Answer
$L=6.24\times10^{34}\frac{kgm^2}{s}$
Work Step by Step
$L=I\omega=\frac{2\pi I}{T}$
$1 year=31536000s$
$L_t=\frac{2\pi I}{11.9 y\times31536000\frac{s}{y}}$
$I_J=\frac{2MR^2}{5}=\frac{2(190\times10^{25}kg)(6.99\times10^7m)^2}{5}=3.71\times10^{42}$
$L_J=\frac{2\pi I}{T}=\frac{2\pi 3.71\times10^{42}}{(11.9y)(31536000)\frac{s}{y}}=6.22\times10^{34}$
$I_S=\frac{2MR^2}{5}=\frac{2(56.8\times10^{25}kg)(5.82\times10^7m)^2}{5}=7.70\times10^{41}$
$L_J=\frac{2\pi I}{T}=\frac{2\pi 7.70\times10^{41}}{(29.5y)(31536000)\frac{s}{y}}=1.50\times10^{32}$
$I_U=\frac{2MR^2}{5}=\frac{2(8.68\times10^{25}kg)(2.53\times10^7m)^2}{5}=2.22\times10^{41}$
$L_U=\frac{2\pi I}{T}=\frac{2\pi 2.22\times10^{41}}{(84.0y)(31536000)\frac{s}{y}}=5.27\times10^{31}$
$I_N=\frac{2MR^2}{5}=\frac{2(10.2\times10^{25}kg)(2.46\times10^7m)^2}{5}=2.47\times10^{41}$
$L_U=\frac{2\pi I}{T}=\frac{2\pi 2.47\times10^{41}}{(165y)(31536000)\frac{s}{y}}=2.98\times10^{31}$
$L_t=6.22\times10^{34}+1.50\times10^{32}+5.27\times10^{31}+2.98\times10^{31}=6.24\times10^{34}\frac{kgm^2}{s}$