The gravitational force exerted by Earth on the Moon and by Moon on Earth, when the mass of Earth is given as
Answer to Problem 35Q
Solution:
Explanation of Solution
Given data:
Mass of the Moon is
The average distance of center of Earth and center of Moon is 384400 km.
From the text, the gravitational force
Formula used:
Newton’s law of Universal gravitation can be stated by an equation as:
Here,
Explanation:
From Newton’s law of gravitation, the gravitational force, F is proportional to the mass and inversely proportional to the square of the distance r.
Use Newton’s equation and write the gravitational force of Earth and Moon:
Distance between Earth and Moon is 384400 km. Convert the unit of distance to m.
Substitute
Hence, the gravitational force between Earth and Moon is
Observe that the force exerted by Earth on Moon is equal to the force exerted by Moon on Earth, according to Newton’s law of gravity.
Observe from equation 1 and compare the force between Earth and Moon,
Conclusion:
Therefore, the force of the Sun on Earth is approximately 178 times more than the force of Earth on the Moon. This is majorly due the huge mass of the Sun as compared to the Moon, and also because of the large distance between the Sun and Earth as compared to the Moon and Earth.
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Chapter 4 Solutions
Universe
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