- #1
kala
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Homework Statement
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.
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 rmax equation, but then i really didn't know where to go from there. any help would be great.