TruthSeeker777 said:
There are a lot of assumptions in the answers which we can't verify empirically.. Why do we assume the sun is a star?
We do not
assume these things. They are part of an established astrophysical model, that has been built up over centuries, and they work extremely well.
You should read the forum rules before proceeding along this line, because it's pretty explicit about "established mainstream science".
TruthSeeker777 said:
Why do we assume the stars at at an infinite distance? Can we verify this?
Not that they "are" - but that they can be "treated as such" for the purpose of the geometry.
A nearly unlimited list of stars and galaxies and other objects are candidates for reference because they all have effectively zero relative movement. Every star we add to a
collective reference frame further cements the justification for treating it as
too far way to affect the parallax measurement of a nearby star.
Imagine I hold up my thumb and try to measure the parallax of my two eyes against some distant mountain peaks. The mountains are not
at infinity, but their actual distance is immaterial to my parallax measurement.
And, if I measure hundred peaks, or a hundred thousand, I see that they
all have zero relative movement between them, then I can indeed, treat the collection of mountain peaks as if it is at infinity for the purpose of the parallax geometry (which is simply the same as saying
the lines of sight (from mountain collective to each eye)
are parallel to within acceptable tolerance for my measurement of the parallax).And
that may be an easier easy of seeing it. The lines of sight (from very distant stars to Earth's winter and summer positions) are
parallel to within a very small margin of error. Againt these parallel lines of sight, we can accurately determine with simple geometry how far away nearby stars are.