In a particular double star system two stars of mass `3.22xx10^(30)` kg each revolve about their common centre of mass `1.12xx10^(11)` on away.
(i). Calculate their common period of revolution, in years
(ii). Suppose that a meteoroid (small solid particle in space) passes through this centre of mass moving at right angles to the orbital plane of the stars. What must its speed be if it is to escape from the gravitational field of the double star?

Answer

(i). `T=4pisqrt((r^(3))/(Gm))`
(ii). `v=sqrt((4Gm)/(r)),r=(d)/(2)`

Explanation

(i) Necessary centripetal force=gravitational force
`impliesomega^(2)r=(GM^(2))/(4r^(2))impliesT=4pisqrt((r^(3))/(GM))`
(iii). COME: KE+PE=0
`implies(1)/(2)mv^(2)-(2GMm)/(r)=0impliesv=sqrt((4GM)/(r)),(r=(d)/(2))`