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

the answer would be c. motion and direction

i hope this : )