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

##### 2 Answers

Increase

#### Explanation:

A *circular* orbit has

An *elliptical* orbit has

A *parabolic* orbit has

A *hyperbolic* orbit has

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

Now, b' =

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

As

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