Problem Diagram
Aphelion and Perihelion Distance between the Earth and the Sun 

During a field trip to a national astrology
center, a park ranger posed a challenging question to the 12^{th} graders
visiting the center. The earth was closest to the sun on that day, and
he wanted to know what is the shortest (i.e., perihelion distance) and
longest distance (i.e., aphelion distance) between the earth and the
sun. It is known that the elliptical orbit of earth around the sun in
polar coordinate is:
where e is the eccentricity and a is the distance of the major axis. 