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.#