<p>To find the width (semi-major axis, see <a href="https://en.wikipedia.org/wiki/Ellipse" rel="noreferrer">Wikipedia</a>) of an orbit, you only need two of the following: <strong>perihelion, aphelion, and eccentricity,</strong> represented by the variables <span class="math-container">$P, A, $</span> and <span class="math-container">$e$</span>, respectively, and <span class="math-container">$a$</span> is the semi-major axis.</p>
<p>If you are given perihelion and aphelion, you can just take the average of the two: <span class="math-container">$a=\dfrac{A+P}{2}$</span></p>
<p>If you are given perihelion and eccentricity, you can calculate <span class="math-container">$a=\dfrac{P}{1-e}$</span>. Similarly, given aphelion, the width of your orbit is <span class="math-container">$a=\dfrac{A}{1+e}$</span>.</p>
<p>If you are talking about the <em>other kind of width (Semi-minor axis)</em>, represented by <span class="math-container">$b$</span>, then the formulas are:</p>
<ul>
<li>Given <span class="math-container">$P \text{ and } A: b = \sqrt{A \cdot P}$</span></li>
<li>Given <span class="math-container">$P \text{ and } e: b = \sqrt{-\dfrac{P(1+e)}{e-1} \cdot P}$</span></li>
<li>Given <span class="math-container">$A \text{ and } e: b = \sqrt{-\dfrac{A(1-e)}{e+1} \cdot A}$</span></li>
</ul>
<p>I hope this helps.</p>

CC BY-SA 4.0
2021-03-25T02:01:17.827Z
2021-03-25T02:01:17.827Z
WarpPrime
<p>I need to find the width/x-radius of an orbit, which is ellipse shaped, knowing variables like the orbit's length(perihelion + aphelion in this case) and the eccentricity. I am not sure if this is even possible, I am pretty new to this. If there is already available data on this that you're aware of, it would solve my problem too.</p>

CC BY-SA 4.0
2021-03-25T01:44:31.273Z
By width, do you mean semi-major axis?
WarpPrime
<orbit><solar-system><orbital-mechanics><eccentric-orbit>
How can I find the width of an orbit knowing some values?
nekiwo
# How can I find the width of an orbit knowing some values?

(Asked by: username_0 on 2021-03-25)

I need to find the width/x-radius of an orbit, which is ellipse shaped, knowing variables like the orbit's length(perihelion + aphelion in this case) and the eccentricity. I am not sure if this is even possible, I am pretty new to this. If there is already available data on this that you're aware of, it would solve my problem too.

**Tags:** orbit, solar-system, orbital-mechanics, eccentric-orbit

> **Comments:**
> **username_1**: By width, do you mean semi-major axis?  

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## 1 answers

### Answer by username_1 on 2021-03-25. Score: 5 | Accepted answer

To find the width (semi-major axis, see [Wikipedia](https://en.wikipedia.org/wiki/Ellipse)) of an orbit, you only need two of the following: **perihelion, aphelion, and eccentricity,** represented by the variables $P, A, $ and $e$, respectively, and $a$ is the semi-major axis.

If you are given perihelion and aphelion, you can just take the average of the two: $a=\dfrac{A+P}{2}$

If you are given perihelion and eccentricity, you can calculate $a=\dfrac{P}{1-e}$. Similarly, given aphelion, the width of your orbit is $a=\dfrac{A}{1+e}$.

If you are talking about the *other kind of width (Semi-minor axis)*, represented by $b$, then the formulas are:

* Given $P \text{ and } A: b = \sqrt{A \cdot P}$
* Given $P \text{ and } e: b = \sqrt{-\dfrac{P(1+e)}{e-1} \cdot P}$
* Given $A \text{ and } e: b = \sqrt{-\dfrac{A(1-e)}{e+1} \cdot A}$

I hope this helps.


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