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 arctic is a region of the planet, north of the arctic circle, and includes the arctic ocean, greenland, baffin island, other smaller northern islands, and the far northern parts of europe, russia (siberia), alaska and canada.

c) up

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