Originally Posted by

**galactus** First, let's find the eccentricity, e. Do not get this mixed up with the log e

The ratio of the perhelion to aphelion for the Sun and Earth is about 59/61.

The smallest distance is a-c and the largest is a+c.

$\displaystyle \frac{a-c}{a+c}=\frac{59}{61}$

$\displaystyle \frac{1-\frac{c}{a}}{1+\frac{c}{a}}=\frac{59}{61}$

$\displaystyle \frac{1-e}{1+e}=\frac{59}{61}$

Solving gives us $\displaystyle e=\frac{1}{60}$

From above $\displaystyle e=\frac{c}{a}=\frac{1}{60}$

So, $\displaystyle c=\frac{a}{60}$

The smallest distance is $\displaystyle a-c=a-\frac{a}{60}=\frac{59a}{60}=\frac{59}{60}(93)=91, 450,000 \;\ miles$

You can now find the ellipse equation which models this.