Chapter 7, Problem 32QP

(a)

To determine

The total mass of all the planets in the Solar System in terms of Earth masses.

Answer to Problem 32QP

The total mass of all the planets in the Solar System in terms of Earth masses is $\underset{\_}{446.66{\text{M}}_{\text{Earth}}}$.

Explanation of Solution

Write the expression for the sum of the mass of the eight planets in our Solar System,

  $M_{total}=M_{Mercury}+M_{Venus}+M_{Earth}+M_{Mars}+M_{Jupiter}+M_{Saturn}+M_{Uranus}+M_{Neptune}$        (I)

Here, $M_{total}$ is the mass of the eight planets in our Solar System, $M_{Mercury}$ is the mass of the Mercury in terms of Earth masses, $M_{Venus}$ is the mass of the Venus in terms of Earth masses, $M_{Earth}$ is the mass of the Earth in terms of Earth masses, $M_{Mars}$ is the mass of the Mars in terms of Earth masses, $M_{Jupiter}$ is the mass of the Jupiter in terms of Earth masses, $M_{Saturn}$ is the mass of the Saturn in terms of Earth masses, $M_{Uranus}$ is the mass of the Uranus in terms of Earth masses and $M_{Neptune}$ is the mass of the Neptune in terms of Earth masses.

Conclusion:

Substitute $0.055\text{Earth}\text{masses}$ for $M_{Mercury}$, $0.815\text{Earth}\text{masses}$ for $M_{Venus}$, $1.00\text{Earth}\text{mass}$ for  $M_{Earth}$, $0.107\text{Earth}\text{masses}$ for $M_{Mars}$, $317.83\text{Earth}\text{masses}$ for $M_{Jupiter}$, $95.16\text{Earth}\text{masses}$ for $M_{Saturn}$, $14.54\text{Earth}\text{masses}$ for $M_{Uranus}$ and $17.15\text{Earth}\text{masses}$ for $M_{Neptune}$ in (I) to find $M_{total}$,

  $\begin{array}{c}{M}_{total}=\left(0.055+0.815+1.00+0.107+317.83+95.16+14.54+17.15\right)\text{Earth}\text{masses}\\ =446.66\text{Earth}\text{masses}\\ =446.66M_{\text{Earth}}\end{array}$

Therefore, the total mass of all the planets in the Solar System in terms of Earth masses is $\underset{\_}{446.66{\text{M}}_{\text{Earth}}}$.

(b)

To determine

The fraction of that total planetary mass is Jupiter.

Answer to Problem 32QP

The fraction of that total planetary mass is Jupiter is $\underset{\_}{71.16\%}$.

Explanation of Solution

Write the expression for the fraction of that total planetary mass is Jupiter.

    $F=\frac{M_{Jupiter}}{M_{total}}\times 100\%$        (II)

Here, $F$ is the fraction of that total planetary mass is Jupiter.

Conclusion:

Substitute $317.83M_{\text{Earth}}$ for $M_{Jupiter}$ and $446.66M_{\text{Earth}}$ for $M_{total}$ in above equation.

    $\begin{array}{c}F=\frac{317.83M_{\text{Jupiter}}}{446.66M_{\text{Earth}}}\times 100\%\\ =0.7116\times 100\%\\ =71.16\%\end{array}$

Therefore, the fraction of that total planetary mass is Jupiter is $\underset{\_}{71.16\%}$.

(c)

To determine

The fraction of that total planetary mass is Earth.

Answer to Problem 32QP

The fraction of that total planetary mass is Earth is $\underset{\_}{0.22\%}$.

Explanation of Solution

Write the expression for the fraction of that total planetary mass is Earth.

    $F_{Earth}=\frac{M_{Earth}}{M_{total}}\times 100\%$        (II)

Here, $F_{Earth}$ is the fraction of that total planetary mass is Earth.

Conclusion:

Substitute $1.00M_{\text{Earth}}$ for $M_{Jupiter}$ and $446.66M_{\text{Earth}}$ for $M_{total}$ in above equation.

    $\begin{array}{c}F=\frac{1.00M_{\text{Jupiter}}}{446.66M_{\text{Earth}}}\times 100\%\\ =0.0022\times 100\%\\ =0.22\%\end{array}$

Therefore, the fraction of that total planetary mass is Earth is $\underset{\_}{0.22\%}$.