Two stars of mass M 1 & M 2 are in circular orbits around their center of mass. The star of mass
M 1 has an orbit of radius R 1 , the star of mass M 2 has an orbit of radius R 2 . (assume that their center of mass is not accelerating and distance between stars is fixed)
.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
M α = 
= 3.376 × 10 29 kg, M β = 2M α = 6.75 × 10 29 kg
Solution:
Since center of rotation is the center of mass of M 1 and M 2 .
M 1 R 1 = M 2 R 2
or 
...................(i)
Since force on M 1 and M 2 must be towards CM their radial line should be along same line therefore
they must have same orbital period
Now T = 
....................(ii)
and 
....................(iii)
from (i), (ii) and (iii)
T = 2 π 
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