P$2.$ A spacecraft is in an elliptical orbit about Pluto with periapsis and apoapsis radii of $1595$ km and

$9195$ km respectively. The spacecraft has a mass of $1,300$kg$,$ of which $100$ kg is propellant, and an

engine with an I$\_($sp$)$ of $230$ s$.$ Can the spacecraft escape from Pluto? If so$,$ what is the maneuver strategy

that should be used? Justify your answers. Data: Pluto surface radius $1,195$km$,\backslash$mu $\_(($h$)/($m$)$o$)=830$k$($m$^(3))/($s$^(2)),$g$\_(0)=$

$9\mathrm{.}81($m$)/($s$^(2)).$ Assume impulsive thrust.

How do i reach this answer?

m$0=1300$ kg

mf $=1300-100=1200$ kg

Max Available DV $=$ Isp$*$g$0*$ln$($m$0/$mf$)=0\mathrm{.}181$ km$/$s

Strategy $1$: get on parabolic orbit from periapsis of elliptical orbit.

v$\_$parabola $($per$)=1\mathrm{.}020$ km$/$s

v$\_$ellipse $($per$)=0\mathrm{.}942$ km$/$s

DV $($per$)=0\mathrm{.}078$ km$/$s $$ Max Available DV

Strategy $2$: get on parabolic orbit from apoapsis of elliptical orbit.

v$\_$parabola $($apo$)=0\mathrm{.}425$ km$/$s

v$\_$ellipse $($apo$)=0\mathrm{.}163$ km$/$s

DV $($apo$)=0\mathrm{.}262$ km$/$s $>$ Max Available DV

Strategy $1$ is the optimal one.