Newton’s cannon ball and the moon

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The discussion centers on the analogy of Newton's cannonball to explain the moon's orbit around the Earth, emphasizing that both are examples of objects falling towards Earth while maintaining a forward velocity. Participants agree with the statement, noting that the moon's orbit is more elliptical compared to low Earth orbit (LEO) satellites. Questions arise about the differences in orbital shapes and the equations governing orbital velocity and radius. Key variables in these equations include gravitational force, mass, and distance from the Earth. Overall, the conversation highlights the fundamental principles of orbital mechanics and their applications.
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This applet was used for the hw: http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html

Explain or critique the following statement: “Just like Newton’s cannon ball, the moon orbits the Earth because it falls around the earth.”

I agree with the statement. Is there a difference between the orbit of an LEO and the moon? I think the moon's orbit is more elliptical but not sure if a cannon ball would also orbit elliptically once launched into orbit.
 
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well, what equations do you know how orbital velocity and radius, what are the variables in them?
 

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