21st Century Astronomy 6E
21st Century Astronomy 6E
6th Edition
ISBN: 9780393690675
Author: Laura Kay, Stacy Palen, George Blumenthal
Publisher: W. W. Norton
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Chapter 7, Problem 32QP

(a)

To determine

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

(a)

Expert Solution
Check Mark

Answer to Problem 32QP

The total mass of all the planets in the Solar System in terms of Earth masses is 446.66MEarth_.

Explanation of Solution

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

  Mtotal=MMercury+MVenus+MEarth+MMars+MJupiter+MSaturn+MUranus+MNeptune        (I)

Here, Mtotal is the mass of the eight planets in our Solar System, MMercury is the mass of the Mercury in terms of Earth masses, MVenus is the mass of the Venus in terms of Earth masses, MEarth is the mass of the Earth in terms of Earth masses, MMars is the mass of the Mars in terms of Earth masses, MJupiter is the mass of the Jupiter in terms of Earth masses, MSaturn is the mass of the Saturn in terms of Earth masses, MUranus is the mass of the Uranus in terms of Earth masses and MNeptune is the mass of the Neptune in terms of Earth masses.

Conclusion:

Substitute 0.055Earthmasses for MMercury, 0.815Earthmasses for MVenus, 1.00Earthmass for  MEarth, 0.107Earthmasses for MMars, 317.83Earthmasses for MJupiter, 95.16Earthmasses for MSaturn, 14.54Earthmasses for MUranus and 17.15Earthmasses for MNeptune in (I) to find Mtotal,

  Mtotal=(0.055+0.815+1.00+0.107+317.83+95.16+14.54+17.15)Earthmasses=446.66Earthmasses=446.66MEarth

Therefore, the total mass of all the planets in the Solar System in terms of Earth masses is 446.66MEarth_.

(b)

To determine

The fraction of that total planetary mass is Jupiter.

(b)

Expert Solution
Check Mark

Answer to Problem 32QP

The fraction of that total planetary mass is Jupiter is 71.16%_.

Explanation of Solution

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

    F=MJupiterMtotal×100%        (II)

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

Conclusion:

Substitute 317.83MEarth for MJupiter and 446.66MEarth for Mtotal in above equation.

    F=317.83MJupiter446.66MEarth×100%=0.7116×100%=71.16%

Therefore, the fraction of that total planetary mass is Jupiter is 71.16%_.

(c)

To determine

The fraction of that total planetary mass is Earth.

(c)

Expert Solution
Check Mark

Answer to Problem 32QP

The fraction of that total planetary mass is Earth is 0.22%_.

Explanation of Solution

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

    FEarth=MEarthMtotal×100%        (II)

Here, FEarth is the fraction of that total planetary mass is Earth.

Conclusion:

Substitute 1.00MEarth for MJupiter and 446.66MEarth for Mtotal in above equation.

    F=1.00MJupiter446.66MEarth×100%=0.0022×100%=0.22%

Therefore, the fraction of that total planetary mass is Earth is 0.22%_.

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