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The angular separation in degrees of two objects is(physical separation times 360 degrees/2 pi distance) if an individual was observing our solar system from Castor at a distance of 9.5 light years What angular resolution in arc seconds is needed to resolve the Sun-Earth system as distinct points of light

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Answer:

[tex]\alpha = (3433\times 10^{-4})"[/tex]

Explanation:

given data:

distance between our solar system & castor is d 9.5 light year

we knwo that  

[tex]1 \ light\  year  =9.46\times 10^{12} km[/tex]

so [tex]d = 8.988\times 10^13 km[/tex]

distance between sun and earth is [tex]149.6\ million\ km = 149.6\times 10^6 km[/tex]

let angular resolution be[tex] \alpha[/tex]

by angular resolution formula  

[tex]\alpha = \frac{s}{2\pi d} 360\ degree[/tex]

          [tex]= \frac{149.6\times 10^6}{2\pi \times 8.98\times 10^{13}} \times360[/tex]

         [tex] = 953.65\times 10^{-7}[/tex]

         [tex] = 95.365 \times 10^{-6}[/tex]

now   [tex]= 95.365 \times 10^{-6} =  = 95.365 \times 10^{-6} \times \frac{60'}{1^o} \times \frac{60"}{1'}[/tex]

[tex]\alpha = (3433\times 10^{-4})"[/tex]

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