Foundations of Astronomy (MindTap Course List)
Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 8, Problem 1SOP
To determine

Is the surface area of the Sun larger than the surface area of Earth.

Is the volume of the Sun larger than the volume of Earth.

Expert Solution & Answer
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Answer to Problem 1SOP

The surface area of the Sun is 12000 times larger than the surface area of Earth.

The volume of the Sun is 1.3million times larger than the volume of Earth.

Explanation of Solution

The diameter of the Sun is 109 times the diameter of Earth. So,

    DSun=109DEarth                                                                                           (I)

Here, DSun is the diameter of the Sun and DEarth  is the diameter of the Earth.

The diameter of the Earth is 12742km.

Write the expression for the surface area of the sphere.

    S=4π(D2)2

    S=πD2                                                                                                     (II)

Here, S is the surface area of the sphere.

Write the expression for the surface area of the Earth.

    SEarth=πDEarth2                                                                                            (III)

Here, SEarth is the surface area of the Earth.

Write the expression for the surface area of the Sun.

    SSun=πDSun2                                                                                                 (IV)

Here, SSun is the surface area of the Sun.

Write the expression for the volume of the sphere.

    V=43π(D2)3

    V=πD36                                                                                                           (V)

Here, V is the volume of the sphere.

Write the expression for the volume of the Earth.

    VEarth=π(DEarth)36                                                                                              (VI)

Here, VEarth is the volume of the Earth.

Write the expression for the volume of the Sun.

    VSun=π(DSun)36                                                                                                   (VII)

Here, VSun is the volume of the Sun.

Conclusion:

Substitute 12742km for DEarth in equation (I) to find DSun.

    DSun=109(12742km)=1.391×106km

Substitute 12742km for DEarth in (III) to find SEarth

    SEarth=π(12742km)2=5.10×108km2

Substitute 1.391×106km for DSun in (IV) to find SSun

    SSun=π(1.391×106km)2=6.09×1012km212000(SEarth)

Substitute 12742km for VEarth in (VI) to find VEarth

    VEarth=π(12742km)36=108.321×1010km3

Substitute 1.391×106km for DSun in (VII) to find VSun

    VSun=π(1.391×106km)36=140.922×1016km3=1.3×106(VEarth)

Therefore, the surface area of the Sun is 12000 times larger than the surface area of Earth.

The volume of the Sun is 1.3million times larger than the volume of Earth.

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Foundations of Astronomy (MindTap Course List)

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