Where is the center of mass of two different size orbiting planets?



Mistake somewhere below:

1. Since T= 2pi sqrt(r^3/G (M+m))

2. therefore if the Mass is different then the orbitng time "T"
should be different for each planet (because "r" is smaller for the
larger planet)

3. If T is different then if we snap a picture of the planets at
different time intervals, the location of center of mass will be
different which is incorrect since it remains the same location at the
following web link:

http://www.astronomynotes.com/starprop/s10.htm

.



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