21st Century Astronomy
21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 11, Problem 37QP
To determine

The tidal force of the Jupiter and Io with respect to that of the Earth and its Moon.

Expert Solution & Answer
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Answer to Problem 37QP

The tidal force experienced by the moon Io of Jupiter is 3.05×105 times stronger than the tidal force experienced by the Earth’s moon.

Explanation of Solution

The tidal force is the gravitational interaction felt by a celestial body towards and away from its centre of mass due to the presence of the other celestial body around it.

Write the expression for the tidal force acting on the moon.

  Ftidal=2GMpMmRmdpm3        (I)

Here, Ftidal is the tidal force on moon, G is the gravitational constant, Mp is the mass of the planet, Mm is the mass of the moon, Rm is the radius of the moon and dpm is the distance between the moon and the planet.

Write the expression for the comparison of the tidal force on Earth-moon and Jupiter-Io system.

  Ftidal-IoFtidal-m=MJupMIoRIodJupIo3MEMmRmdEm3        (II)

Here, MJup is the mass of the planet Jupiter, MIo is the mass of the moon Io, RIo is the radius of the moon Io, dJupIo is the distance between the moon Io and the planet Jupiter, ME is the mass of the planet Earth, Mm is the mass of the Earth’s moon, Rm is the radius of the Earth’s moon and dEm is the distance between the Earth’s moon and the planet Earth.

The mass of the planet Jupiter is 1.898×1027kg whereas the mass of its moon Io is 8.9×1022kg.

The mass of the Earth is 6×1024kg and the mass of the Earth’s moon is 7.34×1022kg.

The radius of the Earth’s moon is 1737km and the radius of Io is 1820km.

The orbital radius of the Earth’s moon is 385,000km and the orbital radius of Io is 422,000km.

Conclusion:

Substitute 1.898×1027kg for MJup, 8.9×1022kg for MIo, 1820km for RIo , 422,000km for dJupIo, 6×1024kg for ME, 7.34×1022kg for Mm, 1737km for Rm and 385,000km for dEm in equation (II).

  Ftidal-IoFtidal-m=(1.898×1027kg)(8.9×1022kg)(1820km(1000m1km))(422,000km(1000m1km))3(6×1024kg)(7.34×1022kg)(1737km(1000m1km))(385,000km(1000m1km))3=4.09×10301.34×1028=3.05×105

Thus, the tidal force experienced by the moon Io of Jupiter is 3.05×105 times stronger than the tidal force experienced by the Earth’s moon.

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