11:55

Algebra and Trigonometry Real Mathematics, Real People

Use the results of Exercises $55$ and $56,$ where for the planet Neptune, $a=4.498 \times 10^{9}$ kilometers and $e=0.0086$ and for the dwarf planet Pluto, $a=5.906 \times 10^{9}$ kilometers and $e=0.2488$.

(a) Find the polar equation of the orbit of each planet.

(b) Find the perihelion and aphelion distances for each planet.

(c) Use a graphing utility to graph both Neptune's and Pluto's equations of orbit in the same viewing window.

(d) Is Pluto ever closer to the sun than Neptune? Until recently, Pluto was considered the ninth planet. Why was Pluto called the ninth planet and Neptune the eighth planet?

(e) Do the orbits of Neptune and Pluto intersect? Will Neptune and Pluto ever collide? Why or why not?