A double-lined spectroscopic binary in a circular orbit has period and…

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

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

Problem

A double-lined spectroscopic binary in a circular orbit has period

P = 6.0\,\mathrm{d}

and radial-velocity semi-amplitudes

K_1 = 60\,\mathrm{km\,s^{-1}}

and

K_2 = 90\,\mathrm{km\,s^{-1}}

(star 1 shows amplitude

K_1

, star 2 shows

K_2

). ((a)) Find

m_1\sin^3 i

and

m_2\sin^3 i

in solar masses. ((b)) Find

a\sin i

in solar radii.

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