Question

What angular resolution would you need to see the Sun and Earth as distinct points of light? If you were looking at it from 13 light years away?

Answer 1

1 light-year = distance light travels in a year = 9.5 x 10¹⁵meters

Earth’s orbital radius is 1.5x10¹¹ m.

The distance 13 ly = 1.23x10¹⁷ m

physical separation (meters) Angular separation = 206.265 arc seconds x distance (meters)

                                            = $\left ( 1.5*10^{11} m./ 1.23*10^{17} m \right )$ * 206,265 arcseconds

                                            = 0.25^''