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Carnegie Mellon University

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Problem 50 Easy Difficulty

(a) What is the magnitude of the gravitational force that the Earth exerts on the Moon? (b) What is the magnitude of the gravitational force that the Moon exerts on the Earth? See the inside front and back covers for necessary information.

Answer

(a) $1.98 \times 10^{20} \mathrm{N}$
(b) $1.98 \times 10^{20} \mathrm{N}$

Discussion

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Watch More Solved Questions in Chapter 4

Video Transcript

silver per day we have. We're going to use Newton's universal law of gravitation and we have the force of the earth on the moon. This would be equal to the gravitational constant multiplied by the mass of the earth multiplied by the mass of the moon, divided by the distance between the center of the earth in the center of the moon quantity squared. This is gonna be equal to 6.67 times 10 to the negative 11th on Newton's meters squared, her kilograms squared. This would be multiplied by the mass of the earth at 5.97 times 10 to the 24th kilograms multiplied by 7.349 times 10 toothy, 22nd kilograms. Of course, all these values are tabulated and then, uh, the product of these three will be divided by 3.84 times 10 to the eighth meters quantity squared. And so we see that the force of the earth on the moon would be equal to 1.98 times 10 to the 20th Newtons and then for part B due to Newton's third Law. Ah, we can say that then the force of the earth on the moon would be equal to the force of the moon on the earth and the opposite direction equal in magnitude, but opposite in direction. And so we can say that then the force. If we considered the force on the Earth on the moon to be positive, we would say that the force of the moon on the earth would be equal to native 1.98 times 10 to the 20th Newtons. That is the end of the solution. Thank you for watching.

Carnegie Mellon University
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