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I am confused about the definition of the period of an eclipsing binary, a binary configuration where one component crosses the other across the line of sight. When people say that an eclipsing binary has a period of T years do they mean that the period of the individual component is T years?
The period (at least in physics) is defined the time an oscilating system needs to get back to its starting point (for a sinus curve its 2*pi).
Now when they say an eclipsing binary has a period of T years, it means that its brightness varies as seen from earth when they are eclipsing (thats how we detect eclipsing stars and planets by the way), and that the curve of its brightness is like an oscilation that gets back to its starting point every T years.
The meaning of this is, that this system consisting of 2 stars will be exactly as you see it now again in T years.