Question

考试中,快,双星间距L,质量为M1和M2.万有引力常量G.问：双星的轨道半径,运行周期,

Answer 1

M1*w^2*R1＝M2*w^2*R2,R1＋R2＝L

R1＝M2*L / (M1+M2),R2＝M1*L / (M1+M2)

GM1*M2/ L^2＝M1* (2π / T)^2*R1

T＝2π根号[L^3 / G(M1+M2)]

V1＝ 2πR1 / T＝M2根号[G/L(M1+M2)]

V2＝ 2πR2 / T＝M1根号[G/L(M1+M2)]