## 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 r

Question

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?

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6 months 2021-08-18T16:47:47+00:00 1 Answers 0 views 0

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 = 2.5×10^6 ly

θ = 3´´

s = (r*θ)/206265´´ = (2.5×10^6 * 3´´)/206265´´ = 36 ly

b) We have:

r = 2.5×10^6 ly

θ = 0.05´´

s = (r*θ)/206265´´ = (2.5×10^6 * 0.05´´)/206265´´ = 0.6 ly

For the radio interferometer is equal to:

r = 2.5×10^6 ly

θ = 0.001´´

s = (r*θ)/206265´´ = (2.5×10^6 * 0.001´´)/206265´´ = 0.012 ly