Question

Two stars in the night sky make an angle of 10^-3 radians at the eye of Matilda. If Arthur, who can just distinguish two spots, 0.5 cm apart, at a distance of 10 m views the stars, can he distinguish them as two distinct objects?

Answer 1

Let's calculate the angle between two spots, 0.5 cm apart,
that are 10m away from you.

1 m = 100 cm
10m = 1,000 cm

The angle between the two spots is very very close to the angle
whose tangent is
0.5cm/1,000cm = 0.0005 .

That angle is tan⁻¹(0.0005) = 0.0005 radian = 0.029 degree .

Matilda is looking at two stars that appear to be 0.001 radian apart.

That's (0.001 / 0.0005) = 2 = TWICE as far apart as Arthur can distinguish.

As long as Arthur and Matilda are on the same planet while looking at
these two stars ... or as long as they're even in the same solar system ...
Arthur will have no trouble separating them.