# Astrophysics Problem (gravitational lensing)

1. Aug 8, 2012

### roam

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:

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

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:

$\theta = \frac{4GM}{c^2(r_E+r_s)}$

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. Aug 8, 2012

### roam

My main question is, how can I find the mass of the lensing object? Without this I can't calculate anything else.