Chapter 8.5, Problem 83E

(Modeling) Solve each problem.

Orbits of Satellites The polar equation

$r=\frac{a(1-e^2)}{1+e\cos \theta }$ can be used to graph the orbits of the satellites of our sun, where a is the average distance in astronomical units from the sun and e is a constant called the eccentricity. The sun will be located at the pole. The table lists the values of a and e.

(a) Graph the orbits of the four closest satellites on the same polar grid. Choose a viewing window that results in a graph with nearly circular orbits.

(b) Plot the orbits of Earth. Jupiter. Uranus, and Pluto on the same polar grid. How does Earth’s distance from the sun compare to the others’ distances from the sun?

(c) Use graphing to determine whether or not Pluto is always farthest from the sun.