The two major detection methods - radial velocity and transit photometry - are prone to biases.
From a purely geometric perspective, the probability that a planet will transit is determined by how far away it is from the star, as well as the size of the star. This relationship is written
_* is the stellar radius and a
is the separation between the two bodies. We can see that as a
increases, the probability that a planet will transit decreases, and therefore the overwhelming majority of planets which transit will be in short-period orbits.
The sensitivity of a planet to detection by radial velocity can be thought of in terms of the amplitude of the velocity of the star throughout its barycentric motion around the system's centre of mass, expressed as
_* is the semi-major axis of the stellar orbit (itself a function of the mass and separation of the planet via Kepler's Laws), i
is the inclination of the orbit with respect to the plane of the sky, such that i
=90 degrees represents an edge-on orbit, P
is the orbital period of the system, and e
is the eccentricity of the orbits. The period and eccentricity of the stellar orbit will be identical to the period and eccentricity of the planetary orbit.
In the case of Doppler spectroscopy, since the detectability of the planet is not contingent on the inclination being in a small range of values, the method is much
more sensitive to planets in longer periods. It is still biased toward short-period planets, but to less of a degree.