Features Extended:

For absolute value of the "c" distance of the focuses from the origin, we have the formula
```
     c = sqrt(a**2-b**2) 
```
(see Wikipedia: Ellipse: Ellipse in Cartesian coordinates). Note c = 0 for circles.
The ellipse eccentricity e is a parameter that is an alternative to c and that is a simple measure of the deviation of an ellipse from a circle. The eccentricity formula:
```
     e = c/a =  sqrt(a**2-b**2)/a = sqrt[1-(b/a)**2]  , 
```
and so e = 0 implies c = 0 (i.e., a circle) and e = 1 implies c = a (i.e., a straight line).
For orbits, the closest/farthest approach to the center of mass is the periapsis/apoapsis. The periapsis distance and the apoapsis distance are, respectively,
```
     r_per = a-c = a(1-e) and  r_apo = a+c = a(1+e) 
```
Now the standard definition of the mean orbital radius is
```
     r_mean = r_per + r_apo = a , 
```
i.e., r_mean is just the semi-major axis.
So we see that orbital eccentricity is the maximum relative deviation of the radius of an elliptical orbit from the standard mean orbital radius.
Note that (100*e) % is the maximum relative deviation as a percentage.