Radial Velocity (RV)

Using precise Doppler measurements, the motion of a star caused by an orbiting planet can be measured. The period, distance and orbital shape as well as the mass of the orbiting planet are parameters which can be revealed using such measurements.

Radial veloctiy measurements however cannot be used to reveal the planet's orbital inclination and the longitude of the ascending node. These can only be measured through astrometry.

The form of the periodic radial velocity variations,
V_r = K[cos(v+ω_*) + ecos ω_*] + γ
is determined by six parameters:

- P, the orbital period - which sets the period of the RV curve
- e, the orbital eccentricity
- K, the semi-amplitude of the signal measured (in units of velocity) - which sets the amplitude of the RV curve
- ω_*, argument of periastron of the star measured from the ascending node
- T₀, the time since periastron passage throught the mean anomaly - which sets the phase of the RV curve
- γ, the bulk velocity of the center of mass of the system

So while, P, T₀, and K set the period, phase, and amplitude of the RV curve, ω_* and e determine the shape of the RV signature of the orbiting planet [1]. Thus if a star has a single companion, the six parameters above can be varied until the numerically obtained curve fits the measured RV curve.


...more to come....

Other detection methods:
Astrometry
Direct imaging
Transits, and
Gravitational microlensing

References:

[1] Wright, J.T., Gaudi, B.S., Exoplanet Detection Methods, (http://arxiv.org/abs/1210.2471).