Question

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

Answer 1

Increase

Explanation:

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`.

Answer 2

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

Explanation:

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. .