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A comet problem

  1. Dec 8, 2008 #1
    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[tex]\rightarrow[/tex]0. Use equations c=l2/[tex]\gamma\ mu[/tex] and rmax=c/1-[tex]\epsilon[/tex], rmin=1+[tex]\epsilon[/tex]to show that in this limit the eccentricity, [tex]\epsilon[/tex] 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. jcsd
  3. Dec 8, 2008 #2
    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.
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