Compute Aphelion from Eccentricity & Perihelion

[Logarythmic]

If I have the eccentricity and the perihelion of an orbit given, how can I compute the aphelion?

 

[Tomsk]

You need to think of what angles correspond the the perihelion and aphelion. Then use the relation between r, e, theta and l to get the aphelion.

 

[Logarythmic]

Can I not just use the relation for an ellipse:

$$e = \frac{d}{a}$$

where d is the distance from the focal point to the center and a is the semi major axis?

 

[Tomsk]

Well yes if you know a and d. You'd get the same result. You might need J as well though.

 

[Logarythmic]

I just used the radial equation

$$r_a = \frac{a(1 - e^2)}{1 + e \cos \pi} = a(1+e)$$

This leads to

$$r_a = \frac{r_p(1+e)}{1-e}$$

where I have used that

$$a = \frac{r_a + r_p}{2}$$

But for $$r_p = 0,2301 AU$$ I get $$r_a = 2988 AU$$ and this is wrong. I should get $$r_a =4699 AU$$. Am I too tired or what is this?
I have that $$e = 0,999846$$