Consider two stars in orbit about a mutual center of mass. If a1 is the semimajor axis of the orbit of star of mass m1 and a2 is the semimajor axis of the orbit of star of mass m2, prove that the semimajor axis of the orbit of the reduced mass is given by a=a1+a2. Hint: Review the discussion of Section 2.3 and recall that r=r2−r1.