Answer
$e\approx0.25$
Work Step by Step
Step 1. Identify the the given quantities: Pluto to the Sun $d_p=4.43\times10^9$ km at perihelion, $d_a=7.37\times10^9$ km at aphelion.
Step 2. Recall the result from Exercise 44 as $d_p=a(1-e)$ and $d_a=a(1+e)$
Step 3. Set up the equations based on the above data:
$\begin{cases} a(1-e)=4.43\times10^9\\a(1+e)=7.37\times10^9 \end{cases}$
Step 4. Add up the two equations to get $2a=11.8\times10^9$ and $a=5.9\times10^9$ km.
Step 5. Back-substitute in one of the system of equations to get $5.9\times10^9(1-e)=4.43\times10^9$ which gives $e\approx0.25$
