# How can I find the width of an orbit knowing some values?

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.

• By width, do you mean semi-major axis? 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.