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consider an isolated binary star system where two stars of mass 2M and 3M are se

ID: 1504765 • Letter: C

Question

consider an isolated binary star system where two stars of mass 2M and 3M are seperated by a distance of R the raidus of each star is negligible compared to R

A) what is the magnitude of the gravitational acceleration aH experinced by the heavier star (express your answer in terms of G,M,R)

B) how far does the center of mass of this binary star system lie from the center of the hevier star (express in terms of R)

C) let vH and vL denote the speed of the lighter and heavier star respectively if the two stars are each traveling in curcular orbits around the center of mass of thesystem what is the ratio of their speed vL/ vH ?

Explanation / Answer

A) F = G*m1*m2/r^3

= G*3*M*2*M/R^2

aH = F/(3*M)

= 2*G*M/R^2

B) Xcm = (m1*r1 + m2*r2)/(m1+m2)

= (3*M*0 + 2*M*R)/(3*M + 2*M)

= (2/5)*R

C) Force on both objects are same

m1*a1 = m2*a2

m1*v1^2/r1 = m2*v2^2/r2

3*M*vH^2/((2/5)*R) = 2*M*vL^2/((3/5)*R)

3*5*vH^2/2 = 2*5*vL^2/3

vL/vH = 3/2

= 1.5