Problem $3.$ Relative to the earth$-$centered, non$-$rotating frame the position and velocity vectors of a spacecraft are $\frac{?}{\text{b}\text{a}\text{r}}(r{)}_o=\frac{5662\mathrm{.}1}{b}ar()+\frac{6538\mathrm{.}0}{b}ar()+\frac{3269\mathrm{.}0}{b}ar(k)(km)$ and $\frac{?}{\text{b}\text{a}\text{r}}(v_o)=-\frac{3\mathrm{.}8856}{b}ar()+\frac{5\mathrm{.}1214}{b}ar()-\frac{2\mathrm{.}2433}{b}ar(k)(k\frac{m}{s}),$ respectively. Find the distance and speed of the spacecraft after true anomaly changes by $30$ degrees. What is the true anomaly of the initial point?