Radial Velocity Question

Lets say that a star's system is moving at 45 degrees relative to us... And a planet is detected, is the measured mass and velocity of the star half of the true mass? Or is there some square function?

And how do they find the mass of a planet given the velocity the star is moving and the mass of the star?

The measured (minimum) mass of a planet will the true mass of the planet times the sine of the inclination.

M_RV = M_true sin i (or simply "m sin i" for short)

And conversely,

M_true = M_RV / sin i.

The amplitude of the RV variations, K, is used to determine the mass of the planet using the following formula.

K = (2πa_star sin i) / P*√(1 - e²)

Where a_star is the semi-major axis of the star around the system barycentre, P is the orbital period, and e is the eccentricity. The K value can be used to find the masses of the two components with the "mass function":

[(m_star sin i)³) / (m_star + m_planet)²)] = P / 2πG * K³(1 - e²)^3/2

Where G is the gravitational constant. In a planetary system, since the mass of the star will be much greater than that of the planet, you can simplify the mass function down to

m_p sin i ~= (P/2πG)^1/3 Km_star^2/3 (1 - e²)^1/2

Interesting! Thanks.