Chapter 10.3, Problem 81AYU

To determine

To write: An equation for the orbit of Jupiter around the sun and mean distance.

Answer to Problem 81AYU

Equation for the orbit of Jupiter around the sun is $\frac{x^2}{234062.44}+\frac{y^2}{233524.2}=1$ and mean deviation is 483.8.

Explanation of Solution

Given:Theaphelion of Jupiteris 507 million miles where from the center of its elliptical orbit to the sun is 23.2 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.

  $perihelion=507-2\times 23.2=460.6$

  $MeanD=507-23.2=483.8$

Now equation of the ellipse is

  $\begin{array}{l}\frac{x^2}{{483.8}^2}+\frac{y^2}{{483.8}^2-{23.2}^2}=1\\ \frac{x^2}{234062.44}+\frac{y^2}{233524.2}=1\end{array}$

Hence, equation for the orbit of Jupiter around the sun is $\frac{x^2}{234062.44}+\frac{y^2}{233524.2}=1$