$\"\"$

The Hale-Bopp comet has an elliptical orbit with eccentricity is $\"\"$ .

The length of the major axis is $\"\"$ .

$\"\"$ .

The polar equation of an ellipse with focus at the sun, semi major axis $\"\"$ , eccentricity $\"\"$ is $\"\"$ .

Substitute $\"\"$ and $\"\"$ .

$\"\"$

$\"\"$ .

The polar equation is $\"\"$ .

The perihelion distance from a planet to the sun is $\"\"$ .

Substitute $\"\"$ and $\"\"$ .

$\"\"$

$\"\"$ .

The closest distance from the comet to the sun is $\"\"$ .

$\"\"$

The polar equation is $\"\"$ .

The maximum distance from the comet to the sun is $\"\"$ .