Chapter 10.6, Problem 25ES

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 Hale-Bopp comet, discovered independently on July 23, 1995 by Alan Hale and Thomas Bopp, has an orbital eccentricity of $e=0.9951$ and a period of 2380 years.

(a) Find its semimajor axis in astronomical units (AU).

(b) Find its perihelion and aphelion distances.

(c) Choose a polar coordinate system with the center of the Sun at the pole, and find an equation for the Hale-Bopp orbit in that coordinate system.

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