[latex]v_I = sqrt{frac{GM}{R}}[/latex] a) M = 1/81MZ R = Rz/3,7 [latex]frac{v_{z}}{v_{k}} = frac{sqrt{frac{GM}{R}}}{sqrt{frac{G frac{M}{81}}{frac{R}{3,7}}}} = frac{1}{0,2}[/latex] v₁ = 0,2 x 7,9km/s = 1,58km/s b) M = 0,107Mz R = 0,5Rz [latex]frac{v_{z}}{v_{k}} = frac{sqrt{frac{GM}{R}}}{sqrt{frac{G 0,107M}{frac{R}{2}}}} = frac{1}{0,46}[/latex] v₁ = 0,46 x 7,9km/s = 3,634km/s ---------------------------------------------------------------------------------------------------- Litterarum radices amarae sunt, fructus iucundiores Pozdrawiam :)
[latex]V_{I_z}=7,9frac{km}{s}\\ V_{I_z}=sqrt{frac{GM}{R}}\\ a)\ Mk= frac{1}{81}Mz, Rk=frac{Rz}{3,7}\\ V_{I_k}=sqrt{frac{Gfrac{Mz}{81}}{frac{Rz}{3,7}}}\\ V_{I_k}=sqrt{frac{3,7}{81}frac{GMz}{Rz}}}\\ V_{I_k}=sqrt{0,046*frac{GMz}{Rz}}\\ V_{I_k}=0,215*V_{I_z}\\ V_{I_k}=0,215*7,9=1,7frac{km}{s}[/latex] [latex] b) Mm = 0,107 Mz, Rm= 0,5Rz \\ V_{I_m}=sqrt{frac{G*0,107Mz}{0,5Rz}}\\ V_{I_m}=sqrt{frac{0,107}{0,5}*frac{GMz}{Rz}}}\\ V_{I_m}=sqrt{0,214frac{GMz}{Rz}}\\ V_{I_m}=0,462V_I_z\\ V_{I_m}=0,462*7,9=3,65frac{km}{s}[/latex]
