Chapter MPS, Problem 9.8MPS

To determine

To find: The length of a Martian year.

Answer to Problem 9.8MPS

The length of a Martian yearis $738$ .

Explanation of Solution

Given information: The Mars is 1.5 times as far from the Sun.

Calculation:

Consider the equation.

  $\begin{array}{l}{t}^2=k{D}^3\\ {\left(365\right)}^2=k{D}^3\\ k=\frac{{\left(365\right)}^2}{D^3}\end{array}$

The time required for mars,

  $\begin{array}{l}{t}^2=k{D}^3\\ t^2=k{\left(1.6D\right)}^3\\ t^2=\frac{{\left(365\right)}^2}{D^3}{\left(1.6\right)}^3{D}^3\\ t=738\end{array}$

Thus, the length of a Martian year is $738$ .