A star is about to go supernova $($explode$)$ and a planet orbiting the star must be evacuated. The starship Enterprise is sent to the planet to assist in the evacuation. The world lines of the Enterprise, the star, and the planet are shown on the space$-$time diagram below. Assume that the planet and star are at rest relative to each other. The plan is for the Enterprise to fly by the planet at a constant velocity and beam up the inhabitants without stopping. The star explodes at space$-$time point $\backslash (\backslash$mathbf$\{$s$\}\backslash )$ and light from the explosion spreads out in all directions, including those shown on the diagram. Use the diagram to answer the following questions.

a$)$ At which of the points labeled $\backslash (\backslash$mathbf$\{$a$\}\backslash )$ through $\backslash (\backslash$mathbf$\{$h$\}\backslash )$ in the space$-$time diagram does the Enterprise arrive at the planet?

b$)$ In the reference frame of the Enterprise, at which point is the star when the Enterprise arrives at the planet?

c$)$ In the reference frame of the Enterprise, does the Enterprise arrive at the planet before the star explodes or after the star explodes? Be sure to reference the space$-$time diagram in your answer.

d$)$ In the reference frame of the planet, does the Enterprise arrive at the planet before the star explodes or after the star explodes? Be sure to reference the space$-$time diagram in your answer.

e$)$ Do the inhabitants of the planet see the supernova before the Enterprise arrives or after the Enterprise arrives? Be sure to reference the space$-$time diagram in your answer.