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

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

100%

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

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