Why Are Gravitational and Centripetal Forces Equal in Moon's Orbit?

[dura]

QUESTION: the mass of the moon is 7.3x10^22 kg and its orbital speed about the Earth is 1024m/s. The distance between the centers of the Earth and moon is 3.844x10^24 m.

a) what is the value of the centripetal force acting on the moon?
b) the mass ofthe Earth is 5.98x10^24 kg and the universal gravitational constant G is 6.67x10^-11 Nm^2kg^-2. What is the value of the gravitational force acting between the Earth and moon?
c) why are the numerical answers to parts a) and b) the same?

Ok, I am fine with a), but b) is confusing me! Can someone help me with the next few steps?

 

[Doc Al]

Originally posted by dura
Ok, I am fine with a), but b) is confusing me! Can someone help me with the next few steps?

For part b) you need to use Newton's law of gravity to calculate the force of attraction between Moon and Earth. Look it up.

 

[dura]

Originally posted by Doc Al
For part b) you need to use Newton's law of gravity to calculate the force of attraction between Moon and Earth. Look it up.

Thank you... you know, its getting late and I have been doing physics all day. I think my brain has quit!

 

[Doc Al]

Originally posted by dura
I think my brain has quit!

I know that feeling all too well!

 

[dura]

Originally posted by dura
QUESTION: the mass of the moon is 7.3x10^22 kg and its orbital speed about the Earth is 1024m/s. The distance between the centers of the Earth and moon is 3.844x10^24 m.

a)what is the value of the centripetal force acting on the moon?
b) the mass ofthe Earth is 5.98x10^24 kg and the universal gravitational constant G is 6.67x10^-11 Nm^2kg^-2. What is the value of the gravitational force acting between the Earth and moon?

c) why are the numerical answers to parts a) and b) the same?

Regarding the last part of this question, how can I relate the fact taht centripetal force between the moon and Earth is the same as the gravitational force acting between Earth and moon.

Isn't this the same thing? The question asks me to explain clearly. I am not sure how to word this?

 

[cookiemonster]

You just said the reason quite nicely, but your teacher might want you to expand on the consequences of the reason a little. What if the force of gravity were greater than the centripetal force? What would happen to the Moon? What if it were less? What's so special about being exactly equal?

cookiemonster

 

[Doc Al]

Originally posted by dura
Isn't this the same thing? The question asks me to explain clearly. I am not sure how to word this?

Let me add a few comments to cookiemonster's advice. If I were asking this question, I'd want you to demonstrate that you understand that "centripetal force" is not a type of force, like gravity, electric force, tension in a string, etc. What you did in part a was apply your knowledge of circular motion to calculate the Moon's centripetal acceleration. Then, applying Newton's 2nd law, you deduced that there must be a centripetal force causing that acceleration. Now you have to find out what is supplying that force. There is only one force acting on the Moon, and you calculated it in part b: the gravitational attraction of the Earth. That gravitational force is the centripetal force. If it turned out that your answer to b did not equal your answer to a, then you would need to look for an additional force so that the net force on the Moon exactly equaled the needed centripetal force.

(I hope I haven't confused you by this ramble.)