Question

Can an eccentricity be negative?

Answer 1

Ecentricty cannot be negative because their are no "negative" traits that shape who we are.

We know what happens when we have eccentricity = 0 - we get a circle.

Between 0 and 1, we get an ellipse, if e = 1 we get a parabola, and if e > 1 we get a hyperbola.

But is there any way (or anywhere, like some kind of wacky non-euclidian geometry) in which a negative eccentricity would make any kind of sense? That seemed to be the only case not covered there (i.e. e < 0).

Looking at it from an orbital perspective, take aphelion [a(1+e)] and perihelion [a(1-e)]. If eccentricity was negative, then the furthest point of the orbit from its focus would be closer to the focus than the perihelion (which would actually be the furthest point from the focus)! This obviously (at least in our own geometry) doesn't make any sense.

That only applies if -1 < e < 0 : if e < -1 then you get really nonsensical results because the aphelion distance then becomes a negative number.