The angular resolution of the Hubble telescope is about .1 arc second (0.1") while that of ACC's (My college) 8 inch reflector is about .5". Could either telescope resolve the individual stars in a binary system 3 parsecs away? Assume the two stars are 1 A.U. apart as measured at right angles to the line of sight from the earth at the time of viewing.

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What we're really asking is this: What is the angle subtended by 1 AU at a distance of 3 parsecs? Is it less or greater than 0.1 arcseconds and 0.5 arcseconds respectively?

So, let's get everything in the same units: Meters is usually a good choice.

A parsec is about 3.1*10^15 m, so 3 parsecs is about 9.3*10^15 m.
An AU is about 1.5*10^11 m.

For angles this small, we can use the approximation

` tan x approx x`

where x is measured in radians. So we want to get 0.1 arcseconds and 0.5 arcseconds into radians. 1 arcsecond is pi/180/3600 radians, or about 4.8*10^-6 radians. So 0.5 arcseconds is about 2.4*10^-6 radians, and 0.1 arcseconds is about 4.8*10^-7 radians.

Now all we need to do is find the ratio of the two distances, which is the tangent of x, which we've just said is very close to x itself.

(1.5*10^11 m)/(9.3*10^15 m) = 1.6*10^-5 radians

This is larger than both of our given angular resolutions, so we can resolve the two stars with either telescope.

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