# Compute Aphelion from Eccentricity & Perihelion

• Logarythmic
In summary, to compute the aphelion of an orbit given the eccentricity and perihelion, you can use the relation between r, e, theta and l or the relation for an ellipse. The radial equation can also be used to determine the aphelion, but it may be necessary to also know the semi major axis and the distance from the focal point to the center. However, for a specific case where r_p = 0,2301 AU and e = 0,9998464, the calculated aphelion of 2988 AU is incorrect and should be 4699 AU.
Logarythmic
If I have the eccentricity and the perihelion of an orbit given, how can I compute the aphelion?

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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.

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?

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

I just used the radial equation

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

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

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 $$e = 0,999846$$

## What is the formula for computing aphelion from eccentricity and perihelion?

The formula for computing aphelion from eccentricity and perihelion is:
Aphelion = Perihelion / (1 - Eccentricity)

## Can you explain the terms "eccentricity" and "perihelion"?

Eccentricity refers to the measure of the elliptical shape of an orbit. It is the ratio of the distance between the foci of an ellipse to the length of the major axis. Perihelion, on the other hand, is the point in an orbit where the object is closest to the sun.

## Why is it important to compute aphelion from eccentricity and perihelion?

Computing aphelion from eccentricity and perihelion can help us understand the shape and size of an orbit, which gives us insight into the dynamics of the solar system and the motion of celestial bodies.

## What units are used for measuring eccentricity and perihelion?

Eccentricity is a unitless quantity, as it is a ratio. Perihelion is typically measured in astronomical units (AU), with 1 AU being the average distance between the Earth and the Sun.

## Can aphelion be greater than perihelion?

Yes, aphelion can be greater than perihelion. In fact, this is the case for most orbits in the solar system, including Earth's orbit around the Sun.

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