A detached eccentric binary of two evolved stars has ,

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Astrophysics & Cosmology · Celestial mechanics and planetary systems

Stars from the Inside, Ch Binary stars: fitted orbits, modelled eclipses and the Roche geometry

Problem

A detached eccentric binary of two evolved stars has m1=2.5 M⊙m_1 = 2.5\,M_\odot, m2=2.0 M⊙m_2 = 2.0\,M_\odot, orbital period P=5.0 dP = 5.0\,\mathrm{d} and eccentricity e=0.30e = 0.30. ((a)) Use Kepler's third law to find the orbital separation aa in solar radii. ((b)) Evaluate the general-relativistic apsidal-motion rate ΔωGR=6πG(m1+m2)c2a(1−e2)\Delta\omega_{\rm GR} = \frac{6\pi G(m_1+m_2)}{c^2a(1-e^2)} per orbit, and convert it to degrees per century.

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