Part 2: Newton's Proof Newton hypothesized that all objects are attracted to all other objects with a force that obeys an inverse square law: F GMm or similarly, that g = = GM %3D %3D By using the motion of the moon and the method you just learned, he produced evidence support his theory. Complete the simplified version of his proof outlined below. to Step 1: Newton knew that the moon has an orbital period of 27.3 days, and that it moves around the earth in a roughly circular path with a radius of 3.8 x 108 m. Use the kinematics equations to calculate a, of the moon. Step 2: Newton knew that the center-to-center distance from the earth to the moon equaled 60 earth radii. Use the method from the previous page and the value of little g to compute the acceleration of the moon in its orbit, gMoon Step 3: Compare: Does Newton's gravity equation predict a gMoon in step 2 equal to the centripetal acceleration computed from kinematics in step 1? If your answers from steps 1 and 2 above differ, go back and check your work. Critical Thinking Question: The acceleration of falling bodies on the moon is 1.6 m/ s2. Does this equal your calculated value for gMoon? Why or why not? 202

Part 2: Newton's Proof Newton hypothesized that all objects are attracted to all other objects with a force that obeys an inverse square law: F GMm or similarly, that g = = GM %3D %3D By using the motion of the moon and the method you just learned, he produced evidence support his theory. Complete the simplified version of his proof outlined below. to Step 1: Newton knew that the moon has an orbital period of 27.3 days, and that it moves around the earth in a roughly circular path with a radius of 3.8 x 108 m. Use the kinematics equations to calculate a, of the moon. Step 2: Newton knew that the center-to-center distance from the earth to the moon equaled 60 earth radii. Use the method from the previous page and the value of little g to compute the acceleration of the moon in its orbit, gMoon Step 3: Compare: Does Newton's gravity equation predict a gMoon in step 2 equal to the centripetal acceleration computed from kinematics in step 1? If your answers from steps 1 and 2 above differ, go back and check your work. Critical Thinking Question: The acceleration of falling bodies on the moon is 1.6 m/ s2. Does this equal your calculated value for gMoon? Why or why not? 202

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter7: Gravitation

Section: Chapter Questions

Problem 89A

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