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

The distance is
`d = 1.5 *10^(15) \ km`

Step-by-step explanation:

From the question we are told that

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

Generally a grid unit is
`(1)/(10)` of an arcsec

This implies that 0.2 grid unit is
`k = (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 = (1)/(k)`

substituting values

`d = (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`