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The peak radial velocity <math>K</math> is the semi-amplitude of the radial velocity curve, as shown in the figure. The orbital period <math>P_\mathrm{orb}</math> is found from the periodicity in the radial velocity curve. These are the two observable quantities needed to calculate the binary mass function.<ref name="podsiadlowski" />
The observed object of which the radial velocity can be measured is taken to be object 1 in this article, its unseen companion is object 2.
Let <math>M_{1}</math> and <math>M_{2}</math> be the stellar masses, with <math>M_{1} + M_{2} = M_\mathrm{tot}</math> the total mass of the binary system, <math>v_{1}</math> and <math>v_{2}</math> the orbital velocities, and <math>a_{1}</math> and <math>a_{2}</math> the distances of the objects to the center of mass, such that <math>a_{1}+a_{2} = a</math>
We start out with Kepler's third law, with <math>\omega_\mathrm{orb} = 2 \pi/P_\mathrm{orb}</math> the [[Angular frequency|orbital frequency]] and <math>G</math> the [[gravitational constant]],
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Using the definition of the center of mass, <math>M_{1} a_{1} = M_{2} a_{2}</math>,<ref name="karttunen" /> we can write
<math>a = a_{1} + a_{2} = a_{1} \left(1 + \frac{a_{2}}{a_{1}}\right) = a_{1} \left(1 + \frac{M_{1}}{M_{2}}\right) = \frac{a_{1}}{M_{2}} (M_{1} + M_{2}) = \frac{a_{1} M_\mathrm{tot}}{M_{2}}.</math>
Inserting this expression for <math>a</math> into Kepler's third law, we find
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which can be rewritten to
<math>\frac{M_{2}^{3}}{M_\mathrm{tot}^{2}} = \frac{\omega_\mathrm{orb}^{2} a_{1}^{3}}{G}.</math>
The peak radial velocity of object 1, <math>K</math>, depends on the orbital inclination <math>i</math> (an inclination of 0° corresponds to an orbit seen face-on, an inclination of 90° corresponds to an orbit seen edge-on)
<math>K = v_{1} \mathrm{sin} i = \omega_\mathrm{orb} a_{1} \mathrm{sin} i.</math>
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