Chapter 8.2, Problem 55E

Solution

The perihelion and aphelion distances of Saturn.

It has been determined that the perihelion distance of Saturn from the Sun is $1347.088$ Gm and the aphelion distance is $\text{1506}\text{.912}$ Gm.

Given:

The eccentricities and semi-major axis of the planets and Pluto.

Concept used:

The eccentricity of an elliptic orbit is given as $e=\frac{c}{a}$ .

The perihelion distance from the Sun is $a-c$ and the aphelion distance is $a+c$ .

Calculation:

It can be found from the given table that the eccentricity of Saturn is $0.0560$ and its semi-major axis is $1427$ Gm.

Then, for Saturn, $e=0.0560$ and $a=1427$ .

Put these values in $e=\frac{c}{a}$ to get,

  $0.0560=\frac{c}{1427}$

Simplifying,

  $c=79.912$

Then, the perihelion distance of Saturn from the Sun is given as,

  $a-c=1427-79.912=1347.088$

Similarly, the aphelion distance of Saturn from the Sun is given as,

  $a+c=1427+79.912=\text{1506}\text{.912}$

Thus, the perihelion distance of Saturn from the Sun is $1347.088$ Gm and the aphelion distance is $\text{1506}\text{.912}$ Gm.

Conclusion:

It has been determined that the perihelion distance of Saturn from the Sun is $1347.088$ Gm and the aphelion distance is $\text{1506}\text{.912}$ Gm.