I am giving planetary lesson as part of general physics class-first time I give this class- and while presenting the trajectory equation for planets-using classic Newtonian law in 2D polar coordinates- A student asked my : but how do we obtain eccentricity and I answered : empirically, we measure eccentricity.
However ,I am really not confident with my answer to that question, I am definitely going back to my textbooks , but as I am doing that do you know if I was mistaken ? Thank you