Question

What does it mean if the the stellar parallax of a star is too small to be measured?

Answer 1

For parallax = 0.01", with observers separated by distance equal to radius of the Earth, the distance is 0.0134 ly only..

Explanation:

The formula used for this approximation is from two isosceles triangles with a common base..
Distance = 6.78 E-10 X sin (28.649) / sin (.1.389 E-06) km =.0134 ly,
The first factor is radius of the Earth in ly.
The sine angles are 0.5 rad in deg and parallax/2 = .005" in deg.
With 0.01" precision, we cannot find the distance of even close by stars that are more than 4 ly away. The precision of the instrument for measurement of angles is the criterion on how far we measure stellar distances..