## Formula for finding the Mass of a Star in a binary system

### Finding the Mass of a Star in a binary system

- First Law - Orbits are conic sections with the center-of-mass of the two bodies at the focus.
- Second Law - angular momentum conservation.
- Third Law - Generalized to depend on the masses of the two bodies.

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where m_{1} and m_{2} are the two masses, P is the period
of revolution, G is the gravitational constant, and v_{1} is the radial
component of the velocity of one of the stars (m_{1}). If both of
the stars' radial velocities are measured, as with visual binaries, the
equation can be manipulated so that both masses can be determined. In the
case of Cygnus X-1, however, only one of the stars can be seen (Cygnus
X-1's visual companion), so in order to determine the mass of the unseen
object, it is necessary to know, or to estimate, the mass of the companion
star. In this case, m_{1} and v_{1} refer to the companion
star and m_{2} refers to Cugnus X-1, the unknown mass for which we
want to solve.

This equation indicates that m_{2} must increase as sin(i)
decreases. It will be necessary for this calculation to make an educated
guess at the value for *i*, the inclination angle.

Click here to estimate the mass of the companion star. | |

Click here to estimate the inclination of the Cygnus X-1 system. | |

Click here to measure the velocity of Cygnus X-1's companion. |

Click here to see how to solve cubic equations. |

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