 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s2/1/2/solution

Eclipses justify an approximately edge-on orbit, and equal velocity amplitudes imply equal masses. The relative speed is 200 km s

^{- 1}

, so

a = (v_{1} + v_{2}) P / (2 π) ≃ 1.50 \times 1 0^{10}

m, or

a ≃ 0.100 AU

. Substitution in the binary period law gives

M_{1} + M_{2} ≃ 4.52 M_{⊙}

, hence

M_{1} = M_{2} ≃ 2.26 M_{⊙}

. Inclination corrections scale the dynamical masses as

sin^{- 3} i

if exact edge-on viewing is relaxed.

 New to topics? Read the docs here!