Mass Function

What
The mass function is applied to binary star systems and is useful for determining the lower limit for the companion star

$$\frac {m _2 ^3}{(m_1 + m_2)^2} sin^3 i = \frac {P}{2 \pi G} v _{1r} ^3$$

The right side of the above equation is known as the mass function

Mass Ratio
We can compute a mass ratio of the two stars in the binary system by dividing the following quanties:

$$\frac {m_2 ^3}{(m_1 + m_2)^2}sin^3i = \frac {P}{2\pi G} v _{1r} ^3$$

$$\frac {m_1 ^3}{(m_1 + m_2)^2}sin^3i = \frac {P}{2 \pi G} v _{2r} ^3$$

We obtain:

$$(\frac {m_2}{m_1})^3 = (\frac {v _{1r}}{v _{2r}})^3$$

$$\frac {m_2}{m_1} = \frac {v _{1r}}{v _{2r}}$$