A $361$ g marble is fired vertically upward using a spring gun. The spring must be compressed $4\mathrm{.}26$ cm if the marble is to just reach a target $19\mathrm{.}0$ m above the marble's position on the compressed spring. $($a$)$ What is the change in the gravitational potential energy of the marble$-$Earth system during the $19\mathrm{.}0$ m ascent? $($B$)$ What is the change in the elastic potential energy of the spring during its launch of the marble? $($C$)$ What is the spring constant of the spring?