The Andromeda galaxy lies about 2.5 million light-years away. To what distances do the angular resolutions of SST (3"), HST (0.05"), and a radio interferometer (0.001") correspond at that distance?

a) s = 36 ly

b) s = 0.6 ly

c) s = 0.012 ly

Explanation:

the 360 ° angular displacement in a circle is the circumference with a radius r. The angle is equal to the length of the arc s. Therefore, we have to:

(360°/θ) = (2*pi*r) / s

Clearing s:

s = ((2*pi*r) / 360°) * θ = (r/360° * (60'/1°) * (60''/1') / 2*pi)) * θ = (r*θ) / 206265''

a) We have:

r = 2.5x10^6 ly

θ = 3''

s = (r*θ) / 206265'' = (2.5x10^6 * 3'') / 206265'' = 36 ly

b) We have:

r = 2.5x10^6 ly

θ = 0.05''

s = (r*θ) / 206265'' = (2.5x10^6 * 0.05'') / 206265'' = 0.6 ly

For the radio interferometer is equal to:

r = 2.5x10^6 ly

θ = 0.001''

s = (r*θ) / 206265'' = (2.5x10^6 * 0.001'') / 206265'' = 0.012 ly