Chapter 10.3, Problem 82AYU

To determine

To write: An equation for the orbit of Pluto around the sun, aphelion and mean distance.

Answer to Problem 82AYU

Equation for the orbit of Jupiter around the sun is $\frac{x^2}{25583364}+\frac{y^2}{4871763}=1$ and mean deviation is 5058.

Explanation of Solution

Given:Theperihelion of Pluto is 4551 million miles where from the center of its elliptical orbit to the sun is 897.5 million miles.

It is given that themean distance of mars from the sun is 897.5 million miles where perihelion of Pluto is 4551 million miles.

  $aphelion=4551+2\times 507=6346$

  $MeanD=4551+507=5058$

Now equation of the ellipse is

  $\begin{array}{l}\frac{x^2}{{5058}^2}+\frac{y^2}{{5058}^2-{4551}^2}=1\\ \frac{x^2}{25583364}+\frac{y^2}{4871763}=1\end{array}$

Hence, equation for the orbit of Pluto around the sun is $\frac{x^2}{25583364}+\frac{y^2}{4871763}=1$