Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Textbook Question
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Chapter 5, Problem 30P

At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull in opposite directions with equal force?

Expert Solution & Answer
Check Mark
To determine

The distance from the Earth where a spacecraft traveling directly from Earth to the Moon experience zero net force.

Answer to Problem 30P

Solution:

  3.46×108m

Explanation of Solution

Given:

The Earth and Moon pull in opposite directions with equal forces.

Formula Used: F (gravitational force) =Gm1m2r2

Where, m1 and m2 aremasses of objects.

r : the distance between m1 and m2 .

G : Universal gravitational constant.

Calculations: Let the zero point be de the distance from Earth and dm distance from the Moon,

Using a 1 kg test mass at this point,

Considering the gravitational forces, Fg on this mass from the Earth and from the Moon is equal.

  Fg=GMe×1de2=GMm×1dm2

  Mede2=Mmd2m

Mass of Earth: 5.97×1024kg

Mass of Moon: 7.35×1022kg

  dedm= M e M m dedm= 5.97× 10 24 7.35× 10 22 dedm=9

  de=9dm

This means, the distance of the point is 910 the distance of the moon from the Earth.

So,

  =0.9×3.84×108=3.46×108m

Conclusion:

The distance from the Earth where a spacecraft traveling directly from Earth to the Moon experience zero net force is 3.46×108m .

Chapter 5 Solutions

Physics: Principles with Applications

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