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Astrophysics Problem (gravitational lensing)

  1. Aug 8, 2012 #1
    1. The problem statement, all variables and given/known data

    I need some help with the following problem:

    http://img543.imageshack.us/img543/9630/lensq.jpg [Broken]

    3. The attempt at a solution

    First I have tried to work out the radius of the Einstein ring:

    [itex]r_E = \sqrt{\frac{4GM}{c^2}}.\sqrt{\frac{D_1D_{1s}}{D_s}} = \sqrt{\frac{4(6.67×10^{11})M)}{(3 \times 10^8)^2}}[/itex]

    And here is a diagram of the situation under consideration:

    http://img841.imageshack.us/img841/2751/ering.jpg [Broken]

    However I can't solve for rE because I don't know M. But if I knew eE I could find θ (the angle of deflection of light by a point mass) as follows:

    [itex]\theta = \frac{4GM}{c^2(r_E+r_s)}[/itex]

    Where rs is the stellar radius, and here is a diagram of the situation:

    http://img542.imageshack.us/img542/8624/deflection.jpg [Broken]

    Where in this case I believe b = rE + rs.

    So how can I solve for rE and θE when I don't know what M is? Furthermore, how can I estimate the effective mass from the figure given in the question? Any help is greatly appreciated.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Aug 8, 2012 #2
    My main question is, how can I find the mass of the lensing object? :confused: Without this I can't calculate anything else.
     
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