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Can we calculate the elliptical properties like the semi-major axis and eccentricity using the state vectors (position and velocity) in the spherical coordinate system?

http://www.braeunig.us/space/orbmech.htm

https://en.wikipedia.org/wiki/Eccentricity_vector

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  • $\begingroup$ Is there anything in particular that makes you think you can't? Spherical coordinates are orthogonal, so dot and cross products exist and are easy to look up or generate; 1, 2. It would be great if you could add a specific example to your question, and mention why you would be interested in doing it this way, because as currently written it might be hard to write a good answer beyond Yes, we can! $\endgroup$ – uhoh Jun 1 at 6:44
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    $\begingroup$ All the sample problems from books I have come across are solved using cartesian coordination for elliptical properties. In my case, I have several vectors in the spherical coordinate system. I can solve them by transforming the spherical into cartesian coordinate. But I would like to know whether we can use them in the formula without transformation. $\endgroup$ – Astrolien Jun 1 at 8:13
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    $\begingroup$ I'm recommending that you take one transformation as an example and then 1) show it worked out first in cartesian coordinates, 2) show the expression in spherical coordinates, and 3) show where you are stuck; at what point you no longer know how to do it in spherical coordinates, and that you 4) do this by editing your original question rather than adding comments. I think your question is a bit broad and open-ended right now, it's hard to answer without seeing more of what you are doing. We use MathJax to enter equations. $\endgroup$ – uhoh Jun 1 at 8:18

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