As orbits get more "out of round" in shape, does eccentricity increase or decrease?

2 Answers
Mar 23, 2016



A circular orbit has #"eccentricity" = 0#.

An elliptical orbit has #0 < "eccentricity" < 1#.

A parabolic orbit has #"eccentricity" = 1#.

A hyperbolic orbit has #"eccentricity" > 1#.

Mar 23, 2016

We can see the orbit getting more out of shape with increase in eccentricity, by fixing semi-major axis a and increasig the eccentricity e


The semi-minor axis b = a#sqrt(1-e^2# = a function of e..

Now, b' = #-e/sqrt(1-e^2) < 0#.

So, b is a decreasing function of e. We can see the orbit shrinking towards the fixed major axis, as e increases.

As #eto1-, bto0#. This is an interesting degenerate case for the ellipse, in becoming a line segment. Note that the focus S (a star for the orbit) #to# the end A of the major axis. The perihelion #to 0#.

If at all this happens, after billions of years, for the closer-to-star orbiter (like Mercury in solar system), It would be the orbiter's apocalypse...

I think that I could possibly make any reader of my answer to ponder over this degenerate case. I like to add that, likewise, the limit of a hyperbola, with fixed a and eccentricity decreasing #to# 1+, could be reviewed. .