Question

Mars The mean distance of Mars from the Sun is $142$million miles. If the perihelion of Mars is $128.5$million miles, what is the aphelion? Write an equation for the orbit of Mars about the Sun.

Short answer

The equation of the orbit of Mars is given as$\frac{x^2}{20164}+\frac{y^2}{19981.75}=1$

Step-by-step solution

Step 1. Given information..

The equation of the orbit is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

The mean distance of Mars from the Sun is $142millionmiles$. This mean $a=142$

The perihelion is $128.5$million miles

The distance of center from the sun is$$\begin{gathered} c=142-128.5 \\ c=13.5 \end{gathered}$$

Step 2. To find the equation of the orbit of the Mars.

The aphelion is

$$\begin{gathered} a+c=142+13.5 \\ a+c=155.5 \end{gathered}$$

We also have,

role="math" localid="1647103052984" $$\begin{gathered} b^2=a^2-c^2 \\ {b}^2={142}^2-{(13.5)}^2 \\ {b}^2=19981.75 \end{gathered}$$

The equation of the orbit of Mars is given as $\frac{x^2}{20164}+\frac{y^2}{19981.75}=1$.