College Physics, Volume 1
College Physics, Volume 1
2nd Edition
ISBN: 9781133710271
Author: Giordano
Publisher: Cengage
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Chapter 5, Problem 54P
To determine

The gravitational force of Jupiter on the earth, and compare the result with the magnitude of gravitational force on earth from the sun.

Expert Solution & Answer
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Answer to Problem 54P

The gravitational force of Jupiter on the earth when it is closest to earth is 1.9×1018N_, The gravitational force of Jupiter on the earth when earth is farthest to earth is 8.8×1017N_, and the gravitational force of the sun on the earth is 3.5×1022N_.

Explanation of Solution

Write the expression for gravitational force of the sun on the earth.

    FSEgrav=GMSunMEarthrEarth2        (I)

Here, FSEgrav is the gravitational force of the sun on the earth, G is the universal gravitation constant, MSun is the mass of the sun, MEarth is the mass of earth, and rEarth is the radius of earth.

Write the expression for gravitational force of Jupiter on the earth when it is closest to earth.

    FJupiter closest =GMJupiter MEarth (rJupiter rEarth )2        (II)

Here, FJupiter closest  is the gravitational force of Jupiter on the earth when it is closest to earth,  MJupiter  is the mass of Jupiter, and rJupiter  is the radius of Jupiter.

Write the expression for gravitational force of Jupiter on the earth when it is furthest to earth.

    FJupiter Furthest =GMJupiter MEarth (rJupiter +rEarth )2        (III)

Here, FJupiter Furthest  is the gravitational force of Jupiter on the earth when it is furthest to earth, MJupiter  is the mass of Jupiter, and rJupiter  is the radius of Jupiter.

Conclusion:

Substitute 6.67×1011Nm2/kg for G, 1.99×1030kg for Msun, 1.50×1011m for rE and 5.97×1024kg for MEarth in equation (I), to find FSEgrav.

    FSEgrav=(6.67×1011Nm2/kg)(1.99×1030kg)(5.97×1024kg)(1.50×1011m)2=3.5×1022N

Substitute 6.67×1011Nm2/kg for G, 1.99×1027kg for MJupiter, 1.50×1011m for rEarth, 7.78×1011m for rJupiter and 5.97×1024kg for MEarth in equation (II), to find FJupiter closest .

    FJupiter closest =(6.67×1011Nm2/kg)(1.99×1027kg)(1.50×1011m)((7.78×1011m)(5.97×1024kg))2=1.9×1018N

Substitute 6.67×1011Nm2/kg for G, 1.99×1027kg for MJupiter, 1.50×1011m for rEarth, 7.78×1011m for rJupiter and 5.97×1024kg for MEarth in equation (III), to find FJupiter furthest.

    FJupiter furthest=(6.67×1011Nm2/kg)(1.99×1027kg)(1.50×1011m)((7.78×1011m)+(5.97×1024kg))2=8.8×1017N

Therefore, the gravitational force of Jupiter on the earth when it is closest to earth is 1.9×1018N_, The gravitational force of Jupiter on the earth when earth is farthest to earth is 8.8×1017N_, and the gravitational force of the sun on the earth is 3.5×1022N_.

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