What Happens to a Comet's Orbit at Aphelion with Decreasing Angular Momentum?

[kala]

Homework Statement

Consider a comet which passes through its aphelion at a distance r_max from the sun. Imagine that, keeping r_max 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 r_max=c/1-$$\epsilon$$, r_{min=1+$$\epsilon$$}to show that in this limit the eccentricity, $$\epsilon$$ of the elliptical orbit approaches 1 and the distance of closest approach r_min approaches zero.

Homework 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.

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 r_max equation, but then i really didn't know where to go from there. any help would be great.

 

[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.