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I know that 1 parsec (pc) is the distance of star at which 1 AU subtends 1 arcsecond.

so $1 pc = \frac{1 AU}{1"}$

Now, if two stars in a binary with a separation of 3" and have a trigonometric parallax of 0.1", what does it mean and what's the difference?

enter image description here

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    $\begingroup$ You can use the parallax info to estimate how far the system is from earth. Then use the separation to figure out how far apart the binary is. Then use the rest of the info to answer the question about masses. $\endgroup$ – user6972 Jun 1 '14 at 3:56
  • $\begingroup$ I'm just confused about why there are 2 angles, $\theta = 0.1"$ and $\theta = 3"$, what's the difference? $\endgroup$ – user44840 Jun 1 '14 at 15:58
  • $\begingroup$ 0.1" is the parallax (based on earth's movement) and 3" is how far apart the two stars are from each other. $\endgroup$ – user6972 Jun 1 '14 at 16:07
  • $\begingroup$ 3" is how far the stars are apart, from where? $\endgroup$ – user44840 Jun 1 '14 at 16:18
  • $\begingroup$ From each other. $\endgroup$ – user6972 Jun 1 '14 at 17:26
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"trigonometric parallax of 0.1" " means the stars are 10 parsecs or 33 light years from Earth.

"separation of 3" " means that an isosceles triangle with Earth at one vertex and the two stars at the other two vertices, has a very short side connecting the two stars and the angle with Earth at its vertex is 3".

Therefore, the distance between the two stars is $2\sin(1.5'') \times 33$ light years.

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