a medieval mindset. It seems you espouse a 19th century view of science, of the clockwork universe.

Science doesn't require reproducibility, nor your weaker requirement of "how to reproduce."

Predictability is the key to science, not reproducibility, though of course those are inexorably tied when it's possible to reproduce something. We can predict that fossils of a certain type will only be found in a specific layer of geological strata. We can predict that hurricanes will be created by and affected by certain wind patterns. We can predict that radioactive atoms will spontaneously decay.

Even though we certainly cannot reproduce those.

Chemistry is a field where it's easy to set up very similar conditions to previous experiments ("reproduce") and where the expected confidence of predictability is quite high. Hence my use of it as an example. It's much harder to reproduce an observation of a supernova, but we have pretty high confidence that when we do see one it will follow certain patterns.

Give me enough money for telescopes, detectors and computers and it is trivial to calculate the motions of the solar system for as long as you want to whatever precision you require.

The resources might be beyond the capabilities of humanity to ever achieve, but that detracts nothing from the point made. "Chaotic systems" aren't "unsolvable systems". The idea that they aren't reproducible to any desired degree of accuracy is laughable.

What part of "the whole Solar System possesses a Lyapunov time in the range of 2–230 million years" don't you agree with? Quote is from http://en.wikipedia.org/wiki/Stability_of_the_Solar_System .

To me it means that no matter how precise you measure everything, at some point even the unpredictability of a single atomic decay is enough to make a difference such that one of the planets may is ejected. As far as I know, that's also the generally accepted meaning.

Did you read your own link?

"In 1989, Jacques Laskar of the Bureau des Longitudes in Paris published the results of his numerical integration of the Solar System over 200 million years. These were not the full equations of motion, but rather averaged equations along the lines of those used by Laplace. Laskar's work showed that the Earth's orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15 metres in measuring the position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time."

So yes, that's exactly what I said.

Would you clarify what it is you mean?

The observation you quoted isn't using the full equations of motion. The next study on that page uses a change of 1 meter and finds that 1% of the 2501 cases Mercury goes into a dangerous orbit, including one where "a subsequent decrease in Mercury’s eccentricity induces a transfer of angular momentum from the giant planets that destabilizes all the terrestrial planets ~3.34 Gyr from now, with possible collisions of Mercury, Mars or Venus with the Earth."

You assert, seemingly as a matter of faith, that it is possible to measure all of the relevant factors such that a prediction can be made. We can't predict when an atom of uranium will decay, but we can make statistical predictions about the population. We can't predict when an air molecule out of a mole of molecule will hit the side of a bottle but we can make predictions about the pressure.

Do you think that we can ever do either of those two cases?

It's the same for the Solar System. As far as we can tell, it's not possible to have accurate enough information to predict the evolution of the Solar System. Even with numerical simulations, the presence of a space craft, or an extra-solar meteorite, might change things after 10 million years - things that can't be predicted.

Do you have anything going for this claim beyond faith?