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 radiansThis is larger than both of our given angular resolutions, so we can resolve the two stars with either telescope.
Saturday, April 22, 2017
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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