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.

  • 1
    $\begingroup$ By width, do you mean semi-major axis? $\endgroup$ Mar 25 at 1:44

To find the width (semi-major axis, see Wikipedia) 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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.