Chapter 10.3, Problem 80AYU

To determine

To write: An equation for the orbit of mars about the sun and perihelion.

Answer to Problem 80AYU

Equation for the orbit of mars about the sun is $\frac{x^2}{20164}+\frac{y^2}{19981.75}=1$ .

Explanation of Solution

Given:Themean distance of mars from the sun is 142 million miles where aphelion of mars is 128.5 million miles.

It is given that themean distance of mars from the sun is 142 million miles where aphelion of mars is 128.5 million miles.

  $\begin{array}{l}h=0\\ k=0\\ a=142\\ c=142-128.5=13.5\end{array}$

Now equation of the ellipse is

  $\begin{array}{l}\frac{x^2}{{142}^2}+\frac{y^2}{{142}^2-{13.5}^2}=1\\ \frac{x^2}{20164}+\frac{y^2}{19981.75}=1\end{array}$

Hence, equation for the orbit of mars about the sun is $\frac{x^2}{20164}+\frac{y^2}{19981.75}=1$