So of course both of these are slight simplifications, but what is the connection between the two? If the earth is basically a circle, is an ellipse just a parabola stretched around a circle? Is a parabola just an approximation of a tiny part of an ellipse? How high do you have to be before you change your calculations of a trajectory?
The Math ain’t mathing.
You can think of a parabola as a segment of an ellipse, yes.
But remember: A stable orbit forms an ellipse. An unstable one doesn’t. And throwing an object from the surface of a planet is, sans incredible math or even more incredible luck, going to be unstable.