- Doppler shift does not tell one distance or size of a celestial body. Only if the object is moving near or far.
Quite true. I never claimed that Doppler shift could tell the distance between us and another object.
- All astronomical distances are attained through parallax. The distance to that planetoid's star was obtained through parallax.
Parallax is not the only tool we have to measure stellar distances, see below.
- Parallax relies on an accurate distance for the AU.
- Parallax relies on the assumption of the earth revolving around the sun.
- The Parsec is just multiples of the AU.
- The AU is intimately dependent on the shape of the earth.
All true. But as I said, the parallax method is not the only way we have to determine the distance to a star. There is another highly confirmed method called spectroscopic parallax, which, despite the name, has nothing to do with measuring physical parallax of the star, and would still work regardless of the Earths motion.
In short, spectroscopic parallax makes use of the known relationship between a stars spectral type (it's color) and it's luminosity. We know how bright Gliese 581 would be if we were standing 10 parsecs away (what we call it's absolute magnitude) and we know how much light we actually do receive from Gliese 581 (it's apparent magnitude.) We also know Gliese 581's color (or more precisely, it's peak wavelength) by simply taking a spectrum of it's light.
Applying the relationship, we can now figure out how far away Gliese 581 is, and it agrees very well with the regular parallax method.
- Size is determined through the degrees of sky the star takes up.
All stars (with the exception of the sun) as seen from Earth are point sources of light. You cannot infer a stars size from its angular width because it's angular width is to small to be measured.
- If the AU is incorrect then the entire universe is incorrect.
True, but the AU isn't incorrect. We have independent ways of measuring it, I will give you a more detailed description of some of the methods if you like.
- Doppler calculations rely on accurate distances for the AU and an accurate distance for the Parsec.
No they don't. Measurements of the Doppler shift of an objects spectral lines can be made without knowing the distance. Where did you get that idea?