Determine the ****** of orbit for the star of mass 3M (A) π√(d^3/GM)

Question

Two stars orbit their common center of mass as shown in the diagram below. The masses of the two stars are 3M and M. The distance between the stars is d.

Determine the ** of orbit for the star of mass 3M

(A) π√(d3/GM)

(B) 3π/4√(d3/GM)

(C) π√(d3/3GM)

(D) 2π√(d3/GM)

(E) π/4√(d3/GM)

Answer 1

Correct option (A) 1/√2R

Since they are orbiting their center of mass, the larger mass has a radius of orbit of 1/4d. The speed can be found from (G(3M)M)/d2 = (3M)v2/d/4 which gives v = √(GM/4d) = (2π(d/4))/T.