# h10s - Homework 10 Solutions 1 Compute the deflection angle...

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Unformatted text preview: Homework # 10 Solutions 1. Compute the deflection angle of a star whose light just grazes the limb of the Sun. Also compute the deflection angle of a star whose light just grazes the limb of a 1 . 4 M neutron star, if the neutron star was at the same distance from the Earth as the Sun. State assumptions. Assume that d Lens << d S , then α = 4 G M / ( bc 2 ). b will be equal to the radius of the lens. For the Sun, we have α = 4 G M R c 2 = 8 . 6 × 10- 6 = 1 . 76 arcsec . For a neutron star, α = 4 G M R c 2 = 0 . 98 = 56 . 4 ◦ . However, this assumes that the deflection angle is small, which is invalid for this case. A full calculation in GR yields a deflection about 21% larger! 2. Use the Plummer potential model, with a value of a = 100 kpc, together with the Viral theorem to infer a value for galaxy masses in Fig. 7.3 assuming that all the galaxies have the same mass. Do not include Stephan’s Quintet in this estimation....
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h10s - Homework 10 Solutions 1 Compute the deflection angle...

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