Chapter 6.4, Problem 55PPS

To determine

If the formula is $d=\sqrt[3]{6t^2}$ where $\left(d\right)$ is the distance of a planet from the sun in millions of miles and $\left(t\right)$ is the number of earth days that it takes for the planet to orbit the sun. And the length of a year on Mars is 687 Earth-day then find the distance of the Mars from the Sun.

Answer to Problem 55PPS

The distance of Mars from the Sun is 141.48 million of mile.

Explanation of Solution

Given information: The given formula is $d=\sqrt[3]{6t^2}$ where $\left(d\right)$ is the distance of a planet from the sun in millions of miles and $\left(t\right)$ is the number of earth days that it takes for the planet to orbit the sun. And the length of a year on Mars is 687 Earth-day.

Calculation: From the formula $d=\sqrt[3]{6t^2}$ where $\left(d\right)$ is the distance of a planet from the sun in millions of miles and $\left(t\right)$ is the number of earth days that it takes for the planet to orbit the sun. And the length of a year on Mars is 687 Earth-day.

Therefore, the distance of the Mars from the Sun can be evaluated by plugging $\left(t=687\right)$ in the formula $d=\sqrt[3]{6t^2}$.

  $\begin{array}{c}d=\sqrt[3]{6t^2}\\ =\sqrt[3]{6{\left(687\right)}^2}\\ =141.48\end{array}$

Hence, the distance of Mars from the Sun is 141.48 million of mile.