Question

How far can we measure stellar parallax?

Answer 1

Assume that the precision in parallax measurement is .001". Then, for observations with an interval of half a year from the same observatory on the Earth, the limit is 6558.5 ly.

Explanation:

For the stated observation with instrument of precision 0.001", the stellar distance for parallax 0.001" = 1.39 E-07 deg, is
cot (1.39 E-97) AU = 4.1253 E+08 AU = 6559 ly, nearly.