Editing Visual binary (section)

==Determining stellar masses ==
Binary systems are particularly important here{{snd}} because they are orbiting each other, their gravitational interaction can be studied by observing parameters of their orbit around each other and the centre of mass. Before applying Kepler's 3rd Law, the inclination of the orbit of the visual binary must be taken into account. Relative to an observer on Earth, the orbital plane will usually be tilted. If it is at 0° the planes will be seen to coincide and if at 90° they will be seen edge on. Due to this inclination, the elliptical true orbit will project an elliptical apparent orbit onto the plane of the sky. Kepler's 3rd law still holds but with a constant of proportionality that changes with respect to the elliptical apparent orbit.<ref>{{cite web 
| url = http://www.astro.caltech.edu/~george/ay20/Ay20-Lec4x.pdf
| title = Kepler's laws, Binaries, and Stellar Masses
| access-date = 2013-11-04
}}</ref>
The inclination of the orbit can be determined by measuring the separation between the primary star and the apparent focus. Once this information is known the true eccentricity and the true [[semi-major axis]] can be calculated since the apparent orbit will be shorter than the true orbit, assuming an inclination greater than 0°, and this effect can be corrected for using simple geometry

:<math> a=\frac{a''}{p''} </math>

Where <math>a''</math> is the true semi-major axis and <math>p''</math> is the parallax.

Once the true orbit is known, Kepler's 3rd law can be applied. We re-write it in terms of the observable quantities such that

:<math> (m_{1}+m_{2})T^2 = \frac{4\pi^2 (a''/p'')^3}{G} </math>

From this equation we obtain the sum of the masses involved in the binary system. Remembering a previous equation we derived,

:<math> r_{1}m_{1} = r_{2}m_{2} </math>

where

:<math> r_{1} + r_{2} = r</math>

we can solve the ratio of the semi-major axis and therefore a ratio for the two masses since

:<math> \frac{a_{1}''}{a_{2}''} = \frac{a_{1}}{a_{2}} </math>

and

:<math> \frac{a_{1}}{a_{2}} = \frac{m_{2}}{m_{1}} </math>

The individual masses of the stars follow from these ratios and knowing the separation between each star and the [[centre of mass]] of the system.<ref name=Binary />