Chapter 5, Problem 36QAP

(a)

To determine

The total mass of all the planets of the solar system.

Answer to Problem 36QAP

The total mass of the planets in the solar system is $446.65M_E$.

Explanation of Solution

The mass of the all the planets in the solar system is the sum of the mass of the planets in terms of the mass of the Earth.

Write the expression for the total mass of all the planets.

$M_T={\displaystyle \sum M_p}$        (I)

Here, $M_T$ is the total mass of all the planets and $M_p$ is the mass of each planet.

Conclusion:

Substitute $0.055M_E$ for $M_{mercury}$, $0.815M_E$ for $M_{venus}$, $M_E$ for $M_{Earth}$, $0.107M_E$ for $M_{mars}$, $317.83M_E$ for $M_{Jupiter}$, $95.16M_E$ for $M_{saturn}$, $14.536M_E$ for $M_{Uranus}$ and $17.148M_E$ for $M_{neptune}$ in equation (I).

$\begin{array}{c}{M}_T=\left\{\begin{array}{l}0.055M_E+0.815M_E+M_E+0.107M_E+317.83M_E\\ +95.16M_E+14.536M_E+17.148M_E\end{array}\right\}\\ =446.65M_E\end{array}$

Thus, the total mass of the planets in the solar system is $446.65M_E$.

(b)

To determine

The fraction of the total planetary mass that is contained by the planet Jupiter.

Answer to Problem 36QAP

The fraction of the planetary mass contained in the Jupiter is $0.711$ part of the total mass of the planets.

Explanation of Solution

The Jupiter is the biggest planet of the solar system. The planet consists of the almost the two-third part of the mass of the whole solar system.

Write the expression for the fraction of planetary mass contained in the Jupiter.

$M_f=\frac{M_{Jupiter}}{M_T}$        (II)

Here, $M_f$ is the fraction of mass and $M_{Jupiter}$ is the mass of the planet Jupiter.

Conclusion:

Substitute $317.83M_E$ for $M_{Jupiter}$ and $446.65M_E$ for $M_T$ in equation (II).

$\begin{array}{c}{M}_f=\frac{317.83M_E}{446.65M_E}\\ =0.711\end{array}$

Thus, the fraction of the planetary mass contained in the Jupiter is $0.711$ part of the total mass of the planets.

(c)

To determine

The fraction of the total planetary mass contained by the Earth.

Answer to Problem 36QAP

The fraction of the planetary mass contained in the Earth is $0.0022$ part of the total mass of the planets.

Explanation of Solution

Write the expression for the fraction of planetary mass contained in the Earth.

$M_f=\frac{M_{Earth}}{M_T}$        (III)

Here, $M_f$ is the fraction of mass and $M_{Earth}$ is the mass of the Earth.

Conclusion:

Substitute $M_E$ for $M_{Earth}$ and $446.65M_E$ for $M_T$ in equation (II).

$\begin{array}{c}{M}_f=\frac{M_E}{446.65M_E}\\ =0.0022\end{array}$

Thus, the fraction of the planetary mass contained in the Earth is $0.0022$ part of the total mass of the planets.