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Simple Geometry Question

  1. Sep 22, 2014 #1
    1. The problem statement, all variables and given/known data

    I just came across a couple of expressions in a textbook I don't particularly understand.

    keuc5h.png Caption: "A point lensing mass L moving with velocity v perpendicular to the line of sight. O is the observer and S' is the projected position of the source in the plane of the lens.

    The textbook is D H Perkins - Particle Astrophysics 2nd edition, Pg 163.

    2. Relevant equations

    An excerpt from the textbook is ".. the right-angled triangle AS'L gives us [itex]LS'^{2} = AS'^{2} + AL^{2}[/itex], where [itex]LS' = D_{L}\theta_{s}[/itex], [itex]AS' = D_{L}\theta_{s}(min)[/itex] .."

    3. The attempt at a solution

    Tried to refresh geometry/trig, looked at sine and cosine rules and different combinations of lines and angles. I still don't understand the last two equations, how does multiplying by the angle give you LS' and AS'? Looks simple but why you can do it escapes me..
     
  2. jcsd
  3. Sep 22, 2014 #2

    jedishrfu

    Staff: Mentor

    Small angles in radian measure approximate their sin() value and that maybe thats whats going on here.
     
  4. Sep 22, 2014 #3

    gneill

    User Avatar

    Staff: Mentor

    In an Astrophysical context, ##D_L## is probably assumed to be very large with respect to other dimensions, making the angles small (as stated by @jedishrfu) so that the sides AS' and LS' are essentially equal to the arc lengths subtended by ##D_L## swept out by those angles. The rest is Pythagoras.
     
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