Question

The smallest shift you can reliably measure on the screen is about 0.2 grid units. This shift corresponds to the precision of positions measured with the best Earth-based optical telescopes. If you cannot measure an angle smaller than this, what is the maximum distance at which a star can be located and still have a measurable parallax

Answer 1

Answer:

The distance is  $d = 1.5 *10^{15} \ km$

Explanation:

From the question we are told that

        The smallest shift is $d = 0.2 \ grid \ units$

Generally a grid unit is  $\frac{1}{10}$ of  an arcsec

  This implies that  0.2 grid unit is  $k = \frac{0.2}{10} = 0.02 \ arc sec$

The maximum distance at which a star can be located and still have a measurable parallax is mathematically represented as

           $d = \frac{1}{k}$

substituting values

           $d = \frac{1}{0.02}$

           $d = 50 \ parsec$

Note  $1 \ parsec \ \to 3.26 \ light \ year \ \to 3.086*10^{13} \ km$

So  $d = 50 * 3.08 *10^{13}$

     $d = 1.5 *10^{15} \ km$