An example of an experimentally measured light curve is given in Figure 1. The shape of the light curve for an eclipsing binary star system depends mostly on the relative brightness and size of the two stars as well as their orbital inclination as seen from Earth. We will now see how you can use simple geometry to generate a light curve. The orbital inclination is measured relative to the observer in degrees and is 90 degrees for edge-on orbits. The star masses and luminosities can be expressed in arbitrary units and the star radii will be expressed in terms of a fraction of the orbit radius of the binary star orbit.
Luminosity is defined to be the amount of energy escaping from a star's surface per unit time.
For spherical, uniformly lit stars we can write If we ignore limb darkening, then we can approximate the measured brightness of the binary star system as seen by an observer as where A 1 and A 2 are the areas of the star disks seen by the observer and K is a constant that can be determined from the area of the observer's detector and the distance between the Earth and the binary star system. A 1 and A 2 can be found by considering the geometry of the eclipses. To find these areas we will need to know the apparent distance between the two stars as seen by an observer. Using Figure 2, we see that this distance is The values for A 1 and A 2 for the different stages of the eclipses are given in the tables below. An example light curve with masses and luminosities expressed in arbitrary units and the star radii expressed in terms of a fraction of the orbit radius of the binary star orbit You will notice that the masses have no effect on the light curve for this simple model.