Chapter 10.3, Problem 81AE

In Problems 79-83, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor axis of the elliptical orbit. See the illustration.

Mars The mean distance of Mars from the Sun is 142 million miles. If the perihelion of Mars is $128.5$ million miles, what is the aphelion? Write an equation for the orbit of Mars about the Sun.