How Far Is the Moon from Earth?

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Homework Help Overview

The discussion revolves around calculating the distance from the Earth to the Moon, assuming a circular orbit with a period of 27.3 days. The problem is situated within the context of rotational and circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the application of Newton's laws and the concept of centripetal acceleration. There are attempts to express the relationship between gravitational force and the motion of the Moon, while some participants express uncertainty about the necessary parameters, such as the mass of the Moon.

Discussion Status

Guidance has been offered regarding the use of Newton's Universal Law of Gravitation and the expression of variables symbolically. Participants are engaging in a back-and-forth regarding the necessary equations and assumptions, with multiple interpretations of the problem being explored.

Contextual Notes

There is a noted constraint regarding the lack of information about the Moon's mass, which some participants believe limits their ability to apply certain equations. The discussion also highlights the assumption of a circular orbit.

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Homework Statement


Assuming the moon's orbit around the Earth is a circular path (360 degree circle) and the moon's orbit around the Earth takes 27.3 days to complete 1 revolution, How far away from the Earth is the moon?


Homework Equations





The Attempt at a Solution


It's a rotational/circular motion problem that i cannot come up with the answer for...in no way can i find a solution to finding the distance between the two...
 
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Hint: Apply Newton's 2nd law. What force acts on the moon?
 
Yeah I know, Gravity. I can't use Newton's Universal Law of Gravitation because i don't know the Force of Gravity acting between the moon and the Earth...and i was only given the Earth's mass not the moon's
 
Just assume the mass is "m" and carry on. You'll find that it cancels out in the end.

Another hint: what's the equation for centripetal acceleration?
 
Acentrip=Vtang^2 * radius

butttttt i don't have acceleration
 
It's equal to Fg/m, no?
 
Blair08 said:
Yeah I know, Gravity. I can't use Newton's Universal Law of Gravitation because i don't know the Force of Gravity acting between the moon and the Earth...and i was only given the Earth's mass not the moon's
Sure you can use Newton's Universal Law of Gravitation. And the mass of the Earth is all you'll end up needing to know. So what does that law tell you the force is? (Represent all the variables by symbols.)
Blair08 said:
Acentrip=Vtang^2 * radius

butttttt i don't have acceleration
But that is the acceleration. Hint: Express the tangential speed in terms of the radius and the period. (Use symbols, once again. Don't plug in numbers until the end.)

Now you have the force and the acceleration. Apply Newton's 2nd law.
 

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