Chapter 9.1, Problem 62E

a.

To determine

To Simplify: The formula $P=\sqrt{d^3}$ .

  

Answer to Problem 62E

The required simplified formula is $P=5.2\sqrt{\left(5.2\right)}$ .

Explanation of Solution

Given information:

The orbital period (in earth years) is given by the formula $P=\sqrt{d^3}$ , where d is the average distance (in AU)

  

Calculation:

Since the average distance d is 5.2 AU

The formula is:

  $\begin{array}{l}P=\sqrt{d^3}\\ P=\sqrt{{\left(5.2\right)}^3}\end{array}$

(Substitute the value of d)

  $P=\sqrt{{\left(5.2\right)}^2\cdot \left(5.2\right)}$

(Factor using the greatest perfect square factors)

  $P=5.2\sqrt{\left(5.2\right)}$

(Simplify)

Therefore, the simplified formula is $P=5.2\sqrt{\left(5.2\right)}$

b.

To determine

To Find: The Jupiter’s orbital period.

Answer to Problem 62E

The required orbital period is $5.2\sqrt{5.2}$ or 11.86 earth years.

Explanation of Solution

Given information:

The orbital period (in earth years) is given by the formula $P=\sqrt{d^3}$ , where d is the average distance (in AU)

  

Calculation:

Since the average distance d is 5.2 AU

The orbital period is:

  $\begin{array}{l}P=\sqrt{d^3}\\ P=\sqrt{{\left(5.2\right)}^3}\end{array}$

(Substitute the value of d)

  $\begin{array}{l}P=\sqrt{{\left(5.2\right)}^2\cdot \left(5.2\right)}\\ P=5.2\sqrt{5.2}\end{array}$

(Simplify)

The Jupiter’s orbital period is $5.2\sqrt{5.2}$ or 11.86 earth years.