Be aware,stars are moving

6 stars of equal masses m each are moving about the center of mass of the system such that they are always on the vertices of a regular hexagon of the side-length having length a each.Their common time period can be determined in the form of \[w \pi \times \sqrt{ \frac {x \sqrt{3} a^{3} }{Gm(y+z \sqrt{3} ) } }\] where w,x,y,z are positive integers.Find w+x+y+z.

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