Chapter 10.3, Problem 79AYU

To determine

To write: An equation for the orbit of earth around the sun and perihelion.

Answer to Problem 79AYU

Equation for the orbit of earth around the sun is $\frac{x^2}{8649}+\frac{y^2}{8646.75}=1$ .

Explanation of Solution

Given:Themean distance of earth from the sun is 93 million miles where aphelion of earth is 94.5 million miles.

It is given that themean distance of earth from the sun is 93 million miles where aphelion of earth is 94.5 million miles.

  $\begin{array}{l}h=0\\ k=0\\ a=93\\ c=94.5-93=1.5\end{array}$

Now equation of the ellipse is

  $\begin{array}{l}\frac{x^2}{{93}^2}+\frac{y^2}{{93}^2-{1.5}^2}=1\\ \frac{x^2}{8649}+\frac{y^2}{8646.75}=1\end{array}$

Hence, equation for the orbit of earth around the sun is $\frac{x^2}{8649}+\frac{y^2}{8646.75}=1$