# A comet problem

1. Dec 8, 2008

### kala

1. The problem statement, all variables and given/known data

Consider a comet which passes through its aphelion at a distance rmax from the sun. Imagine that, keeping rmax fixed, we somehow make the angular momentum l smaller and smaller though not actually zero; that is we let l$$\rightarrow$$0. Use equations c=l2/$$\gamma\ mu$$ and rmax=c/1-$$\epsilon$$, rmin=1+$$\epsilon$$to show that in this limit the eccentricity, $$\epsilon$$ of the elliptical orbit approaches 1 and the distance of closest approach rmin approaches zero.

2. Relevant equations

the equations posted above look funny, but for c it should be c=l2/gamma*mu
rmax=c/1-epsilon and rmin= c/1+epsilon.

3. The attempt at a solution
Well, I know that I am going to need to take limits. what i tried was to substitute in the c for the rmax equation, but then i really didn't know where to go from there. any help would be great.

2. Dec 8, 2008

### flatmaster

Well, physically what happened if you too l--> 0 What you reall did is take your orbital velocity to zero.

L = mV X R

You assumed aphelion, so R was fixed. Assuming mass went to zero would just make the commet float away. What wil happen is the commet will make a b-line straight for the sun.