$(13$ pts $)$ Pluto is an amazing rocky$/$icy world. It has a radius of $1188$ km $($smaller than our Moon$)$ and a mass of $1\mathrm{.}30{10}^{22}kg($about $18\%$ of our Moon's mass$).$

Calculate the freefall acceleration near the surface of Pluto.

$($a$)$ Draw a not$-$to$-$scale pictorial of something freefalling near the surface of Pluto, representing Pluto as a large circle. Choose a coordinate system of $+y$ either toward or away from the surface. This is a linear $1$D vertical problem, not an orbit. Define your variable names in this pictorial.

$($b$)$ What is the system?

$($d$)$ Draw a FBD of the system. Don't forget the coordinate system!