Chapter 10.6, Problem 26ES

Use the following values, where needed:

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

Mars has a perihelion distance of 204,520,000 km and an aphelion distance of 246,280,000 km.

(a) Use these data to calculate the eccentricity, and compare your answer to the value given in Table 10.6.1.

(b) Find the period of Mars.

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

(d) Use a graphing utility to generate the orbit of Mars from the equation obtained in part (c).