# How to Derive an Equation.

1. Dec 6, 2007

### petern

Derive Kepler's Third Law of Planetary Motion from Newton's Law of Universal Gravitation.

I know the Law of Universal Gravitation is Fg = (Gm1m2)/(r^2) and the Third Law of Planetary Motion is T^2 = kr^3

What should I do next?

Last edited: Dec 6, 2007
2. Dec 6, 2007

### rock.freak667

Start from here:
The gravitational force of attraction between two masses provides the centripetal force required to keep the mass in a circular orbit.

so that (Gm1m2)/(r^2)=m1(w^2)r

3. Dec 6, 2007

### petern

Which equation does the m1(w^2)r come from?

4. Dec 6, 2007

### rock.freak667

the centripetal force is given by these equations:
$$F_C=m\omega^2r = \frac{mv^2}{r}=mv\omega$$

I just used the first equality

5. Dec 6, 2007

### petern

We haven't learned about m(w^2)r yet so I don't think that's what we're suppose to use. What is the w? However, we've learned about (mv^2)/r.

6. Dec 6, 2007

### petern

I think I set (Gm1m2)/(r^2) = (mv^2)/(r). I then plug the equation v = (2*pi*r)/T into the one I previously listed. After that, I cancel m1 out and get r1^3 = (Gm2T^2)/(4*pi). After that I don't know how to get rid of the G, m1, 4, and pi so that I'll end up with the equation T^2 = kr^3.

7. Dec 6, 2007