To develop this problem it is necessary to apply the concepts related to the angular resolution of a telescope as well as to the arc length.
The arc length can be defined as
[tex]s = r\theta[/tex]
Where
r= Radius
\theta = Angle
At the same time the angular resolution of a body is given under the proportion
[tex]\theta = 1.22\frac{\lambda}{D}[/tex]
Where
[tex]\lambda[/tex]= Wavelength
D = Diameter
Our values are given as
[tex]\lambda = 550*10^{-9}m[/tex]
[tex]D = 6.5m[/tex]
[tex]r = 3.82*10^5Km = 3.82*10^8m[/tex]
Then the angle of separation of the two objects seen from the observer is of
[tex]\theta = 1.22 \frac{550*10^{-9}}{6.5}[/tex]
[tex]\theta = 1.032*10^{-7}[/tex]
Finally, using the proportion of the arc length, in which we have the radius and angle we can know the separation of the two objects by:
[tex]s = (3.82*10^8)(1.032*10^{-7})[/tex]
[tex]s = 39.43m[/tex]
