Consider an elliptic orbit with semi$-$major axis a $=10,000$ km and eccentricity e $=0\mathrm{.}33.$

x $,$ x$$

yy$$

cb

sc

$($x$,$y$)$

r $\backslash$theta

a$)$ With the orbit equation and independent variable $\backslash$theta $,$

r $=$ a$(1-$ e$2)$

$1+$ e cos$\backslash$theta

compute and plot the orbit $($x vs$.$ y$,$ solid black curve$).$

Use Matlab for computations and plots.

b$)$ With the algebraic equation and independent variable x$,$

x$2$

a$2+$ y$2$

b$2=1$

compute and plot in overlay fashion on part a$)$ the orbit $($x vs$.$ y$,$ dash red curve$).$

Use Matlab for computations and plots.

c$)$ Do the differently computed orbits match?