Solving for Aphelion of a Comet: What am I Doing Wrong?

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SUMMARY

The discussion focuses on calculating the aphelion of a comet with a perihelion of r_{per} = 0.2301 AU and an eccentricity of e = 0.999846. The user initially applies the formula r_{aph} = a(1+e) and mistakenly derives r_{aph} = 2988 AU. The correct calculation reveals that the aphelion should be r_{aph} = 4698 AU. The user concludes that small variations in eccentricity and perihelion significantly impact the aphelion result.

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Logarythmic
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It is given that the perihelion for a certain comet is [tex]r_{per} = 0,2301 AU[/tex] and the eccentricity is [tex]e = 0,999846[/tex].
My mission is to find the aphelion.
I know that this is given by

[tex]r_{aph} = a(1+e)[/tex]

And I have used that

[tex]a = \frac{r_{per} + r_{aph}}{2}[/tex]

This gives me

[tex]r_{aph} = \frac{r_{per}(1 + e)}{1-e}[/tex]

and then I get that [tex]r_{aph} = 2988 AU[/tex]. This all seems very simple so what am I doing wrong?

The correct answer should be [tex]r_{aph} = 4698 AU[/tex]
 
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Ok, I got it. Small variations in [tex]e[/tex] and [tex]r_{per}[/tex] will give a big difference in the aphelion. ;)
 

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