Chapter 8.5, Problem 41E

Solution

To find: The perihelion and aphelion distances for this famous comet.

The perihelion and aphelion distances for this famous comet are $0.54\text{AU}$ and $35.64\text{AU}$ , respectively.

Given information:

The distance of semimajor axis is $a=18.09\text{AU}$ . The eccentricity is $e=0.97$ .

Formula used:

The perihelion distance is the nearest distance from the Sun (focus) to the comet (one endpoint of the major axis), $a-c$ . The aphelion distance is the farthest distance from the Sun (focus) to the comet (one endpoint of the major axis), $a+c$. This is illustrated below:

  

Calculation:

Find the value of $c$ as follows.

  $\begin{array}{c}c=ae\\ =18.09\left(0.97\right)\\ =17.5473\text{AU}\end{array}$

Find the perihelion distance as follows.

  $\begin{array}{c}\text{perihelion distance}=a-c\\ =18.09-17.5473\\ =0.54\text{AU}\end{array}$

Find the aphelion distance as follows.

  $\begin{array}{c}\text{aphelion distance}=a+c\\ =18.09+17.5473\\ =35.64\text{AU}\end{array}$

Therefore, the perihelion and aphelion distances for this famous comet are $0.54\text{AU}$ and $35.64\text{AU}$ , respectively.