Explain the principle of calculating distances to the stars using parallax?

Question

When using parallax to estimate distances to the stars from Earth, which stars have the larger parallax and why? Best answer gets 10 points!

Answer 1

The Parallax method of distance measurement uses the triangle formed by the distant object and two different observing positions. In astronomy, the distant object is a star and the observing positions forming the base of the triangle are the Earth at two points in its orbit. The positions of very distant stars are used as a reference.

Using a baseline, b, perpendicular to the distance, you can calculate the distance as b/Θ, where the parallax angle Θ is the angle at the star end of the triangle. Obviously the nearer objects will have larger parallax angles. The largest baseline possible using this method is the diameter of Earth's orbit, 2 AU (astronomical units). Astronomers use the equation with b in AU, Θ in arc-seconds, and distance in parsecs. The parsec is just a convenient unit to avoid needing a conversion factor; it's about 3.26 light years.

Answer 2

it should basically be the stars that are wide out
as assuming that we see a star from a very steep angle lesser than about 30 degrees as
the distance as we see it will be cos of our ange and cos of an angle closer to 0 is greater (trig ratios)
and using this and the horizontal distance to right below the star which makes it perpendicular to the star we can find out the actual distance.
Thank you was a nice question

Answer 3

tanparallex=1AU/d=(tan1'')(1pc)/d

This is cos tan1''=1AU/1pc=(tan1")(1pc)