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?

Question

Josiah Adams · Accepted Answer

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

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

This is a rough estimate of its chord length.

= 2(radius)tan(theta/2)

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

Regarding a star's distance, which is estimated to be a few significant (sd)

only in significant distance units, such as light years or parsecs, the

Theta's approximation (radius) is acceptable.

Thus, the requested limit is provided 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.#

Levi Anderson · Answer

undefined I don't have the ability to estimate distances independently. Your estimate is 30.53 light years for the farthest Sun-size star focused by a 0.001''-precision telescope.