The radial-velocity curve of a single-lined spectroscopic binary is plotted against…
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
The radial-velocity curve of a single-lined spectroscopic binary is plotted against orbital phase. Over most of the cycle the velocity varies slowly and stays close to a broad minimum of −38kms−1; then, in a brief interval, it rises sharply to a sharp maximum of +132kms−1 before falling back just as quickly. Velocities averaged over many cycles give a systemic velocity γ=12kms−1. An astrometric orbit of the same pair shows that the velocity maximum falls exactly at periastron passage, when the star moves fastest.
((a)) State the value of the argument of periastron ω that this shape implies, with your reasoning.
((b)) Find the velocity semi-amplitude K and the eccentricity e.