How Far Is the Moon from Earth?

[Blair08]

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...

 

[Doc Al]

Hint: Apply Newton's 2nd law. What force acts on the moon?

 

[Blair08]

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

 

[ideasrule]

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?

 

[Blair08]

Acentrip=Vtang^2 * radius

butttttt i don't have acceleration

 

[ideasrule]

It's equal to Fg/m, no?

 

[Doc Al]

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.)

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.