- From the centre of mass, we get
M1R1=M2R2−−−−−−1
- Force acting on both starts i.e. gravitational force and centripetal force are balanced.
R2GM1M2=R1M1V12=R1M1V12−−−−−−2
As we know, {V}_{1}=\frac{2{\pi R}_{1}}{{T}_{1}}&{V}_{2}=\frac{2{\pi R}_{2}}{{T}_{2}}
Substituting equation 3 in equation 2, we get
(T1)2M1R1=(T2)2M1R2−−−−−−4
From equation 1, we conclude in eqution 4
(T1)2=(T2)2orT1=T2