Loose Leaf For Explorations:  Introduction To Astronomy
Loose Leaf For Explorations: Introduction To Astronomy
9th Edition
ISBN: 9781260432145
Author: Thomas T Arny, Stephen E Schneider Professor
Publisher: McGraw-Hill Education
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Chapter 8, Problem 2P

(8.1) Calculate the densities of Venus and Jupiter (use the masses and radii given in the appendix). How do these numbers compare with the density of rock (about 3 grams per cm3) and water (1 gram per cm3)? (Note: Be sure to convert kilometers to centimeters and kilograms to grams if you are expressing your answer in grams per cm3.)

Expert Solution & Answer
Check Mark
To determine

The densities of Venus and Jupiter and compare these densities with rock and water.

Answer to Problem 2P

The densities of Venus and Jupiter is 5.25g/cm3 and 1.24g/cm3. Using this Venus has large density than that of rock, Jupiter is denser than water.

Explanation of Solution

Write the expression for density of the object.

  ρVenus=MVenusV        (I)

Here, ρVenus is density of the Venus planet, MVenus is the mass of the Venus planet, and V is the volume of the planet.

The volume of the Venus planet is,

  V=43πRVenus3        (II)

Here, RVenus is the radius of the Venus planet.

Substitute equation (II) in equation (I).

  ρVenus=MVenus43πRVenus3        (III)

Similarly the density of the Jupiter planet is,

  ρJupiter=MJupiter43πRJupiter3        (IV)

Here, ρJupiter is density of the Jupiter planet, MJupiter is the mass of the Jupiter planet, and RJupiter is the radius of the Jupiter planet.

Conclusion:

Substitute 4.87×1024kg for MVenus and 6,051km for RVenus in equation (III) to find ρVenus.

  ρVenus=(4.87×1024kg)(103g1kg)43π[(6,051km)(105cm1km)]3=(4.87×1027g)43(3.14)(6,051×105cm)3=5.25g/cm3

Substitute 1.9×1027kg for MJupiter and 71,492km for RJupiter in equation (IV) to find ρJupiter.

  ρJupiter=(1.9×1027kg)(103g1kg)43π[(71,492km)(105cm1km)]3=(1.9×1030g)43(3.14)(71,492×105cm)3=1.24g/cm3

Therefore, the densities of Venus and Jupiter is 5.25g/cm3 and 1.24g/cm3. Using this Venus has large density than that of rock, Jupiter is denser than water.

Since the density of rock is about 3g/cm3, so that Venus has larger density than that of rock suggested that it is due to the iron core of rock material.

Since the density of water is about 1g/cm3, so that Jupiter is slightly denser than water, suggesting that it is largely made of lighter materials such as hydrogen.

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