This velocity must be projected along the line of sight. The system of axes chosen for this purpose is defined by a z-axis along the line of sight, increasing away from the observer. The x-axis is defined by the intersection of the plane of the sky and the orbital plane of the planet, increasing towards the point crossed by the planet when it approaches the observer (point Tin Fig. 6.1). The y-axis is defined such that the system of axes is direct.

The measured velocity is the component of the star's velocity along the z-axis added to the velocity of the system's barycentre, VG:

where K is the semi-amplitude of the variation in the radial velocity, and rn is the longitude of periapsis of the planet's orbit. Then:

For a Jupiter-type planet orbiting a solar-type star, and if i = 90°, K is equal to 12.7 m/s.

The radial velocity is considered to be positive when the star is receding from the observer. For a non-circular orbit, the variation in f is not uniform, and thus the curve for Vz is not sinusoidal (Fig. 6.2). Modelling the curve enables us to determine the eccentricity, the position of periapsis, and the 'mass function' f (M, m, i) of the system:

m 2na sin i

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