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Astronomy - Parallax error calculation.

  1. Nov 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Two stars belong to the same cluster, the parallax measured to one star is
    (2±1)x10^-3 arcseconds, towards the other the parallax is
    (4±2)x10^-3 arcseconds.

    Find the distance to both objects seperatly and also compute the distance when both measurements are combined.


    2. Relevant equations

    D = LaTeX Code: \\frac{1}{p}

    where D is the distance in pc
    and p is the parallax in arcseconds

    3. The attempt at a solution

    If it werent for the error in the parallax angle this would be easy but i'm not sure how to go about it. here is my attempt at it:

    Star 1: D = 1/p = 500pc

    calculating error in D: (LaTeX Code: \\Delta D)^2 = (LaTeX Code: \\frac{dD}{dp} LaTeX Code: \\Delta p)^2

    (LaTeX Code: \\Delta D)^2 = (LaTeX Code: \\frac{1}{p^2} LaTeX Code: \\Delta p)^2

    (LaTeX Code: \\Delta D)^2 = (250000 x 0.001)^2

    (LaTeX Code: \\Delta D) = ± 15.8 pc

    does this seem reasonable?
    I'm not too great with error calculation, does this seem right?

    I have done exactly the same for the second star, have no idea what the last bit of the question means at all 'when both measurements are combined'. anyone have any ideas?
     
  2. jcsd
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