Discuss the motion of binary (double) stars in astronomy.

(N/A) If there are no external forces,the centre of mass of a double star system moves like a free particle,as shown in figure $(a)$.
The trajectories of the two stars of equal mass are also shown in figure $(a)$. They appear complex.
If we transform to the centre of mass frame,we find that the two stars are moving in a circular orbit about the centre of mass,which remains at rest. The positions of the stars are diametrically opposite to each other,as shown in figure $(b)$.
In our laboratory frame of reference,the trajectories of the stars are a combination of:
$(i)$ Uniform motion in a straight line of the centre of mass,and
$(ii)$ Circular orbits of the stars about the centre of mass.