Chapter 10.6, Problem 23ES

Use the following values, where needed:

$\begin{array}{|l|}\hline \text{radius of the Earth}=\text{4000 mi}=\text{6440 km}\hfill \\ \text{1 year }\left(\text{Earth year}\right)=\text{365 days }\left(\text{Earth days}\right)\hfill \\ \text{1 AU}=\text{92}\text{.9}\times {\text{10}}^{\text{6}}\text{mi}=\text{150}\times {\text{10}}^{\text{6}}\text{km}\hfill \\ \hline\end{array}$

The dwarf planet Pluto has eccentricity $e=0.249$ and semimajor axis $a=39.5\text{ AU}.$

(a) Find the period T in years.

(b) Find the perihelion and aphelion distances.

(c) Choose a polar coordinate system with the center of the Sun at the pole, and find a polar equation of Pluto's orbit in that coordinate system.

(d) Make a sketch of the orbit with reasonably accurate proportions.