Question

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

Answer 1

`\alpha = (3433* 10^(-4))`

Step-by-step explanation:

given data:

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

we knwo that

`1 \ light\  year  =9.46* 10^(12) km`

so
`d = 8.988* 10^13 km`

distance between sun and earth is
`149.6\ million\ km = 149.6* 10^6 km`

let angular resolution be
`\alpha`

by angular resolution formula

`\alpha = (s)/(2\pi d) 360\ degree`

`= (149.6* 10^6)/(2\pi * 8.98* 10^(13)) *360`

`= 953.65* 10^(-7)`

`= 95.365 * 10^(-6)`

now
`= 95.365 * 10^(-6) =  = 95.365 * 10^(-6) * (60')/(1^o) * (60`

`\alpha = (3433* 10^(-4))`