# Conservation of Angular Momentum and Energy

1. Homework Statement
We measure a comet at perihelion to have a radial distance r1 and a velocity v1. Find the radial distance and velocity when it reaches aphelion.

2. Homework Equations
L=mvr=I*$$\omega$$
E=.5mv^2+U

3. The Attempt at a Solution
My professor skipped the chapter on Newton's Gravitation, F=GMm/r^2, so I don't think it applies here.

The book is entirely symbolic--the answer expected should be in terms of v1 and r1.

I labeled the radial distance and velocity r2 and v2, respectively. Since L is constant, m*v1*r1 = m*v2*r2, or v1*r1=v2*r2. Of course, this equation only gives the unknown radial distance in terms of the unknown velocity, or vice versa.

I don't think U = -GMm/r would apply here, since, again, my professor skipped the chapter on gravitation. I tried solving using a second equality, .5m*v1^2-GMm/r1=.5m*v2^2-GMm/r2, but when I solved the system of equations with Mathematica, I got a gigantic mess for an answer.

I think both your equations correct, you just did something wrong with the calculations. 