What is the Relationship between Kepler's law and universal gravitation law?

[LukeyD]

What is the Relationship between Kepler's law and universal gravitation law?

(IT HAS SOMETHING TO DO WITH THE CENTRE OF MASS)I know this;

Newton's Law of Universal Gravitation F=mGM/r^2 derived Keplers Third Law r^3/t^2= constant:

mGM/r^2 = mv^2/r gives GM/ (2pi)^2 = r^3/t^2.

Read more: http://wiki.answers.com/Q/What_is_t...vitation_and_kepler's_third_law#ixzz1FWdmdjyI

But I have to do 300 words on it :(
I don't know any more!

 

[supratim1]

for Newton, orbits are circular, but kepler proves its elliptical.

 

[LukeyD]

Thanks for the fast reply, is there anyway you can elaborate on that as I'm still slightly confused :S

 

[LukeyD]

Also is it the third law that has a relation ship with universal gravitation?

 

[supratim1]

yes the third law is consistent with gravitation.

 

[LukeyD]

Do you have any articles that explain this as its what I have to do.

 

[tiny-tim]

for Newton, orbits are circular, but kepler proves its elliptical.

Nonsense!

Newton (1643-1727) was after Kepler (1571-1630)

 

[supratim1]

sorry sir, i mean, Newton's gravitation assumes orbits to be circular. am i wrong?

 

[tiny-tim]

yes!

 

[cepheid]

sorry sir, i mean, Newton's gravitation assumes orbits to be circular. am i wrong?

Yes, you are dead wrong. The fact that the orbits can be any sort of conic section (circle, ellipse, parabola, or hyperbola) comes directly from Newton's universal law of gravitation.

To the original poster: Keplers law was an empirical (observational) law. He came up with it because it fit the data, but he did not know why it was true. Newton explained why. In other words you can derive Kepler's 3rd law from Newton's law of gravitation. In general this gets a bit complicated, but for the specific case of a circular orbit, this is easy to do. Try it!

Edit: nevermind, you have already done it in your first post. Hopefully this illustrates that Newtons law is fundamental, and Keplers is merely a result of it.

 

[supratim1]

thank you sir, i understood it now.