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No earth-based observation of the planets can disprove the Tychonian model (planets orbit sun, which orbits the earth). It takes very fine stellar observations, which couldn't be done in the 17th century.

Would a space based observation do it? Where would it have to be from, and what would be the differences?

Edit: I'd like answers that ignore stellar observations and only look at planets or the Sun- something like: "From the surface of Mars the positions of the planets show the model is incorrect."

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With today's instruments, we can do it from Earth. It has been routine for almost two centuries.

What is important is the parallax - the apparent shift in position on the sky for a star, because we view it from a slightly different angle when the Earth orbits the sun. The Earth's orbit around the Sun gives us a very good "Space-based" baseline of 2AU, or roughly 300 million kilometers. Larger distance from the sun gives longer baseline and stronger parallax, so anything orbiting the sun outside Earth orbit would be an improvement.

Space-based measurements are generally more precise than ground-based ones, because turbulence in Earth's atmosphere makes the image of any star "dance" around (the apparent "twinkle" of the star), smearing the image over longer time exposures. Satellites do not have this problem. The ESA Gaia mission has just released parallax based distances to 1.3 billion stars.

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  • $\begingroup$ Thanks- I was looking for something solar system specific- like "from Mars we can see the Tychonian system is incorrect?". I should have been more clear... $\endgroup$ – AKA May 8 '18 at 11:30
  • $\begingroup$ @AKA We can see it from Earth. Tycho's instruments just were not precise enough (telescopes were not even invented then). From Mars, the same measurements will be a bit easier, because the orbit is further out, so there is a longer distance between Summer and Winter position, and so the parallax is stronger. But you don't need to go there from Mars, you can see it from Earth with proper instruments. $\endgroup$ – Thriveth May 9 '18 at 18:25
  • $\begingroup$ ...As soon as you can see periodic parallax from the stars, you have the Tychonian model proven wrong. And that happened more than 150 years ago (apart from all the philosophical problems that come with the Tychonian model, it doesn't exactly stand for Occam's Razor etc.). $\endgroup$ – Thriveth May 9 '18 at 18:28
  • $\begingroup$ You're 100% correct- I'm not some flat-Earther trying to deny parallax or posit that the Magic Space Dragon moves the planets around the Sun, which is then locked in the Quintessential Sphere of Beauty ;)... $\endgroup$ – AKA May 9 '18 at 20:22
  • $\begingroup$ ... But I'm just trying to understand whether the Tychonian model of the SS breaks down when you change the reference point. It's really a question about reference-frames, rather than astronomy per se. $\endgroup$ – AKA May 9 '18 at 20:24
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Even if you stay on Earth, to describe the movement of the planets, asteroids and comets (and then spacecrafts) you will have to use the Newton's laws in the accelerated reference frame. You will have to introduce very complicated universal forces that will depend on every single factor that influences Earth orbit. E.g. the position of every single object in the world however distant or massive would depend on the position of the Moon.

However complicated nothing really prevents you from using this description for any process in the world even it is happening on Mars or in another galaxy. That would be extremely stupid but still possible.

So it's not really the star movement that is important but rather that the dynamics in the inertial frames is much more simple and meaningful. However historically the idea of the absolute space tied to the "fixed stars" was important so were the observations of the stellar abberation and later of the stellar parallax.

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