Question

双星质量为m1,m2.他们之间的距离为L.求双星运行轨道半径r1,r2,以及运行周期T

Answer 1

F向心力=Gm1m2/L^2=m1w^2r1=m2w^2r2 所以r1/r2=m2/m1

又因为r1+r2=L 所以r1=m2L/(m1+m2) r2=m1L/(m1+m2)

w=√[(Gm1m2/L^2)/(m1m2L/(m1+m2))]=√[G(m1+m2)/L^3]

T=2π/w=2π√[L^3/G(m1+m2)]