My estimate for the distance of the farthest Sun-size star that could be focused as a single-whole-star, by a 0.001''-precision telescope, is 30.53 light years. What is your estimate? Same, or different?

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Answer 1 · 2016-10-07T02:08:24

If $theta$ is in radian measure, a circular arc, subtending an

$angle theta$ at its center, is of length $(radius)Xtheta$

This is an approximation to its chord length

# = 2(radius)tan(theta/2)

$=2(radius)(theta/2+O((theta/2)^3))$ , when $theta$ is quite small.

For the distance of a star approximated to a few significant (sd)

digits only in large distance units like light year or parsec, the

approximation (radius) X theta is OK.

So, the limit asked for is given by

( star distance ) $X (.001/3600)(pi/180)$ = size of the star

So, star distance d = (star size)/ $(.001/3600)(pi/180)$

=(diameter of the Sun)/ $(4.85 X 10^(-9))$ , for a sun-size star

$=(1392684/4.85) km$

$2.67 X 10^14 km$

$=(2.67/1,50) X 10^6 AU$

$=1.92 X 10 ^6 AU$

$=(1.92 X 10 ^6)/(6.29 X 10^4) light years (ly)$

$=30.5 ly.$